Cellular Complexity

CELLULAR COMPLEXITY BY Kais Al-Rawi . Julia Koerner . Marie Boltenstern w w w . c e l l u l a r - c o m p l e x i t y. b l o g s p o t . c o m

M A S T E R O F S C I E N C E D I S S E R TAT I O N EMERGENT TECHNOLOGIES AND DESIGN A R C H I T E C T U R A L A S S O C I AT I O N SCHOOL OF ARCHITECTURE LONDON - UNITED KINGDOM SEPTEMBER 2012

ARCHITECTURAL ASSOCIATION SCHOOL OF ARCHITECTURE GRADUATE SCHOOL PROGRAMMES COVERSHEET FOR SUBMISSION 2011-2012

Programme: Emergent Technologies and Design 2012 Term: 4th STUDENT NAMES: Kais Al-Rawi, Julia Koerner, Marie Boltenstern SUBMISSION TITLE: CELLULAR COMPLEXITY COURSE TITLE: DISSERTATION MSc COURSE TUTOR

: Michael Weinstock, George Jeronimidis, Evan Greenberg, Mehran Gharleghi

SUBMISSION DATE: 14/09/2012 DECLARATION: “I certify that this piece of work is entirely my/our own and that any quotation or paraphrase from the published or unpublished work of others is duly acknowledged.”

Signature of Students:

Kais Al-Rawi

Julia Koerner

CELLULAR COMPLEXITY

Marie Boltenstern

7

CONTENTS ACKNOWLEDGEMENTS ABSTRACT INTRODUCTION

11 13 15

1.0

CELLULAR SYSTEMS

16

1.1

PROPERTIES OF CELLULAR SYSTEMS

17

1.2

NATURAL CELLULAR SYSTEMS

20

1.3

IMAGING NATURAL CELLULAR SYSTEMS

24

1.4

INTERNAL STRUCTURE ANALYSIS

30

1.5

GEOMETRY OF NATURAL CELLULAR SYSTEMS

34

1.6

CLOSEST PACKING STRUCTURES

35

1.7

CELLULAR SYSTEMS IN ARCHITECTURE

36

1.8

OVERVIEW

41

2.0

GEOMETRICAL DEVELOPMENTS

44

2.1

GRADIENT EXPLORATION

46

2.2

KELVIN PACKING STRUCTURE

48

2.3

TETRAHEDRON PACKING STRUCTURES

56

2.4

TRUNCATED CUBE - OCTAHEDRON STRUCTURE

58

2.5

SUBDIVISION

60

2.6

FINITE ELEMENT ANALYSIS

64

2.7

OVERVIEW

67

3.0

FABRICATION

68

3.1

ADDITIVE MANUFACTURING

70

3.2

SHEET MATERIAL PRODUCTION

72

3.3

CASTING CELL

74

3.4

CASTING PANEL

76

3.5

JOINTS AND TUBES

78

3.6

JOINTS, STRUTS AND PLATES

80

3.7

EVALUATION: FABRICATION METHODS

82

3.8

CASE STUDIES

88

3.9

HYBRID FABRICATION METHODS

92

3.10

OVERVIEW

95

8

4.0

THE SYSTEM

97

4.1

POROSITY GRADIENT

98

4.2

CELL POROSITY CATALOGUE

100

4.3

FINITE ELEMENT ANALYSIS

102

4.4

PARAMETRIC DESIGN TOOL

108

4.5

TYPOLOGY STUDIES

109

4.6

FABRICATION EFFICIENCY

114

4.7

OVERVIEW

118

5.0

ARCHITECTURAL APPLICATION

5.1

TYPOLOGICAL CASE STUDY

5.2

APPLICATION: COMPETITION

5.3

PROGRAMMATIC REQUIREMENTS

5.4

SITE ANALYSIS

5.5

PROGRAM DATA CATALOGUE

5.6

STRUCTURE-SPAN VARIATION

5.7

PROGRAM ALLOCATION

5.8

SITE INTEGRATION

5.9

COMPETITION ENTRY

5.10

OVERVIEW

5.0

SYSTEM DEVELOPMENT

149

5.1

PROGRAM-STRUCTURE TYPOLOGIES

151

5.2

ENVIRONMENTAL ANALYSIS

156

5.3

FACADE DAY LIGHTING ANALYSIS

160

5.4

STRUCTURAL DEVELOPMENT

162

5.5

SYSTEM ARCHITECTURAL APPLICATION

164

5.6

GRADIENT CONDITIONS

166

5.7

FURTHER POTENTIALS

168

5.8

OVERVIEW

121 122 126 132 133 136 138 140 141 142 147

172

JURY COMMENTS CONCLUSION SELECTED BIBLIOGRAPHY APPENDIX

174 176 178 183

CELLULAR COMPLEXITY

9

10

ACKNOWLEDGMENTS We thank with the deepest gratitude, the contributors to this research.

First we would like to thank our families and friends for supporting us throughout this postgraduate course.

Especially Mr. and Mrs. Koerner for providing us with natural cellular artefacts for CT scanning. Therefore, we would like to also thank Dr. Marc Pelling for referring us to Shirley Featherstone from St Mary’s Hospital. She was so kind to provide us with CT scanning facilities for digital analysis of these natural cellular artefacts.

Furthermore we would like to thank Studio 1PLUS2D and Andreas Koerner for 3D printing test geometries on their in-house additive manufacturing machines. For further introduction into fabrication methods we would like to thank Trystrem Smith from the model making workshop at AA. Lastly Jack Chandy Francis for his support on the Solar Analysis for the Suckerpunch Competition.

Finally we would also like to thank the EmTech faculty: Michael Weinstock, George Jeronimidis, Evan Greenberg and Mehran Gharleghi for their support and guidance throughout the entire dissertation.

CELLULAR COMPLEXITY

11

12

ABSTRACT Keywords: INTEGRATED FACADE, CELLULAR STRUCTURE, POROSITY, INTRICACY, SPATIAL HIERARCHY, DIFFERENTIATION This research investigates the potential of porous and cellular systems within an architectural context. The current application of such systems within architecture is limited to the abstraction of basic structure and aesthetics; often overlooking their efficient structural capabilities and passive performative qualities. The aim is to assimilate these qualities into a single architectural façade system which responds to given programmatic and environmental conditions.

Conventional­­ façades consist of several separate sub-systems, contradictory to how nature integrates material, form and structure. The ambition is to achieve a material efficient system with spatial and structural properties. The digital fabrication of this system considers additive manufacturing, allowing for material efficient production of double-curved geometries within a differentiated component based system. The question becomes which properties of cellular systems are appropriate at each of these levels and which degree of scaling is possible without compromising the effectiveness.

‫ والتن تمنما الخالينا المتناهينة ال نلرح البحنث ي ند‬،‫هذا البحث يتطرق الى االنضمة الطبيعية و باالخص انظمة الخاليا و المسامات ضمن عددا منن السنتويات‬ ‫استحداث الية لتوظي خ ائص هنذ االنضنمة فن سنياق الت نمي المعمنار ح التطبينق الحنال ل نذ االنظمنة فن ت نمي المعمنار يقت نر علنى تجريند ال يكنا‬ ‫ اضافة الى بعض النواح الجمالية؛ وغالبا يت اهماا القدرات الفطرية ل ذ االنظمة الت تمما الكفاءة ف هيكا البنية بجانب عددا منن القندرات الفعالنة‬، ‫األساس‬ ‫ قادر على التعاما مع الظرو البيئية و المن جية ف المبان ح ان الواج ات التقليدينة تتكنون‬،‫ح ال د هو دمج هذ ال فات الفعالة ف نظا معمار واحد‬.‫االخر‬ ‫ هذا المبدأ يتعارض مع نمط الطبيعة بدمج المكا والبنية ف المادةح ال د هو تحقينق نظنا معمنار‬،‫من عدة طبقات منف لة و تحو عددا من االنظمة الفرعية‬ ‫ و فن االخنص‬،‫فعاا و ذو كفاءة ف المادة وبنفس الوقت يتمتع بخ ائص هيكلية و جودة روح المكانح سنو ينت بحنث نظن الت ننيع و البنناء الحديةنة و الرقمينة‬ ‫نظ الت نيع الت تستخد تكنلوجيا االضافة الطبقية نظرا المكانيت ا ف ت نيع امكاا ذات تقويس باتجاهين و ذلك مع كفاءة بنالمواد و امكانينة تقندي نظنا مركنب‬ ‫ مننن هننذ‬.‫ يمكننن اسننتخدا و تحجنني خ ننائص األنظمننة الخلويننة المناسننبة فن كننا مسننتو‬.‫يحتننو علننى عنندة متليننرات فن المكوننناتح ي ننب السننلاا الننى ا منند‬ ‫ هذ الفعاليةح‬.‫ حيث ال تمس درجة التحجي مد‬،‫المستويات‬

Diese Dissertation widmet sich der Erforschung von zellulären und porösen Strukturen und deren Potenzial in der Anwendung im Bereich der Architektur. Die gegenwärtige Anwendung solcher Strukturen innerhalb der Architektur beschränkt sich auf Grundschema von Konstruktion und Ästhetik; deren Potenzial für effiziente Tragwerkskonstruktionen und Statik, sowie deren thermische und akustische Eigenschaften werden dabei oft vernachlässigt. Ziel ist es, diese Qualitäten in ein einziges singuläres System zu integrieren, welches sich dynamisch den gegebenen Umweltbedingungen anpasst und dieses System durch den Entwurf einer dreidimensionalen, tragenden Fassaden-Struktur zu manifestieren. Im Gegensatz zu konventionellen Fassaden, die sich üblicherweise aus verschiedenen Bausubstanzen und Schichten zusammensetzen, vereinen natürliche Strukturen Material, Form und Tragwerk. Dies bildet den Ausgangspunkt der Entwicklung eines materialeffizienten, dreidimensionalen Tragwerksystems mit räumlichen sowie bautechnischen Eigenschaften. Durch Entwicklung mathematischer Algorithmen mittels spezieller 3D Software werden jene Strukturen digital beschrieben.

Fortschreitende Technologien wie 3D-Druckverfahren und numerische Fertigungsmethoden ermöglichen die präzise Herstellung komplexer Geometrie innerhalb eines solchen modularen Systems. Es stellt sich die Frage welche Eigenschaften zellulärer und poröser Systeme, in welchem Bereich des Entwurfes, eine Anwendung finden und inwieweit jene skalierbar sind ohne die Effizienz des Systems einzuschränken.

This research investigates the potential of porous and cellular systems within an architectural context.

The

current

application

of

ULAR COMPLEXITY suchC E L Lsystems within

architecture

is

limited

to

13 the

14

INTRODUCTION Within the field of Architecture and Engineering, the application of cellular materials such as ceramics, polymers and foam metals are about to open up a new range of performance and material potentials. The abstraction of permeable and ductile structures has been applied at an architectural scale in projects such as the Aquatics Center by PTW architects.

While most projects integrate the aesthetics and basic structure of such cellular systems, the potentials of structural, environmental and spatial integration has yet to be developed. At smaller scales, the use and development of porous materials is within a more complex level. For example, in the medical field porous resin tissues can be reproduced and designed according to certain needs very accurately already. Porous structures also act as passive environmental modulators, capable of regulating temperature and humidity through absorbing and transporting heat energy and moisture.

Additionally they provide lightweight and material efficient structural capabilities. Mathematical and geometrical studies of porous systems will lead to the design of an integrated façade system. As in biological systems where there is no distinction between structure and material, the facade system will intricately operate on structural, spatial and performative levels.

The question becomes which properties of cellular systems are appropriate at each of these levels and which degree of scaling is possible without compromising the effectiveness.

Current means of researching natural cellular systems include biomimetic strategies that investigate the integration of form, material and structure. In medicine, 3D tomographic imaging is used as a method of analysing porous mediums.

Existing computational strategies for the geometrical modelling of packing organisations refer to mathematical logics of Plateau laws and Weaire-Phelan structure. Cellular structures occur in nature at various scales such as Sponges, Corals and Bones which will be analysed through 3D scanning, fluid dynamic analysis and structural simulations. The material properties that become relevant within the analysis of varying porous structures include absorption, thermal energy transfer and structural strength. This will be tested on physical models with specific fabrication methods such as 3d printing polymer, laser sintering, casting and investigation into composite materials. Evolutionary computation allows the generation of multiple formal variations that are constantly evaluated against pre-determined criteria. Evaluation criteria will include spatial and structural properties such as material efficiency against usable area, in addition to functional criteria such as environmental responsiveness.

Façade systems typically consist of several separate subsystems and layers, dealing with each building floor as an isolated entity where flows are transferred only between one level and another. Similar to how nature integrates multiple functions within a material, this research aims to assimilate the structural, material and performative properties of cellular systems into a single façade system. The design will respond to given environmental conditions, such as wind, rain and sun. The system will initially be designed for northern temperate climate; yet adaptable to various locations through modifications and variations within a further study. The system will be responsive in a dynamic way, yet non-mechanic. The application of the façade system will suit an architectural scale that includes medium scale buildings. The current development of large-scale additive manufacturing becomes of particular interest within digital fabrication. This allows for material efficient production of double curved geometries within a unit-based system that allows for unique variation within each unit; while operating as a coherent system at the global scale. The organization of the material and geometry that informs the design will generate functional intermediate spatial conditions as part of the dynamic response to environmental conditions, coupled to the material efficient structure.

CELLULAR COMPLEXITY

15

16

CELLULAR SYSTEMS Cellular Systems are low density solids that exist in both natural and manufactured forms; this includes common materials such as wood, cork, corals and sponges.

They are a network of interconnected plates or struts which are respectively the faces or edges of the cells 1.

The two main types of cellular solids are two-dimensional and three-dimensional cellular solids, also known as honeycombs and foams. Three-dimensional cellular solids can be further classified to have either open-cells or closed-cells; the first is made up of struts, and the second plates. Open-cell foams have interconnected voids and are constrained by the cell edges, whereas closed-cell foams have sealed cells which are enclosed by plates.

This chapter investigates cellular solids, their characteristics and properties, in addition to a range of natural cellular systems and their underlying geometrical principles and the current architectural application of such systems.

Left: Fig 1.1 The underside of the boletus mushroom consists of a system of closest packed tubules

CELLULAR COMPLEXITY

17

THE MORPHOLOGY OF CELLULAR SYSTEMS

The most important characteristic and feature in any cellular system is porosity. The porosity is a measure of the amount of solid to void volume, the higher the porosity, the less material per volume the system contains.

The cell shape and morphology is an important characteristic of any cellular system, often considered more significant than the cell size. For example, the elongation or flattening of a cell can create directionality and anisotropy.

Fig. 1.2 Cellular structure of wood

Two-Dimensional cellular systems which are known as honeycombs can have regular geometries including triangular, square and hexagonal; random geometries with varying cell sizes and edges also exist, particularly in natural systems.

Three-Dimensional cellular systems, also known as foams may have mathematical space-packing geometries such as Plateau’s rhombic dodecahedron and Kelvin’s tetrakaidecahedron which was thought to be the most efficient in terms of minimal surface area per unit volume.

Weaire and Phelan identified an even more efficient structure using computational software. Their geometry is made of six 14-sided cells with two pentagonal dodecahedra; of which all have equal volumes.

Natural foams typically have geometries similar to space-packing geometries which only pack properly in a distorted manner; a dominant force in their formation is surface tension 2 .

Fig. 1.3 Cellular structure of bread

In general, the morphology of natural cellular systems contains random elements which generate geometries that are a distortion from the mathematical models. This is typically due to external environmental forces interfering with the formation. The mathematical models remain to be as more efficient and ideal structures which are found in manufactured cellular systems.

Fig. 1.4 Hexagonal honeycomb

The relevant characteristics in honeycombs include: density, edge connectivity, edges per cell, symmetry, edge thickness, largest and small cell dimension, characterizing angle and any exceptionally large cells or broken walls 3 . In foams, of importance are: open or closed cells, edge connectivity, face connectivity, number of faces per cell, face and cell edge thickness, principle cell dimensions and dispersion of cells 4 .

THE PROPERTIES OF CELLULAR SYSTEMS Fig. 1.5 Natural honeycomb

Foams can exhibit a range of unique features including structural, thermal and acoustic properties. Cellular geometries which use efficient mathematical space-packing geometries reduce the amount of material required within the structural system. Furthermore, cellular systems can provide exceptionally low thermal conductivity and an ability to absorb sound 5 , providing thermal and acoustic insulation.

STRUCTURAL Fig. 1.6 Weaire-Phelan structure

The mathematical models such as Kelvin’s or Weaire Phelan are able to provide the least amount of surface area within a given volume, providing an efficient structure. The structural behaviour of cellular systems is mostly determined by the material behaviour and the manner in which they fail. The use of non-regular geometries can decrease the strength of the cellular system by roughly 25% in comparison to idealized geometries 6 . Additionally, any missing cells walls can sharply decrease young’s modulus and the compressive stress 7 .

Fig. 1.7 Natural Bubbles

18

CELLULAR SYSTEMS

THE PROPERTIES OF CELLULAR SYSTEMS

properties

parameters

subset

structural deformations with forces: in-plane and out of plane deformations:

CELLULAR SYSTEMS

shear deflection - bending and rotation elastic buckling - elastomers plastic collapse - metals

- material (and properties: modulus, etc.

- arrangement of cells and structure: geometry (optimized or variable/random) cell properties (size, thickness, etc.)

thermal very low thermal conductivity in foams: this requires: -small cell size -high porosity

- for optimization at scale thickness of cellular system temperature difference across

good in absorbing sound (that comes from within the same room/space) -porous materials absorb sound and convert it to heat (negligible) -surfaces need to be open and not sealed

structure thickness material

- cell size - porosity - material - gas in pores

acoustic

geometry cell shape cell packing porosity density

environment

site data temperatures

- porosity - open cell not closed cell -material

THERMAL The most common use of foams is thermal insulation, closed-cell foams in particular display one of the lowest thermal conductivity. There are several factors that limit heat flow in foams, these include the low volume fraction of the solid phase. In addition, the small cell size reduces both convection and radiation though absorption and reflection at cell walls; and low conductivity of the gas within the cells8.

The thermal conductivity has four main contributors: the conduction through the solid, the conduction through the gas, the convection within the cells, and the radiation through cell walls and across the voids9. The biggest contributor of the four is the conduction through the gas. What is fascinating within the thermal properties is that the density of the material in the solid has small minimal contribution towards the thermal conductivity. This means that the geometry of the system becomes more important than the actual material it is made of. However this is only true at a certain scale, at larger scales the density does contribute towards the performance. The larger the cell size becomes the larger the heat transfer, as convection starts to take effect as one of the four contributors.

Fig. 1.8 Honeycomb sandwich panel for structural purposes

Fig. 1.9 Weaire-Phelan structure used in Beijing Aquatic Centre

For each given insulation problem, there is an optimum foam density and cell size for the best thermal insulation. For example, the insulation needed for a coffee cup is different from that of a cavity wall. The main factors which determine the optimum requirements include the temperature difference across the insulation and the thickness of the insulation10.

ACOUSTICAL Cellular solids exhibit acoustic properties which hold potential for sound management in buildings. The main mechanisms of sound management are absorption, insolation and isolation. Cellular systems are able to absorb sound waves and convert them to heat; they are considered good absorbers and bad insulators11. The absorption mechanism is useful for absorbing sound that is generated from the same space, avoiding disturbance to the outside.

Materials that are porous and high flexible like low-density polymeric and ceramic foams are particularly useful due to their intrinsic damping and wave propogation12. The geometry of open-celled foams are particularly useful due to the connectivity of cells, the sound is able to travel and dissipate throughout the cells13.

Fig. 1.10 Cellular organization in thermal insulation sheets

Fig. 1.11 Cellular organization in acoustic tiles

CELLULAR COMPLEXITY

19

NATURAL CELLULAR SYSTEMS

2D - PATTERN / RELIEF In almost every natural substance cellular structures can be found when looking at the right level of magnification 14

Cellular structures in nature occur in a large number of outcomes and variations. They exist as patterns, reliefs, extrusions and also mostly common in three dimensional geometries. What they have in common is that they all affiliate to a certain kind of closest packing geometry, which is the most viable arrangement of cells to fill up a volume.

Fig. 1.12 Girraffe Pattern

The system of a specific natural structure is based on a clear logic which results in an infinite number of different outcomes in different artefacts through reaction and optimization towards outer impacts.

Through variation in the size of components and the porosity gradients at different levels; the system can address structural and environmental parameters. The cells in this case can be open or closed and regular or irregular.

These parameters are further tackled at various hierarchies of scales within the same structure. Therefore it can be stated that natural systems operate on both, a micro level and on a macro level with the same geometrical logic. In nature there is no distinction between structure, form and material 15. The fact that natural materials are limited to only four different substances - cellulose, collagen, chitin and silk - proves that not simply the material, but moreover the geometrical arrangement of cells plays the biggest role in terms of their efficient structure 16.

Fig. 1.13 Earth Cracking

The strength and ductility is intimately tied to the highest efficiency in distribution of material and structure 17. They make the structure of natural cellular systems of special interest for this research. What natural systems have in common and what makes them so appealing is that the simple logic behind their structure stays the same, while according to given environmental conditions and changes over time, the outcome of them is extremely wide ranging and differentiated.

With a minimum of rule sets, a maximum of diverse outcomes can be created18.. The various scales of cell sizes, cell porosities and cell arrangements and shapes are used to address specific conditions that a plant or animal needs to adapt to. Therefore the component-based geometries allow for variation and adaptation towards the required efficiency through differentiation.

Fig. 1.14a,b Amardillo Skin

Fig. 1.15a,b Pentapora closeup

In the example of the Poppy Seeds as shown in Fig.1.17, the cellular arrangement is caused by surface tension 19. Due to a loss of moisture, the outer shell collapses onto the inner shell. The surface tension forces are similar to such that occur in soap bubble formations. Through this a minimal surface condition is created, which means most efficient relation of surface area to volume.

Fig. 1.16a,b Pollen grain

The efficiency of those structures can be illustrated by the example of the bee honeycomb shown in Fig 1.25. In this hexagonal packing arrangement, the greatest amount of honey is combined with an efficient minimum material use for the structure of the cell walls, therefore it requires the least energy from the bees to build up the cells 20.

Most of the examples in the 2D extruded natural cellular structures are roots or stems which need to resist forces and bend in one direction as their overall morphology is elongated and extremely defined through directionality. The arrangement and change of size of cells allows for perfect adaptation to such extreme conditions through variation in section 21.

Of special interest in this research are certainly the three dimensional cellular systems and how those structures react to and deal with environmental influences as the goal is to abstract those structures in order to create an architectural system which responds to given environmental conditions. For this purpose some of the structures were chosen to be examined further such as the sea urchin and the coral as they show a wide variety in porosity ranges as well as cell shapes and arrangements.

20

CELLULAR SYSTEMS

Fig. 1.17a,b Poppy Seeds

Fig. 1.6a,b Philodendron

2D - EXTRUDED

Fig. 1.19a,b Redwood Root

2D - LAYERED

Fig. 1.25 Honeycombs

3D SPATIAL

Fig. 1.32a,b Human Bone

Fig. 1.20a,b Maple Root Fig. 1.26a,b Juncus

Fig. 1.33a,b Coral

Fig. 1.21a,b Quercus Alba Root

Fig. 1.27a,b White dead nettle Stem

Fig. 1.22a,b Reed

Fig. 1.28a,b Boletus Mushroom

Fig. 1.35a,b Magma Vesicles

Fig. 1.29a,b Prairie Plant

Fig. 1.36a,bSpongia Agaricina

Fig. 1.24a,b Mare’s Tail

Fig. 1.30a,b Cork

Fig. 1.37a,b Alveoli Human Lung

Fig. 1.19 Boa Skin

Fig. 1.31 Sepia

Fig. 1.38a,b Tarantula Leg

Fig. 1.23a,b Cucurbit Root

CELLULAR COMPLEXITY

Fig. 1.34a,b Culcita Novaguineae

21

MULTITUDE OF SCALES

The diagram on the right relates - in a first step - a number of the examined natural structures to properties which are in a later stage important for the development of an architectural system. It illustrates the potentials of the different 2D and 3D structures in terms of structural, thermal, acoustic and other environmental performances. It shows that the different systems are built up to address various impacts which are relevant in their environment by their structures. The structures in return are built up by environmental processes which lead the growth, appearance and performance of the structures.

Figures 1.39 - 1.41 which show a sea urchin, a sea urchin spine and a starfish at several levels of magnification were chosen to be examined in further detail, as their structures show a wide range of porosity scales within one single structure. Furthermore, geometrically they grow from an open to closed celled structure in a smooth gradient transition. In this example it becomes clear how natural systems operate with spacepacking structures at various hierarchies.

Within the same natural structure, similar geometries appear at various, utterly different scales. At each scale, the specific structure addresses certain properties the natural substance has to fulfil.

1000um = 1mm

Fig. 1.39a,b Sea Urchin

1mm

300um

100um

Fig. 1.40a,b Sea Urchin Spine

100um

10um

2um

Fig. 1.41a,b Iconaster Longimanus

300um

100um

50um

22

CELLULAR SYSTEMS

1D RELIEF

GEOMETRY all these geometries are GIRRAFFE PATTERN

based on closest packing

EARTH CRACKING

POPPY SEEDS MINIMAL SURFACE

PHILODENDRON

2D - EXTRUSION

CLOSED - CELLED

REED

MARE’S TAIL

REDWOOD ROOT PROPERTIES

DIRECTIONAL

2D - LAYERED

STRUCTURAL HONEYCOMBS

BOLETUS MUSHROOM

UNIVERSAL

POLLEN GRAIN

STRUCTURAL

CORK THERMAL SEPIA

ACOUSTIC 3D - SPATIAL

SOAP BUBBLES

SPATIAL

HUMAN BONE VISUAL CORAL FILTRATION

SPONGIA AGARICINA

JUNCUS

VENTILATION

ALVEOLI LUNG

CELLULAR COMPLEXITY

23

IMAGING NATURAL CELLULAR SYSTEMS

Following our interest in natural artefacts and thier cellular organization, a method of analysing and investigating these systems was required. Typically, architects and designers utilize 3D-scanning sonar devices to obtain a three-dimensinonal computer model of complex objects or natural artefacts. However there are several technical limitations within 3D-scanning and the results only provide an exterior morphological view or reconstruction of the scanned object. What we were rather interested in was the interior structure of the object and the organization of cells, their variation and the reason behind these variations. Furthermore, the interest was in relating natural models which contain aspects of redundancy and randomness for variation within the morphology, to the mathematical geometrical models and comparing aspects of each.

The field of Radiology within the medical discipline is considered to be one of the most advanced in terms of imaging and tomography. Computed Tomography scans also known as CT were developed to produce sectional images through a body or organism for diagnosis purposes. The technology uses X-ray images within a single axis of rotation to image slices which can be reconstructed to three-dimensional images.

Fig. . Philips Brilliance CT-Scanner http://www.uchospitals.edu/images/cms/uch_008020.jpg

For our research purposes and investigation of natural cellular systems we undertook a number of computed tomography scans for various natural artefacts. The CT scans were done at the Imaging Department in St. Mary’s Hospital, London. Senior Radiographer: Shirley Featherstone The equipment at the facility is a Philips Brilliance 64 and 256-slice scanner. The scans provide slices at an interval of 0.4mm in two directions, coronal and transverse. The digital resolution of the slices are at 500x500 pixels. The format of these slices are DICOM which is the common format within the medical Industry. The images are monochrome and based on an Xray where the image is entirely about the contrast received from the scan.

CT-scan in progress at NHS Imperial - St Mary’s Hospital

For our research purposes and investigation of natural cellular systems we undertook a number of computed tomography scans for various natural artefacts. The CT scans were done at the Imaging Department in St. Mary’s Hospital, London. Senior Radiographer: Shirley Featherstone The equipment at the facility is a Philips Brilliance 64 and 256-slice scanner. The scans provide slices at an interval of 0.4mm in two directions, coronal and transverse. The digital resolution of the slices are at 500x500 pixels. The format of these slices are DICOM which is the common format within the medical Industry. The images are monochrome and based on an X-ray where the image is entirely about the contrast received from the scan.

Throughout the analysis and use of the DICOM slices, multiple softwares were used for both viewing the images and reconstructing the slices to a three-dimensional model. For viewing purposes MicroDicom and Agnosco Dicom Viewer and RadiAnt DICOM viewer. For the reconstruction of the slices to obtain a geometrical 3D model, InVesalius 3.0 was utilized.

Objects on CT scanner Bed ready for scan

24

CELLULAR SYSTEMS

NATURAL ARTEFACTS

During the arrangements for the Computed Tomography scans, we prepared a range of natural artefacts which could be analysed to provide potential knowledge of natural cellular systems and the variety within them. The objects scanned included: corals, tree bark, sea horse, sea stars, lava stone, pumice stone, cork and spider crab. The size of most objects was small and did not exceed 100mm in length.

Therefore, the resolution of the performed CT-scan was ideal for certain objects, and for other less relevant for our analysis purposes. This depends on the scale of cells or pores in relation to the object. Shown below, are images taken by the scanner of each object scanned, in addition to a selected slice which shows the object most clearly.

The resolution of the slices obtained from the scan is sufficient to provide an observation towards the structure that would be visible by human eye if the object is sliced. The slices however were not at a resolution where microscopic structures or features could be examined.

The two objects that were of main interest were the coral and pumice stone, this is due to the clarity of the structure within the given slice resolution where the cells can be observed throughout the slices.

These two were taken for further investigation, specifically in terms of the variations they hold within the different cells.

CORAL

SPIDER CRAB

CORAL

LAVA STONE

SEA STAR

PUMICE STONE

SEA STAR

CORK

SEAHORSE

TREE BARK

CELLULAR COMPLEXITY

25

PUMICE STONE: CORONAL SLICES

In the areas where the cells meet the exterior of the object, the cells become open to the exterior and have similarities with open-celled systems. There are specific cells throughout the object which are exceptionally larger. Furthermore there are parts of the objects with dense and closed cells.

The following images are the slices obtained from the CT scanner which are taken at 0.4mm intervals, with a total of 200 slices. These slices are taken in a coronal direction, cutting through the object sectionally in a vertical plane with the scanner bed shown at the bottom of each slice.

The slices presented on this page are half of the complete set, and are therefore at an interval of 0.8mm.

The slices exhibit various qualities of the object, where it is evident that cells have a relatively similar size. The three-dimensional structure appears to be that of a closed-cell cellular system.

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CS- 8.00

26

CELLULAR SYSTEMS

PUMICE STONE: TRANSVERSE SLICES

The following images are the slices obtained from the CT scanner which are taken at 0.4mm intervals, with a total of 67 slices, of which 63 are presented. These slices are taken in a transverse direction, cutting through the object sectionally in a horizontal plane.

The transverse slices of the object demonstrate that the organization of cells is similar in both directions: coronal and transverse. There is no elongation which provides the structure with anisotropy. The same characteristics which were noticed in the coronal slices appear again in the transverse slices.

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CELLULAR COMPLEXITY

27

CORAL: CORONAL SLICES

The following images are the slices obtained from the CT scanner which are taken at 0.4mm intervals, with a total of 162 slices. These slices are taken in a coronal direction, cutting through the object sectionally in a vertical plane with the scanner bed shown at the bottom of each slice.

80 slices are presented on this page are half of the complete set, and are therefore at an approximate interval of 0.8mm.

The slices exhibit various qualities of the object, it is evident that there is a range of cell sizes which is variable throughout the object. There are also a number of larger cells that pass through the object sectionally. In some cases there are intersections between the various cells.

The cells generally posses the qualities of closed-cell systems, where they intersect they are somewhat similar to open-cell systems.

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28

CELLULAR SYSTEMS

CORAL: TRANSVERSE SLICES

The following images are the slices obtained from the CT scanner which are taken at 0.4mm intervals, with a total of 30 slices. These slices are taken in a transverse direction, cutting through the object sectionally in a horizontal plane.

Although the coronal slices show these elongated cells passing through the entire object, they are not completely open and you cannot see through the object. This is likely due to their intersection with other cells and solid parts, alongside the angle they run through the object.

The transverse slices exhibit qualities that are very different from those of the coronal slices. The cell size appears to be very similar throughout these slices. Based on the coronal slices, these are elongated cells which pass through the object, this elongation suggest qualities such as anisotropy which may provide additional strength in the vertical direction.

TS- 0.08

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CELLULAR COMPLEXITY

TS- 0.72

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29

INTERNAL STRUCTURE ANALYSIS

Further geometrical and structural analysis of the objects was undertaken. For each object, a specific slice was selected in each direction, and at a finer scale the cells where identified, in addition to any distinct features. The centre points of all identified cells were marked as a point-grid. Furthermore, the point grid was used to generate two-dimensional voronoi cells.

In the pumice stone, the cells are diagrammed where the degree of size variation is shown, some larger cells do exist, and areas with dense material are also marked. The voronoi generates mathematical cells which are similar to the morphological cells. However, as shown in the coronal slice, when there is significantly larger cells than the rest of the cells, the variation is not as evident within the voronoi cells.

TRANSVERSE ANALYSIS

selected slice for analysis

close-up of the selceted slice 75 x 57 x 43 mm

overlaying of cells Reconstruction of slices into 3D Model

PUMICE STONE

location of cells within slice

point-grid based on cell centres

2D-voronoi from point-grid

30

CELLULAR SYSTEMS

CORONAL ANALYSIS

INTERNAL STRUCTURE ANALYSIS

Similarly the geometrical and structural analysis was undertaken for the coral to provide a comparison. In the coral, the cells hold a larger degree of variation and complexity. Within the coronal slice, an irregular distribution of cells and variety of cell sizes is evident. In the transverse slice, the distribution follows a more regular pattern with similar cell sizes. The voronoi generated based on the cells point-grid does not illustrate strong similarity with the slice, as in the case of the pumice stone.

TRANSVERSE ANALYSIS

CORONAL ANALYSIS

selected slice for analysis

close-up of the selceted slice 62 x 48 x 14 mm

overlaying of cells Reconstruction of slices into 3D Model

CORAL

location of cells within slice

point-grid based on cell centres

2D-voronoi from point-grid

CELLULAR COMPLEXITY

31

OBJECT RECONSTRUCTION DIGITALLY

As further analysis in three-dimensions, the slices that were obtained from the Computed Tomography scans in DICOM format can be reconstructed from two-dimensions to create a three-dimensional model. Since the distance between slices is 0.4mm, the resolution of the 3D model is high.

A block of 20mm x 20mm was selected in plan, for further analysis. The block was extracted through boolean operations, and a mesh was obtained digitally from the STL file.

The slices of the coral were reconstructed using InVesalius 3.0, which created a 3D STL format file which is typically used for stereo lithography. This is a format which can be used to 3D print the coral in different materials.

Reconstruction of CT slices to produce STL digital model of the scanned coral

20mm x 20mm x ~14mm section block of the scanned coral is extracted for analysis

32

A digital mesh is produced from the Three-Dimensional Geometry of the chosen block

CELLULAR SYSTEMS

MATHEMATICAL RECONSTRUCTION OF OBJECT

Furthermore, the obtained mesh is porous due to the structure of the coral, and there are therefore voids within it. These voids were extracted digitally and separate meshes were created for each void. The voids represent the cell boundaries, where the coral is the solid that surrounds it.

a mathematical structure that is based on surfaces from the morphological structure. What is evident in this analysis is the aspect of redundancy in the morphological coral, and the effect of environmental factors (mainly water) in changing its morphology.

Through the use of GrassHopper, we were able to generate a 3D-voronoi structure from these surfaces. This provided us with

A mathematical reconstruction of the coral based on the voids of the morphological model

The voids or cell cavities within the mesh are extracted as a separate digital mesh

A Three-Dimensional Voronoi is generated in grasshopper using the mesh of the cell cavities / voids

CELLULAR COMPLEXITY

33

GEOMETRY OF CELLULAR SYSTEMS

Most cellular structures affiliate to a certain kind of closest packing geometry. Closest packing is the most efficient arrangement of regular or irregular cells.

The geometrical principles that lie behind cellular structures are based on closest packing or space filling geometries 22. The closest packing arrangement is the most effective arrangement of regular or irregular cells, which means that the single components are arranged in a manner which leaves the least possible void space between the cells.

Therefore this arrangement positions the cells in the principle of least use of energy in the end - configuration, as well as the least amount of used material for an arrangement of certain cells.

As shown in the diagrams below to the right, space filling occurs in geometries of regular and irregular cells. The closest packing is called ‘space packing’ when it fills up a whole volume without leaving any void.

The principle of space packing is the basis for almost every occurring structure in cellular systems. It exists in 2D as well as in 3D. Fig. 1.42 and 1.43 show the difference between an open and a closed cellpacking. Different structures use either open or closed cells, depending on the properties tackled. Other structures combine structures of both open and closed cells.

Fig. 1.42 Open Celled Structure

Fig. 1.43 Closed Celled Structure

Fig. 1.44 Metal foam

Fig. 1.45 Soap Bubbles

STRUCTURES AND DUAL-NETWORK

Fig. 1.44 and Fig. 1.45 show an aluminium alloy structure next to soap bubbles. The pictures demonstrate that similar cell arrangements can occur in wildly different substances and are then hardly distinguishable in morphology when displayed 23. This proves that closest packing structures are built up regardless of scale and material, simply the geometry counts in the effectiveness of such structures.

As in the same substance as well as in different systems, the same packing structure can occur at utterly different scales, it can be stated that closest packing structures operate regardless of scales 24. Simply, the arrangement of cells is most important, not the scale or the material of cells. What counts is the number of cells and their efficient arrangement in relation to required properties. This gives the opportunity of having hierarchical structures with which their cellular systems address different extrinsic and intrinsic forces 25. The investigation of transitions in these scales, their geometrical arrangement and the resulting performance lies in the main focus of our research.

Space FIlling Structure - Circles

Dual Network Closest Packed Circles

Space Packing Structure - Hexagons

Dual Network Closest Packed Hexagons

Space Packing Structure - Irregular Cells

Dual Network Irregular Cells

THE DUAL NETWORK By connecting the centres of all neighbouring cells, the dual network of a cell arrangement is created. As visually displayed in the diagrams on the right, the dual network results in a triangulated structure, which again emphasizes the high efficiency of the closest packing arrangement - it is proven that the triangle is the only form that is stable by the nature by its geometry 26. When hinging the edges of a triangle, it will still remain in position. This is why closest packing structures can be considered highly effective in structural terms. Through the Dualnetwork, the Dual-geometry is created, this is valid in 2D structures, in which the Dual Polygon is created and for 3D structures, in which the Dual 3D-Polyhedra results.

TRANSITIONS OF POROSITIES POROSITY Within cellular systems, porosity occurs in a variety different ways.

The transition from different states of porosities within single packing structures is of special interest. In cellular systems, porosity occurs geometrically by either subtracting an offset of the cell itself or by subtracting an offset of the respective dual-cell. Different scales of this offset lead to various porosity percentages. When these numbers change gradually from one cell to its neighbouring cells, a smooth transition can be found. In both, the Cell as well as the Dual-cell offset, the structural efficiency is still guaranteed, as the principal geometrical arrangement was not changed.

34

Cell offset

CELLULAR SYSTEMS

Dual-cell Offset

CLOSEST PACKING 3D STRUCTURES

Three dimensional space-packing structures have similar properties as the two dimensional arrangements discussed before. In the following space-packing examples, the structures consist of equal, regular or semi-regular Polyhedra.

When filling a space with equal spheres as shown below, the filled space is not fully occupied by the packed spheres - concave voids are left.

This means that the sphere, which as a single object has the smallest surface area in relation to volume and is therefore highly efficient, is in an array not as efficient any more. To eliminate the concave void spaces, the spheres can be swollen to the rhombic dodecahedron, which still is not the most efficient structure 27.

One of the most efficient structures is the truncated octahedron which can be packed in the Kelvin packing mechanism. The octahedron packing is resultant of constructing the dual Polyhedra of Sphere packing. Spheres can be packed to a stable condition as they tend to array in triangular manner - opposing to the cube, which will always be in an unstable condition when packed. This can be improved by truncating the cube and adding a second Prism - the Octahedron and combining the two Polyhedra in an efficient packing structure.

SPHERE SPACE FILLING

CUBE PACKING

leaves concave voids

unstable condition

RHOMBIC DODECAHEDRON

TRUNCATED CUBE + OCTAHEDRON

swollen spheres

+

OCTAHEDRON PACKING Sphere Dual Polyhedron

TRUNCATED OCTAHEDRON Kelvin Paking

CELLULAR COMPLEXITY

35

CELLULAR GEOMETRIES IN ARCHITECTURE THE NATIONAL AQUATIC CENTRE BEJING, PTW (AUSTRALIA) AND ARUP (UK)

Following our investigation into various packing geometries, we wanted to investigate the current use of such geometries within an architectural context. The best known example to utilize cellular geometries and efficient structural geometries in architecture is the Water Cube, known as The National Aquatic Centre.

The case study of the Aquatic Centre in Beijing exhibits the use of cellular systems for structural performance and an integrated building envelope.

The design of the structure and building is based on the Weaire-Phelan structure which consists of twelve and fourteen sided polyhedrons. This structure is considered to be the most efficient space-packing geometry in terms of surface area to volume.

The Kelvin Structure

The Kelvin structure from 1887 was considered to be the most efficient space-packing structure, it uses a single geometrical shape that is repetitive throughout the structure. In 1993, Denis Weaire and Robert Phelan used computer simulations for foams, and were able to discover a structure that is more efficient than Kelvins. It uses two different polyhedra, one is an irregular dodecahedron (12 sided) and another that is tetrakaidecahedron (14 sided). The two have equal volumes, and pack together to create this structure. The surface area is 0.3% less than Kelvin’s structures. Until today it remains the most efficient packing geometry.

The structural system had to respond to seismic conditions on site and the large span structural requirements of the program. The combination of geometrical non-directional space frame structure and the lightweight pneumatic ETFE facade skin system made it possible to reduce gravity loads and lateral loads. The large dimensions in depth of the walls and roof provide the possibility of a large spanning structure with high interior ceilings. Further the three dimensional orthotropic load-bearing structure is an extremely efficient form of construction that requires roughly 30% less steel than a column-and-beam system on a span of hundred meters and height of seven meters.

The ETFE pockets act as a protecting cover for the structure from the corrosive properties of the pool water and the polluted air of Beijing. As well the facade acts as a mediating climate control system within the interior spaces of the building. Geometries from nature which have such performative aspects have been an inspiration to the PTW’s team.

The design process of the building involved the generation of a closed packing system of such cells, which were then rotated and chopped into a square global form. The resulting structure has the ability to span over large distances without supporting columns while at the same time evoking the effect of randomness and complexity. The system is generated out of fifteen different cells in the elevation walls and seven different cells in the ceiling. Because of the combination of the cells in different ways each laser-cut ETFE sheet is different and unique. The cells are generated out of three different nodes and four different members. An additional face structure was added at the edges to finalise the rectangular box section to complete the structure.

The repetition and rotation of cells is an efficient way to achieve high complexity within the system and to overcome the problem of too many different pieces. The mathematical geometries of closed packing cellular systems allowed for high structural properties which enable spanning large distances. The analysis of the three dimensional structural facade system is a case study for the integration of structure into the envelope. However in this project there is no variation in cellular organization and porosity to address different conditions; an aspect we aim to tackle throughout our research.

36

CELLULAR SYSTEMS

The Weaire Phelan Structure

THE NATIONAL AQUATIC CENTRE BEJING, PTW (AUSTRALIA) AND ARUP (UK)

11.

10.

2.

9.

12.

3.

15.

1.

7.

4.

6.

5.

13.

14.

Cellular Organization within the Structure - Elevation

30.00 m

7.60 m

The 15 repetitive cells throughout the vertical elements of the building are highlighted - walls There are 7 repetitive cells for the horizontal roof elements of the building

3.70 m 160.00 m 177.00 m

Three-Dimensionality of the Cellular Facade - Section Fig. 1.46 - The large span of 160m is illustrated above, where the facade also becomes thick in its depth, reaching about eight meters for the roof, and almost four meters in the thin parts of the walls

CELLULAR COMPLEXITY

37

CASE STUDY: TYPICAL DOUBLE SKIN FACADE THE TELUS HEADQUARTERS (WILLIAM FERRELL BUILDING), VANCOUVER PETER BUSBY AND ASSOCIATES, 2001

dampers open fan on

27°

The general concept of a double-skin facade is the idea of two layers with a cavity in between. The first skin acts as a rain screen, protecting from environmental conditions, often not fully sealed. The intermediate buffer zone allows for increased thermal and acoustic insulation. Whereas the second skin encloses the enterior spaces, often with operable windows to the controlled buffer zone.

In the facade of the Telus Headquarters in Vancouver this concept is applied, and hereby illustrated. Its double skin facade system is based on the same multi-layer principle, a combination of external layer, intermediate space and inner layer. Within the external layer there are openings which allow for ventilation. The air exchange in the intermediate layer is activated by the solar induced thermal buoyancy and different wind effects.

27° 27° 26° 26° interior windows closed 24°

26°

exterior windows opened 26°

26°

The intermediate layer which is the buffer zone is controlled by dampers on the top and fans on the bottom of the cavity to ensure a good airflow within both layers.

In summer the exterior windows are open and let the air inside the cavity, it heats up and rises to the top of the cavity and exits through the dampers, while the interior windows stay closed to keep the heat outside of the spaces. In winter the dampers are closed and the fan is turned off as well the exterior and interior windows stay closed. This provides a thermal buffer zone which prevents the cold air from outside to enter the building.

Both conditions for Summer and Winter are illustrated, showing the variation in performance within a singular system.

SUMMER

The concept of double skin facades is able to address multiple parameters including thermal, acoustic and visual. However most double skin facades are uniform in their appearance and do not have variation. This suggests that it is a solution that does not change with different changes in the building, including program. Furthermore this system adds complexity and layers, separating the facade into different parts that do not operate within a heirarchy.

dampers closed fan off

6° 6° 7° 7° 7° interior windows closed 24°

7°

exterior windows closed -7°

6°

WINTER Fig. 1.47 - Facade performance in summer and winter

38

CELLULAR SYSTEMS

CASE STUDY: THREE-DIMENSIONAL FACADE THE NATIONAL AQUATIC CENTRE BEJING, PTW (AUSTRALIA) AND ARUP (UK)

hot cavity air vented to outside

In comparison to the double skin facade, the Aquatic Centre has a three dimensional facade that is integrated within structural system. The combination of two layers of ETFE pockets with cavities in between the cells that are used for the structural system provide a performative similar to that double skin facade.

ETFE switched on or off

ETFE transparent to acoustic low frequency, internal skin absorbs high frequency

It is designed for different seasonal conditions. In summer, when external weather conditions are hot and humid, the internal layer is sealed. Through an opening on the bottom edge air, cooled by passing over water around the building perimeter, enters the cavity between both layers and heats up, rises and is exhausted by roof vents.

Both layers are sealed during the winter months to minimise heat loss and in order to maximise the thermal performance of the envelope. Further the thermal mass of the water and concrete inside the building capture the heat collected during the day and release it in the evenings.

45°

controls daylight to areas that do not have glare

diffuse indirect light through ETFE switched to ‘OFF’ position 36° 30°

28°

cool air drawn in over outside water for ventilation

SUMMER

The main difference between the three-dimensional cellular facade and the double skin facade is the integration within structure. The double skin facade acts as a separate layer and system to that of the buildings structure and is independent of it.

The potential that the three-dimensional facade unveils is the ability to use the spaces created within the cells for programmatic conditions. At the moment, the facade can be entered into spatially only for maintenance purposes and remains inaccessible to the building users.

This case study however still disregards variation in the major parameter of cellular systems - porosity. There is a potential to reduce or increase porosity, in response to program, light, structure and other factors. The variation becomes particularly weak in this case when considering transitions and cases between the facade and roof.

maintainance platform for easy access to lights and services

double skin facade acts like a highly insulated greenhouse

Lights in cavity act as indirectly heating of internal space

maximising passive solar gain into pool, solar heat gain is higher then heat loss 28°

thermal mass of structure and water absorbs the heat

WINTER Fig. 1.48 - Facade performance in summer and winter

CELLULAR COMPLEXITY

39

40

CELLULAR SYSTEMS

CELLULAR SYSTEMS overview Throughout this research phase of the project, the general characteristics of cellular systems were investigated. A range of properties were discovered including efficient structural capabilities, low thermal conductivity and good acoustic insulation. These properties however exist at different scales and have a range of parameters affecting them. The parameters can be generally classified to material, geometry and environment.

Of particular interest within the research were natural cellular systems and their geometrical transitions and gradients. Imaging technology from the medical radiology discipline was used to analyse natural artefacts through computed tomography scans. The slices obtained were analysed for their organization and relation to mathematical models. An aspect of redundancy was noticed in most natural systems, their formations are also part of emergent form-finding methods which rely on metabolic processes and environmental factors.

Furthermore, the current use of cellular systems in architecture was investigated through a case study which is compared to conventional systems. In general, the current use of cellular systems does not exploit their opportunity in creating variation through porosity. This variation could address different conditions within a building, and not addressing the entire building through one repetitive solution.

Additionally, the cellular systems provide potential for three-dimensional spatial qualities, while maintaining a unified system that integrates multiple performative aspects; where there are no layers and separation between various elements.

There is however an underlying principle between all cellular systems, and this is the closest-packing arrangement. This creates triangulation which results in structural properties, and an efficient use of material.

CELLULAR COMPLEXITY

41

references

image references

1 - p.2, Gibson, L. J., & Ashby, M. F. (1997). Cellular solids (Second

Fig. 1.1

http://3.bp.blogspot.com/-zhvYMSqPP3E/T7y1QRjSLxI/

AAAAAAAAAKM/0CFLSacXWPs/s1600/mushroom.jpg

ed.). Cambridge: Cambridge university press.

2 - p.30, Ibid

Fig. 1.2

3 - p.45, Ibid

p8_1.jpg

http://www.engr.wisc.edu/alumni/perspective/06.4/Photo_

4 - p.47, Ibid

Fig. 1.3

5 - p.283, Ibid

c20crumbcloseupusethisone.jpg

6 - p.133, Ibid

Fig. 1.4

http://w3.antd.nist.gov/wctg/netanal/honeycomb.gif

7 - Ibid

Fig. 1.5

http://fr.wikipedia.org/wiki/Fichier:Honey_comb.jpg

8 - p.285, Ibid

Fig. 1.6

http://www.structuremag.org/images/0908-f2-8.gif

9 - p.289, Ibid

Fig. 1.7

http://samjshah.files.wordpress.com/2008/08/rd_love_bub-

10 - p.293, Ibid

bles.jpg

11 - p.303, Ibid

Fig. 1.8

http://en.wikipedia.org/wiki/File:CompositeSandwich.png

12 - p.307, Ibid

Fig. 1.9

http://www.designbuild-network.com/projects/watercube/

13 - p.309, Ibid

images/10-watercube.jpg

14 - p. 11, Pearce, P. (1990). Structure in nature is a strategy for design.

Fig. 1.10 http://www.jetsongreen.com/images/old/6a00d8341c67ce53e

http://i567.photobucket.com/albums/ss116/shiaopinghu/

f0133f6454521970b-500wi.jpg

Cambridge: MIT Press. (Original work published 1978)

Fig. 1.11 http://farm5.static.flickr.com/4019/4636848809_e3d6195efb.

15 - p. 92, Jeronimidis, G. (2004). Biodynamics. Emergence:

jpg

morphgenetic design strategies, London: Wiley-Academy.

16 - Ibid

Fig 1.12

17 - p. 34, Weinstock, M. (2006). Self-Organisation and Material

stcatid=43&listitemid=1182&ind=21&page=1

http://www.jameswarwick.co.uk/do/ecco/view_item?listid=2&li

Constructions. Techniques and technologies in morphogenetic

Fig 1.13

design, London: Wiley-Academy.

Fig 1.14a http://www.flickr.com/photos/jrosenk/6848040787/

http://www.newscientist.com/gallery/mars-cracks-driedlakes/2

18 - p. xiii, Pearce, P. (1990). Structure in nature is a strategy for

Fig 1.14b http://www.maya-culture.de/category/flora-fauna/page/6/

design. Cambridge: MIT Press. (Original work published 1978)

Fig 1.15a http://neogenebryozoans.myspecies.info/category/bryozoa/

19 - p. 16, Ibid

bryozoa/gymnolaemata/cheilostomata/ascophora/bitectiporidae/penta-

20 - p. 10, Ibid

pora

21 - p. 33,34, Weinstock, M. (2006). Self-Organisation and Material

Fig 1.15b http://www.nhm.ac.uk/research-curation/staff-directory/

Constructions. Techniques and technologies in morphogenetic

zoology/m-spencer-jones/index.html

design, London: Wiley-Academy.

Fig 1.16a http://www.ucmp.berkeley.edu/esem/pollen.gif

22 - p. 11, Pearce, P. (1990). Structure in nature is a strategy for design. Cambridge: MIT Press. (Original work published 1978)

Fig 1.16b http://cache.zazna.com/selection/Qfb0lSFVmJ,proxy.html Fig 1.17a http://en.wikipedia.org/wiki/File:Poppy-seeds.jpg

23 - p. 14, Ibid

Fig 1.17b http://purpleopurple.com/health-benefits/poppy-seeds.html

24 - p. 9, Ibid

Fig 1.18a http://www.panoramio.com/photo/5489858

25 - p. 11, Ibid

Fig 1.18b http://owlsmall.info/59-philodendron-silk-plant-real-touch.php

26 - p. 3, Ibid

Fig 1.19a http://mfareview.wordpress.com/2011/12/16/architectural-

27 - p. 5, Ibid

cyborgs-nanotechnology-and-the-potential-for-living-architecture/ Fig 1.19b http://magickcanoe.com/blog/2006/11/27/in-the-redwoodspart-four/ Fig 1.20a http://botweb.uwsp.edu/anatomy/images/dicotwood/pages/ SEM0222.htm Fig 1.20b http://www.stockphotopro.com/photo_of/root/A841K2/silver_maple_Tree_roots Fig 1.21a http://www.probelog.com/2007/07/quercus-alba-wood.htm Fig 1.21b http://rowva-jh-hist.wikispaces.com/Megan+and+HannahSymbols

42

CELLULAR SYSTEMS

Fig 1.22a http://www.probelog.com/span/

Fig 1.38a http://www.flickr.com/photos/pixelprobe/3122457509/

Fig 1.22b http://www.public-domain-image.com/plants/flowers/slides/

Fig 1.38b http://www.wallpaper-gratis.eu/tier/natur/tier10.php

high-reed-grass.html

Fig.1.39a http://eveningswithpeter.blogspot.co.uk/2011/08/tonights-

Fig 1.23a http://www.metisllc.com/store/index.php?main_

menu-saffron-risotto-with-sea.html

page=product_info&products_id=3

Fig 1.39b http://www.probelog.com/

Fig 1.23b http://www.omafra.gov.on.ca/IPM/english/cucurbits/index.html

Fig.1.40a http://echinoblog.blogspot.co.uk/2010_05_01_archive.html

Fig 1.24a http://www.corbisimages.com/stock-photo/rights-managed/

Fig 1.40b http://www.probelog.com/

DK011811/crosssection-of-a-mares-tail-plant-stem

Fig 1.41a http://tidechaser.blogspot.co.uk/2012/03/sea-stars-class-

Fig 1.24b http://www.wetlandplants.co.uk/acatalog/info_hipvul.html

asteroidea-of-singapore.html

Fig 1.25

Fig 1.41b http://www.probelog.com/

http://www.wisdomportal.com/Haikus/Number6inNature.html

Fig 1.26a http://botany.cz/en/plant-tissues/

Fig. 1.42

Fig 1.26b http://www.naturalmedicinalherbs.net/herbs/j/juncus-

technical/insulation/qii-hers-credit-now-allows-open-cell-spray-foam/

effusus=soft-rush.php

Fig. 1.43

Fig 1.27a http://www.sciencephoto.com/media/28835/view

technical/insulation/qii-hers-credit-now-allows-open-cell-spray-foam/

Fig 1.27b http://commonground08.wordpress.com/2010/08/03/plant-of-

Fig.

the-week-white-dead-nettle/

digest-166.html

Fig 1.28a http://3.bp.blogspot.com/-zhvYMSqPP3E/T7y1QRjSLxI/

Fig. 1.45

AAAAAAAAAKM/0CFLSacXWPs/s1600/mushroom.jpg

Soap-Bubble-Foam.htm

Fig 1.28b http://www.slowmotiondoomsday.com/boletus.html

Fig. 1.46

Fig 1.29a http://www.probelog.com/2007/07/prairie-plant.htm

uncategorized/page/2/

Fig 1.29b http://www.thebattery.org/plants/plantview.php?id=241

Fig. 1.47

Fig 1.30a http://maceracio.blog.hu/2012/05/29/hogy_is_van_ez_

processes/envelope/1_double-skins/6_case%20studies/case%20

palackzaras_1

studies.html

Fig 1.30b http://www.furniturehomedesign.com/category/flooring/

Fig. 1.48

Fig 1.31a http://www.probelog.com/span/

watercube.html

http://greencomplianceplus.markenglisharchitects.com/

http://greencomplianceplus.markenglisharchitects.com/

1.44

http://archive.nrc-cnrc.gc.ca/eng/ibp/irc/cbd/building-

http://chemistry.about.com/od/bubbles/ig/Bubble-Photos/

http://moreaedesign.wordpress.com/category/

http://myweb.wit.edu/viridis/green_site/projects/2_

http://fabricarchitecturemag.com/articles/0508_f2_

Fig 1.31b http://digital-photography-school.com/discover-seven-waysto-create-sepia-images-in-photoshop Fig 1.32a http://futurismic.com/2008/12/16/we-can-rebuild-you-injectable-artificial-bone-paste-developed/ Fig 1.32b http://larrytanner.blogspot.co.uk/2012_05_01_archive.html Fig 1.33a http://larrytanner.blogspot.co.uk/2012_05_01_archive.html Fig 1.33b http://www.ammonite.free-online.co.uk/brcoral.htm Fig 1.34a http://www.nhm.ac.uk/research-curation/research/projects/ echinoid-directory/intro/stereom.html Fig 1.34b http://tidechaser.blogspot.co.uk/2012/03/sea-stars-classasteroidea-of-singapore.html Fig 1.35a http://www.probelog.com/ Fig 1.35b http://geology.com/rocks/scoria.shtml Fig 1.36a http://www.probelog.com/ Fig 1.36b http://www.asturnatura.com/especie/spongia-agaricina.html Fig 1.37a http://www.britannica.com/EBchecked/media/3362/Scanningelectron-micrograph-of-the-adult-human-lung-showing-alveolar Fig 1.37b http://www.umm.edu/patiented/articles/normal_lungs_alveoli_000413.htm Fig 1.38a http://www.flickr.com/photos/pixelprobe/3122457509/

CELLULAR COMPLEXITY

43

44

GEOMETRICAL DEVELOPMENT Following our research into cellular systems, and developing an understanding towards the underlying geometrical principles behind these systems, we commenced explorations within the geometrical realm of cellular systems.

The ambition of our geometrical development was to create variation in porosity within cell-based geometries.

The creation of these geometries was be based on the closest-packing principles investigated earlier.

Furthermore, the use of network offsets, and dual networks guided the process towards creating a gradient in porosity by gradually adjusting the offset of the network, or dual-network.

The geometrical development occurs in both 2D and later 3D. A variety of efficient space-packing structures were chosen for development. This section displays the various opportunities to develop a gradient of porosity, which would address various properties throughout the application of the system.

CELLULAR COMPLEXITY

45

GRADIENT DEVELOPMENT: TWO-DIMENSIONS

As an initial step towards the development of a cellular system and its geometry, several explorations were undertaken in two dimensions where there is a possibility to develop a porosity gradient. The first two explorations examine the possibility of use of an offset network on either a triangular or hexagonal tessellations in two-dimensions. The amount of offset would determine the porosity; where the application of the offset amount through intervals would create a gradient.

46

Throughout the process, the centre point of each tessellation is taken, and the tessellation is scaled down by an interval factor, towards this centre point. The offset tessellation is then subtracted from the original to create a void which generates the porosity. The process is illustrated below.

TRIANGULAR TESSELLATION OFFSET NETWORK

HEXAGONAL TESSELLATION OFFSET NETWORK

Triangular Tessellation Pattern

Hexagonal Tessellation Pattern

Tessellation centre points

Tessellation centre points

Tessellation offset from centre points

Tessellation offset from centre points

Generated Gradient

Generated Gradient

GEOMETRICAL DEVELOPMENT

GRADIENT DEVELOPMENT: TWO-DIMENSIONS

As a further development of the two-dimensional gradient, a dualoffset network is tested. The dual network is generated by connected the centre points of multiple tessellations. In the case of a triangular tessellation, connecting each six triangles will generate a hexagon.

For the hexagonal tessellation connecting each three hexagons will generate a triangle. The offset is then applied on the dual geometry and not the original tessellation. This allows for alternation between geometries where a triangular tessellation grid can have porosity through hexagonal voids and vice versa.

TRIANGULAR TESSELLATION DUAL-OFFSET NETWORK

HEXAGONAL TESSELLATION DUAL-OFFSET NETWORK

Triangular Tessellation Pattern

Hexagonal Tessellation Pattern

Tessellation centre points

Tessellation centre points

Connection of centre points for dual-network

Connection of centre points for dual-network

Offset of tessellation dual-network

Offset of tessellation dual-network

Generated Gradient

Generated Gradient

CELLULAR COMPLEXITY

47

KELVIN PACKING STRUCTURE DUAL GEOMETRY OFFSET

The principles applied in two-dimensions are now tested in threedimensional geometries. The basis for the first developed porous structure is the Kelvin packing structure. The primitive cell is a Truncated Octahedron. By connecting the centers of each cell, the Dual-Polyhedron is created, in this case the Rhombic Dodecahedron. This Dual Polyhedron is then partitioned into Tetrahedra, which are offset in gradually increased values throughout the structure. By subtracting these Dual-Polyhedra from the initial cells, desired Porosities are created in the single cells and in the overall structure. To achieve an even higher range of porosity the cell is then offset and also subtracted from a certain point in the structure. Through the principle investigated earlier on the structural quality of a Dual-Network, the structural efficiency is still guaranteed, even with the porous cells.

INITIAL CELLS

48

DUAL OFFSET

DUAL SUBTRACTED

TRUNCATED OCTAHEDRON

OFFSET CELLS

GEOMETRICAL DEVELOPMENT

KELVIN PACKING

RESULTING POROUS STRUCTURE

CELLULAR COMPLEXITY

49

KELVIN PACKING STRUCTURE DUAL SYSTEM OFFSET

In this structure, the Kelvin packing is again the basis for the geometrical development. The centres of the packed Truncated Octahedrons are connected in order to create the Dual-Network. This Network is then extruded with offsets of the cell walls. Throughout the structure, the Extrusion-Offset Number increases, therefore the thickness of the generated Dual-structure increases. By subtracting this Dual-Structure from the initial cells, a Porosity gradient is created throughout the system.

TRUNCATED OCTAHEDRON

INITIAL CELLS

50

DUAL EXTRUDED

DUAL IN CELLS

DUAL SUBTRACTED

GEOMETRICAL DEVELOPMENT

KELVIN PACKING

RESULTING POROUS STRUCTURE

CELLULAR COMPLEXITY

51

KELVIN PACKING STRUCTURE DUAL SYSTEM AS STRUCTURE

In this structure, the same principle as in the previous example is applied - The Dual-Network of the Kelvin Packing System is generated and offsets of the cell walls are extruded along it in various thicknesses.

In this case, the Dual-Structure is not subtracted from the initial cells, it is used as a structure on its own. What is particularly interesting in this structure, in relation to the former two is the change in cell size.

Previously the cell size remained the same due to the base primitive.

In this case the cell becomes smaller due to the change in the network offset size. This is the first attempt to create a gradient in porosity, and change in cell size.

TRUNCATED OCTAHEDRON

INITIAL CELLS

52

DUAL EXTRUDED

KELVIN PACKING

RESULTING POROUS STRUCTURE

GEOMETRICAL DEVELOPMENT

CELLULAR COMPLEXITY

53

KELVIN PACKING STRUCTURE: NETWORK OFFSET POROSITY GRADIENT

As a further analysis of the porosity gradient. The amount of cell offset is documented, in relation to the porosity of the cell. This investigates the relationship between the geometrical changes and porosity changes. Furthermore, by creating a graph of this relationship, it is possible to determine the amount of offset needed to create a specific porosity. Generally, cellular systems which are porous have a porosity on average around 30%, in this geometry and offset network, the focus range would be between 0.1 to 0.5 - 40%-90% porosity, as outlined below.

DUAL-NETWORK OFFSET

NETWORK OFFSET Geometry

Offset

Porosity

Geometry

Offset

1.2

Porosity

1

0

0

0

0.8

0

0.6

0.9

0.9

0.978

0.999

0.4 0.2

0.8

0.8

0.921

0.992

0 0

DUAL-NETWORK OFFSET Porosity

Geometry

0

0.978

0.921

0.833

0.724

54

0.7

0.833

0.7

0.973

0.6

0.724

0.6

0.936

0.5

0.602

Offset

Porosity

1.2

0.4

0.474

1

0

0

0.8

0.3

0.348

0.6

0.9

0.999

0.2

0.232

0.8

0.992

0.1

0.134

0.7

0.973

0.6

0.936

0.5

0.875

0.4

0.784

0.2

0.4

0.6

0.8

0.2

0.4

0.6

0.8

Far Left: offset - porosity data Left: Network Offset Geometry Below: offset - porosity graph

1.2 1 0.8

0.3

0.657 0.6

0.4

0.2

0.2

0.4

0.488

network 0.2 offset

0 0

0.2

GEOMETRICAL DEVELOPMENT

0.4 0.1

0.6 0.271

0.8

1

0 0

fset et

9

8

KELVIN PACKING STRUCTURE: DUAL-NETWORK OFFSET POROSITY GRADIENT

The same analysis is undertaken for the dual-network offset. In this case the relationship is not as linear but becomes sharper as the offset increases, due to the geometry. In this case the offset focus range would be only between 0.1 and 0.3 in relation to 0.1 and 0.5 in the network offset structure. This establishes the fact that the type of network and geometry creates variable changes in porosity within a given offset.

DUAL-NETWORK OFFSET DUAL-NETWORK OFFSET Porosity Porosity

Geometry Geometry

Offset Offset

Porosity Porosity

1

0

0

0

0

0

0

0.978 0.978

0.9 0.9

0.999 0.999

0.921 0.921

0.8 0.8

0.992 0.992

0.4 0.4

0

0.973 0.973

6

0.724 0.724

0.6 0.6

0.936 0.936

5

0.602 0.602

0.5 0.5

0.875 0.875

4

0.474 0.474

0.4 0.4

0.784 0.784

0.3 0.3

0.657 0.657

0.232 0.232

0.2 0.2

0.488 0.488

0.134 0.134

0.1 0.1

0.271 0.271

0

0.2 0.2

0.4 0.4

0.6 0.6

0.8 0.8

1

1

Far Left: offset - porosity data Left: Dual-Network Offset Geometry Below: offset - porosity graph 1.2 1.2 1

0.348 0.348

network network offset offset

0 0

0.7 0.7

1

0.8 0.8

0.2 0.2

0.833 0.833

2

1

0.6 0.6

7

3

1.2 1.2

1

0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0

0 0

0

0.2 0.2

CELLULAR COMPLEXITY

0.4 0.4

0.6 0.6

0.8 0.8

1

1

dual dual network network offset offset

55

OCTAHEDRON PACKING STRUCTURE

Further geometrical development was continued towards different spacepacking structures from the Kelvin. This structure consists of closest packed octahedrons which are oriented in three different directions in order to fill up a volume without leaving any voids. By connecting the centre of each Octahedron with the centres of all its neighbouring cells, the Dual Polyhedra of the Octahedron Packing structure are created.

In this case the Dual structure consists of two different Polyhedra - The Truncated cube combined with the Octahedron itself. By scaling the Dual Polyhedra in their centres gradually throughout the structure, a porosity gradient is generated.

OCTRAHEDRON

INITIAL CELLS

56

DUAL OFFSET

DUAL SUBTRACTED

GEOMETRICAL DEVELOPMENT

OCTRAHEDRON PACKING

RESULTING POROUS STRUCTURE

CELLULAR COMPLEXITY

57

TRUNCATED CUBE - OCTAHEDRON STRUCTURE

This structure is built up out of two different Polyhedra - The Truncated Cube and the Octahedron. The Dual-Polyhedron of this structure is the Octahedron. It is, like in the previous geometries generated by connecting the centres of the original cells. The Dual-Polyhedra are then gradually scaled throughout the structure in order to achieve the desired porosity gradient. The Dual Polyhedron is then subtracted from both, the Truncated Cube and the Octahedron.

+

The interesting aspect in this specific geometry is the transition not only in porosity, but in cell type, where it changes from closed cells with plates towards open cells with struts.

TRUNCATED CUBE - OCTAHEDRON PACKING

INITIAL CELLS

58

DUAL OFFSET

DUAL SUBTRACTED

GEOMETRICAL DEVELOPMENT

RESULTING POROUS STRUCTURE

CELLULAR COMPLEXITY

59

VARIATION IN CELL SIZE THROUGH SUBDIVISION

Not only gradient in cell porosity, but also gradient in cell size is and important factor when looking into the structure of cellular systems.

Subdivision was investigated as a strategy of variation in cell size, where it is possible to subdivide a large cell into a number of smaller identical cells. In the first example shown below, a simple subdivision of the initial cell is shown. The initial cell, the Rhombic Dodecahedron can be subdivided into smaller cells, which are in fact just equal to the scaled initial cell. In this system, several sizes of cells can be combined in one single, continuous system in order to address various required properties.

Below, the initial Truncated Octahedron cell is shown, and its Dual Structure Polyhedron, the Rhombic Dodecahedron. In this example, cell porosity is created by subtraction of the offset Dual structure on the initial cell. The same operation is executed on the Dual-cell itself. The new, porous Dual-cell can then be placed in the initial cell, where it was taken out before.

This operation can possibly be repeated in a desired amount of iterations with the desired amount of porosity at each level. Therefore hierarchies in cell size as well as in porosity are created within one single, controlled system.

VARIATION IN CELL SIZE DUAL OFFSET

SUBDIVISION OF THE RHOMBIC DODECAHEDRON

TRUNCATED TETRAHEDRON GENERATION OF DUAL NETWORK AND POLYHEDRON OCTAHEDRON

DUAL DUAL

SUBDIVISION TETRAHEDRON

TRUNCATED OCTAHEDRON

0.9

SUBDIVISION TETRAHEDRON

60

GEOMETRICAL DEVELOPMENT

RHOMBIC DODECAHEDRON

TRUNCATED OCTAHEDRON

S S T T

EDRON EDRON DUAL

DUAL

DUAL OFFSET DUAL OFFSET

0.5 0.5 0.5

RHOMBIC DODECAHEDRON

TRUNCATED OCTAHEDRON

0.9 0.9 0.9

0.5 0.5 0.5

DUAL SCALE

DUAL SCALE

0.9 0.9 0.9

DUAL SUBTRACTION

DUAL SUBTRACTION

COMBINATION OF POROUS INITIAL AND POROUS DUAL

CELLULAR COMPLEXITY

61

SPACE-PACKING STRUCTURES: POROSITY GRADIENT

The results of the geometrical development of a porosity gradient through space-packing structures are presented below. Three variations were produced for the kelvin structure which utilizes the same cell primitive repetitively. The various offset networks create the change in geometry and porosity. Furthermore a tetrahedron packing is also investigated, in addition to a two-primitive packing strategy with truncated cubes and octahedrons. Overall, there are various ways to develop the gradient geometrically. Further investigation and comparison of these structures is required for their evaluation.

KELVIN PACKING CELL OFFSET

62

KELVIN PACKING - DUAL

GEOMETRICAL DEVELOPMENT

KELVIN PACKING DUAL OFFSET

TETRAHEDRON PACKING DUAL OFFSET

TRUNCATED CUBE - OCTAHEDRON DUAL OFFSET

CELLULAR COMPLEXITY

63

FINITE ELEMENT ANALYSIS

The structural efficiency of the examined space-packing geometries was tested in a Finite Element Analysis in Strand7. In the first test, the different geometries were compared to each other by abstracting them to their basic shape. In each case the structure consists of eight cells which fill up a volume of 5 x 5 x 5 meters. The overall material volume used for each structure is 1.5m³ and each structure is vertically loaded with 10kN. This setup makes the tests a pure comparison of the geometries, therefore it is material independent - the material used in this case is stainless steel. The structures were compared in both, mean stress and displacement in load direction. Due to the small number of

cells used, this serves as a first overview to give a feeling of the relation of all the structures.

The results show that the Truncated Cube - Octahedron structure is the structurally most effective in this setup. The Kelvin-Dual is structurally not strong because of the small number of cells, this causes the cells on the edges to perform weak in displacement and stress. The structural performance of the Kelvin Structure is comparable to the Truncated Cube - Octahedron.

TEST 01

DISPLACEMENT

STRESS

Kelvin - Dual

biggest displacement: 3.21 mm

biggest stress: 3.3 MPa average stress: 2.9 MPa

Kelvin - Packing

biggest displacement: 0.39 mm

biggest stress: 2.8MPa average stress: 0.007MPa

Truncated Cube/ Octahedron-Packing

biggest displacement: 0.03mm

biggest stress: 0.27MPa average stress: 0.045MPa

64

GEOMETRICAL DEVELOPMENT

In a continuation of this Analysis, the Kelvin-Dual was chosen to test the effect of increasing the number of cells for structural efficiency. Again, the overall material volume, the overall filled up dimension and the applied load remain the same - only the number of cells changes. The results of the second test show clearly, that the structural performance can be significantly improved by increasing the cell number. By filling up the volume with cells which are one third in size compared to the initial cell, which means that the number of layers is tripled.

The structural efficiency of the what was considered the weakest structure in test 01 becomes now comparable with the most effective structure, the Truncated Cube - Octahedron Structure. Also, when looking at the third case in test 02, the results show that not only the number of cells, but also the cell arrangement plays a very important role. The top right row in the shown tests is much weaker that the top left row, caused by the fact that it only connects to one underlying row.

TEST 02

DISPLACEMENT

STRESS

8 CELLS

biggest displacement: 3.21 mm

biggest stress: 3.3 MPa average stress: 2.9 MPa

biggest displacement: 1.8 mm

biggest stress: 3.5 MPa average stress: 0.9 MPa

biggest displacement: 0.9 mm

biggest stress: 3.4 MPa average stress: 0.5 MPa

10 kN

5m 5m

43 CELLS 10 kN

5m 5m

250 CELLS 10 kN

5m 5m

CELLULAR COMPLEXITY

65

66

GEOMETRICAL DEVELOPMENT

GEOMETRICAL DEVELOPMENT overview Based on the studies on geometrical and structural principles of cellular systems, several 2D and 3D structures, containing a controlled porosity gradient were developed. In both, 2D and 3D a chosen closest packing structure made of one or more regular or semi-regular cells was the basis. By connecting the centres of neighbouring cells, the Dual-Network of the initial structure was generated. Different further operations were carried out with the generated DualPolygons and Dual-Polyhedra in order to create porosity throughout the structure.

The results of the porosity evaluation demonstrate that in different structures, the same scale factors can create different porosity percentages. This suggests that, for developing a system of desired porosity with different structures, different geometrical and offset-network factors have to be taken into account.

However through cataloguing, a controlled system of porosity generation can be developed.

Further, initial theoretical steps investigated a method to develop not only a change in Porosity within the system, but also a change in cell size through various subdivision strategies.

The studied and developed structures set the foundation for the architectural system by making use of these different porosity gradients which can be created in a controlled way in order to address the required properties. These structures were tested through Finite Element Analysis for a comparative evaluation of the geometries, throughout these tests several an understanding was developed towards their structural capabilities and particularly with variation in aggregations.

However, the structures, base geometries and networks require further investigation for application, viability and performance within an real scale architectural system.

The porosity in the system is generated in a gradient, in constant fields as well as random distributions.

Because of the fact that the whole porosity is based on either the initial network itself or the relating DualStructure, it is assumed that the structural performance and efficiency is still guaranteed within the system.

CELLULAR COMPLEXITY

67

68

FA B R I C AT I O N Following our research towards the geometrical development of cellular systems, and in particular the creation of a gradient in space-packing structures; the interest lies in the viability and fabrication of these structures.

Most of the structures contain complex geometrical transitions, hollow sections and continuous elements.

Therefore, a range of fabrication methods are examined and evaluated. These methods are evaluated based on their applicability towards a real-scale architectural application.

While first fabrication tests utilize advanced additive manufacturing technologies and their ability to produce almost highly complex geometries. The further tests include more conventional fabrication methods due to the range of limitations within additive manufacturing.

The tests also consider hybrid methods combining different means of fabrication. Due to our developed interest in this realm, a range of case studies are investigated, particularly for real-scale fabrication viability and application.

CELLULAR COMPLEXITY

69

FABRICATION METHODS ADDITIVE MANUFACTURING

ADDITIVE MANUFACTURING OF GEOMETRY

This fabrication tool is able to build up the geometrical system layer by layer (additive manufacturing) by the means of a 3DThis fabrication is able to build up the geometrical system layer by theis means of printer.

Thetoolgeometrical system which waslayer 3Dbyprinted shown a 3D-printer. The geometrical system which was 3D printed is shown in the drawing on the in the the right.

The of the the intervals printer right.

Thedrawing layers of theon intervals the printer goeslayers through for additive processthe is illustrated goes through for used the toadditive processmodels is illustrated below. This below. This method was produce presentation of selected geometries, any complex geometry can be 3D as long as it is generatedmodels as a solidof andselected contains method was used to printed produce presentation minimum thickness above 1mm. geometries, any complex geometry can be 3D printed as long as it is generated as a solid and contains minimum thickness of 1mm.

00.00

00.50

01.00

01.50

02.00

02.50

03.00

03.50

04.00

04.50

05.00

05.50

06.00

06.50

07.00

07.50

08.00

08.50

09.00

09.50

10.00

10.50

11.00

11.50

12.00

12.50

13.00

13.50

14.00

14.50

15.00

15.50

16.00

16.50

17.00

17.50

18.00

18.50

19.00

19.50

Layers of Geometrical System processed by 3D-printer

70

FA B R I C AT I O N

3D-PRINTING TECHNOLOGY

The models were 3D printed in the digital prototyping lab at AA (DPL).

The equipment used is a ZCORP 310 plus rapid prototyping machine which has a maximum build size 203x254x203 mm. The machine uses an additive process of layers of gypsum-based powder and glue. These five models were produced in one printing box and took about 24 hours to print. The machines need to be manually prepared and cleaned and the models need a manual processes of extracting and de powdering which took about two hours.

After taking the models out of the machine they need to be infiltrated to achieve strength and durability. This technology features highly

Fig. 3.1

complex configurations such as these geometries, which would have not been able to print with any other 3D printing technology in such short time. As plastic printers for example take much more time as well as support material and this causes very long production times.

The photographs display the initial 3D printed cellular systems of the following selected geometries: Fig. 3.1 Kelvin Dual Network, Fig. 3.2 Kelvin Dual Offset Fig. 3.3 Tetrahedron Dual Offset, Fig. 3.4 Kelvin and Cell Offset Fig. 3.5 Truncated Cube Octahedron Dual Offset

Fig. 3.2

Fig. 3.3

Fig. 3.4

Fig. 3.5

CELLULAR COMPLEXITY

71

FABRICATION METHODS SHEET MATERIAL PRODUCTION OF SINGLE CELL

SHEET PRODUCTION OF INDIVIDUAL CELL This fabrication method attempts to produce the cell through sheet material, using a laser-cutter. Cells with various porosities This fabrication method attempts to produce the cellresultant through sheet material,contains using a have different nets for assembly.

The system laser-cutter. Cells with various porosities have different nets for assembly. The resultant a large number of joints between cut elements, which becomes system contains a large number of joints between cut elements, which becomes more more ascomplex as the porosity increases. The chosen cell complex the porosity increases. geometry is shown to the right, in addition to an overall global aggregation.

Diagrams: Right: Individual Cell ; Far Right: Geometrical System

exploded axonometric of assembly

cell geometry with varying porosity

net of cell geometry for laser-cutting

72

FA B R I C AT I O N

LASER-CUTTING FABRICATION

This method was used to investigate into the fabrication of single cells of a cellular system within a larger scale . For the fabrication the laser cutter at the DPL at AA was used for cutting cardboard sheet material (1mm thickness) . The diagrams Fig. 3.6-3.8 display the gradient thickness change throughout the cellular system . The thick line is the cutting edge and the thin lines are the scored lines for folding. Each drawing is the cutting and folding line of one individual cell. For further investigation one would need to think of connection methods of these single cells. Because there were too many pieces this model was not finished.

Fig. 3.6

Fig. 3.7

Fig. 3.8

CELLULAR COMPLEXITY

73

FABRICATION METHODS CASTING CELLS INDIVIDUALLY

CASTING OF INDIVIDUAL CELL This fabrication method attempts to produce the cell through casting in a multi-part mould. The mould consists of a base and This methodsides attemptswith to produce the cell through in a multi-part mould. The six fabrication removable a vacuum formcasting of the CNC-machined mould consists of a base and six removable sides with a vacuum form of the CNC-milled voids voids of geomtery. the cell’s of the voids of the cell’s The geometry. vacuum forms The of the vacuum voids within forms the cell would assemble within within the cell would toghether a bounding box assemble that fixes them together toghether for within casting. a bounding box that fixes them together for casting. The chosen cell geometry is shown to the right,Cell in ;addition to an overall Diagrams: Right: Individual Far Right: Geometrical System global aggregation.

plaster

complete mould with box

mould bounding box Laser-cut MDF or Perspex

exploded axonometric

step001

step002

step003

cell geometry positive

cell interior voids

mould for positive

cell closed exterior net CNC-milled MDF

seperated assembling voids CNC-milled high density foam

assembled sides to void Vacuum form of assembled MDF and high density foam

74

FA B R I C AT I O N

MULTI-PART MOULD FOR SINGLE CELL CASTING

As illustrated and described on the left side, this fabrication method investigated into the possibility of casting an individual cell. The mould was separated into multiple pieces and the elements were computerized numerical controlled (CNC) machined out of polyurethane block material (Fig. 3.12). This hard foam provides high precision in geometry and detail level. As it is a very hard and strong material it can be used for vacuum forming technology. The elements were vacuum formed using plastic sheet material.

Fig. 3.9

Due to the interior elements sharp straight angles (90 degrees) it was impossible to take the elements out of the sheets once they were vacuum formed (Fig. 3.9) The plates for the surrounding mould frame were CNC machined out of medium-density fibreboard (MDF).

Unfortunately it was not possible to machine them with a small sized milling bit, for that reason the edges had incorrect angles and did not fit well together. Due to those facts this model stayed incomplete.

Fig. 3.10

Fig. 3.11

Fig. 3.12

CELLULAR COMPLEXITY

75

FABRICATION METHODS FABRICATION METHODS PANEL-BASED CASTING OF CELLS

PANEL PANELCASTING CASTINGOF OFCELLULAR CELLULARSYSTEM SYSTEM This fabrication method attempts to produce the global geometrical system through casting panels which contains a This fabrication attempts totoproduce global through This fabrication method attempts produce the globalgeometrical geometrical system throughcasting castingpanels panelswhich which portion ofmethod multiple cells.

Thethe mould would system be CNC-machined contains containsa aportion portionofofmultiple multiplecells. cells.The Themould mouldwould wouldbe beCNC-machined CNC-machinedand andplaster-cast plaster-casttotoachieve achievethe the and(with plaster-cast to achieve the panel (with possibility of vacuum panel possibility forming the would face panel (with possibilityofofvacuum vacuum forming themould). mould).The Thepanels panels wouldassemble assemble facetotoface facewith with intermediate cells which cast the forming individual the mould).

The panels would assemble face to face with intermediate individual cellsininbetween between whichare are castusing using thesame samemethod. method. intermediate individual cells in between which are cast using the same method. The chosen cell geometry is shown to the right, in Diagrams: Right: Cell Geometrical addition to Individual an overall Diagrams: Right: Individual Cell; Far ;global FarRight: Right:aggregation.

GeometricalSystem System

plaster plaster

plaster plaster

unit unita a

unit unitb b

step001 step001

CNC-machine CNC-machinemould mouldand andplaster plastercast cast modules modules

1x1xunit unita a 1x1xunit unitb b

76

plaster plastercasting casting

two-part two-partmould mould

step002 step002

step003 step003

module moduleassembly assemblytotopanel panel

panel panelsystem systemassembly assembly

2x2xunit unita a

2x2xunit unita a 18x 18xunit unitb b

FA B R I C AT I O N

CNC-MACHINED CASTING PANELS

This method was used to generate the cellular system not by single cells , but rather translating the cellular system into panels. Those panels would inherit one side / half of a multiple cellular network. This method was developed to overcome connection details in previously tested single cell fabrication methods. The Panels were machined with CNC out of polyurethane block material. These panels fit together very precisely and leave a gap on one side of the box to infill the plaster for casting.

Prior to applying plaster into the mould, the panels need to be sealed due to the porous nature of the foam block. A sealing wax was used to seal the foam. This was done in three layers with manual polishing treatment in-between. A test cast was done on one small panel which unfortunately still locked the plaster in. this proofed that we would have not been able to take the plaster out of the mould after casting due to the tolerances in the angles. Instead it would have been more efficient to CNC the positive panel and use the method of silicon mould; a method for further investigation.

Fig. 3.13

Fig. 3.14

Fig. 3.15

Fig. 3.16

Fig 3.17

CELLULAR COMPLEXITY

77

FABRICATION METHODS CELL AGGREGATIONS THROUGH JOINTS+STRUTS

CAST JOINT AND TUBE SYSTEM This fabrication method combines the use of custom made components at connection nodes, and readily available This fabricationinmethod combines the use ofThe custom made components connection nodes, elements between - tubes. custom joint isatfirst additively and readily available elements in between - tubes. The custom joint is first additively manufacmanufactured through 3D-printing, a silicone mould is created tured through 3D-printing, a silicone mould is created from the print. This silicone mould is from theto print.

This the silicone mould is then used to mass-produce then used mass-produce joint in various materials. the joint in various materials. The chosen cell geometry is shown to the right, in addition to an overall global aggregation.

Diagrams: Right: Individual Cell ; Far Right: Geometrical System

mm 4mm 6mm 8mm 10mm 12mm 14mm 16mm 18mm 20mm

small x 28 medium x 4 22 37 20 34 19 31 17 28 16 26 14 22 13 20 11 17 10 15

tubes cut in 3 different lengths

tubes + joints

assembly of joints and tubes in various sizes

step001

3D-print required joint sizes

step002

cast silicone to 3D-print joint in box

step004

step003

retrieve 2-part silicone mould

plaster cast joint

plaster

78

FA B R I C AT I O N

large x 4 44 40 38 34 32 28 26 22 20

CAST JOINTS AND TUBES SYSTEM

The following diagrams Fig. 3.18-3.20 illustrate the combination of the tube and joint system. These were used as visualisation methods to see the results of a rectangular cellular system inheriting a gradient in thickness by varying tubes and joints sizes. The joints were 3D-printed at AA DPL lab and the plastic tubes were cut in the AA model workshop.

The fabrication and cutting of the elements was more labour intensive then the actual assembly of the pieces.

For connecting and fixing the system together, glue was used as some intolerances appeared between tubes and joints and therefore had to manually adjusted. Overall the fabrication method revealed stiffness and durability throughout the whole system and was in fact the fastest, simplest and cost efficient fabrication method.

Fig. 3.18

Fig. 3.19

Fig. 3.20

Fig. 3.21

Fig. 3.22

Fig. 3.23

CELLULAR COMPLEXITY

79

TEST JOINTS - 3D PRINTING

Further tests were done with the Printer of “1PLU2D” where the machines achieved a similar detail level with the high resolution printing method (Fig. 3.27-3.29). Only at the points where angles reach over 135 degrees the printer had issues with printing the cantilevering geometry perfect. Thus we decided to not go ahead with these machines for the fabrication method for the Joints, but rather use the 3D printer at the AA DPL lab and investigate into casting methods (Fig. 3.33).

As the initial starting point we decided to fabricate the joints with additive manufacturing method. First tests were done with the AA DPL 3D Printer, which is a Powder Printer and the final geometry printed is very fragile and not very strong in its structural properties (Fig. 3.33).

Thus we undertook another experiment with the in-house 3D Printer UltiMAKER which is able to 3D print in Plastic and the final object is very strong and durable (Fig 3.24-3.26). To evaluate the detail level in comparison with the powder printer the machines are not able to achieve the same detail level as the AA DPL Printer does.

3D PRINT TEST BY ANDREAS KOERNER [ULTIMAKER]

Fig. 3.24

Fig. 3.25

Fig. 3.26

3D PRINT TEST BY STUDIO INTEGRATE / 1PLUS 2D

Fig. 3.27

Fig. 3.28

Fig. 3.29

Fig. 3.30

Fig. 3.31

Fig. 3.32

3D PRINT TEST AT AA DPL LAB

Fig. 3.33

80

FA B R I C AT I O N

CUSTOM SILICONE MOULD FOR JOINTS

For the Replication of joint, with plaster casting method, one joint 5x5 centimetres was 3D printed using the AA DPL Powder Printer. The joint was printed with closed ends but hollow inside in order to keep the weight and price low. Because the powder 3D prints are not permeable to water and other liquids the pores of the surface had to be sealed with a waterproof plastic seal (Fig. 3.34). The sealing liquid had to be applied with a brush in three thin layers with 30 minutes waiting time inbetween. Once the surface was fully sealed and dry the joint was glued with super glue into a prepared perspex box.

1 Litre of Silicon was used to produce a silicon mould around the 3D printed joint (Fig. 3.35). Once the silicon had dried, the cube was cut half open and the joint was taken out. In total 5 plaster joints and one low melt alloy joint were produced with this negative mould. The precision of the replicates surface detail increased throughout the process and because of low waiting time and fast production this was the method we continued investigating further.

Fig. 3.34

Fig. 3.35

Fig. 3.36

Fig. 3.37

Fig. 3.38

Fig. 3.39

Fig. 3.40

Fig. 3.41

Fig. 3.42

Fig. 3.43

Fig. 3.44

Fig. 3.45

CELLULAR COMPLEXITY

81

CUSTOM JOINTS WITH PLATES AND STRUTS FABRICATION METHODS

Cast - 3D Print Joints / Plates and Struts As the initial starting point we decided to fabricate the joints with additive manufacturing method. First tests were done with the AA DPL 3Dfabrication Printer,method whichcombines is a Powder and joints the final geometry printed The the use ofPrinter custom made and pre fabricated plates and is struts. the level of variation and in irregularity within theproperties fabricated part, the joints veryAccording fragile toand not very strong its structural (Fig. 3.33). are either 3D printed or cast. Depending on the quantity of each type an evaluation of Thus we undertook experiment with the in-house feasibility of each method hasanother to be decided.

In the model, plate thicknesses stay3D the Printer same UltiMAKER which is able to 3D print in Plastic and the final object is throughout the change of porosity. very strong and durable (Fig 3.24-3.26). To evaluate the detail level in comparison with the powder printer the machines are not able to achieve the same detail level as the AA DPL Printer does.

82

plates 01

plates 02

struts 03

struts 04

joint 01

joint 02

joint 03

joint 04

FA B R I C AT I O N

Study structure containing closed and open cells, plates and struts respectively

CELLULAR COMPLEXITY

83

Since a 3D printer was used, we were able to customize each joint for the condition it was at (corner, edge, etc.)

Joints for connection with plates, in comparison to joints shown above - customizing for a material gradient and continuity of elements

84

FA B R I C AT I O N

The laser-cut plates and struts elements - the point where they fit into the joint is unified, therefore it is possible to mass-produce the joints

Top Perspective view of the fabricated model, combining 3D printed joints, laser-cut struts and plates.

CELLULAR COMPLEXITY

85

EVALUATION: FABRICATION TESTS

In general, the fabrication methods investigated were to consider alternatives to 3D-printing which are viable for producing complex geometry. The intention is to compare fabrication methods for feasibility and efficiency for an architectural scale system. For the tests, the machinery and materials have set the initial constraints.

The resulting models were compared in terms of production time, cost and effectiveness and the already common methods such as investment casting or lasercut sheet material are set into a relation to the additive manufacturing process.

GEOMETRICAL SYSTEM

Systems 01 and 02 are methods which combine customized joints with standardized plates and struts elements. The joint can be either cast or 3D-printed, depending on what is most economical and efficient at a given case. For systems 04 and 05, entire individual cells were produced as separate units, first mentioned through a CNC-milled mould, and in the second one through laser-cut sheet material which were then connected through countless joints.

System 03 also requires several joints between panels, layering the method and increasing its complexity.

KELVIN DUAL

TRUNCATED CUBE OCTAHEDRON

system 01 system 02 system 03 system 04 system 05

system 01

3D printing structure additive manufacturing

Joints and Tube System 3D printing joints

Joints and Tube System Casting joints

COST

£ 45.00

£ 75.00

£ 48.00

£ 100.00

TIME (machine h / man h)

30h - 50h / 1h

10h / 15h

10h / 15h

10h / 15h

SIZE

70 x 70 x 180

200 x 200 x 500

70 x 70 x 70

350 x 350 x 450

any geometry possible high detail / precision

medium cost low machine hours 3D printed joints - variation of angles

production of open and closed cells possiblle wide variety of scales

DISADVANTAGES

high cost high machine hours scale limited to machine

bound to available tube dimensions closed cells are not achieved

assembly is difficult

POSSIBLE REAL

3D printed concrete contour-crafting

3D printed/cast joint steel tubes

3D printed/cast joint steel/wood/glass panels

METHOD

system 02

Joints - Struts and Plates 3D printing joints

MODEL

ADVANTAGES

SCAL MATERIAL

86

FA B R I C AT I O N

The advantage in methods 01 and 02 are their hybrid approach, where joints are minimized yet complex and fabricated through advanced methods. The larger elements become standardized sheet material or extruded profiles which are cut through traditional methods. These hybrid fabrication methods become of particular interest are therefore require further investigations through real-scale case studies.

manufacturing, not as a way to produce the whole system, but rather as an opportunity for producing only complex parts or joints of the system which allow for the use of standardised elements within a highly complex Three-Dimensional system. The experiments showed that the 3D print process is viable and efficient from a point where each part/ joint is different from the others. If elements are complex but repeated, casting with accurate moulds becomes a more efficient strategy.

The tests developed our perspective towards looking at additive

OCTAHEDRON

KELVIN

system 03

system 04

system 05

Casting panelized part of system

Casting Individual Cell

Sheet material Individual Cell

£ 50.00

£ 30.00

£ 9.00

10h machine

5h machine / 15h man

2h machine / 30h man

400 x 400 x 400 mm

100 x 100 x100 mm

100 x 100 x 900 mm

medium cost low machine hours like tilt up construction

low cost - 1 mould low machine hours

low cost low machine hours

difficult to release piece from mould lots of screws

preparation and assembly of mould

about 300 joints within the system assembly labour intensive

pre-cast concrete

pre-cast concrete

wooden plates steel plates

CELLULAR COMPLEXITY

KELVIN

87

CASE STUDY: WELDED STEEL JOINTS THE NATIONAL AQUATIC CENTRE BEIJING, PTW (AUSTRALIA) AND ARUP (UK)

Due to our interest in the development of joints for the system, we investigated a number of case-studies for their use of joints within complex systems at an architectural scale. These include the Aquatic Centre by PTW, The Quantom Cloud by Antony Gormley and the EmTech canopy at the Architectural Association in London.

The only way to solve this highly complex construction was to use Rapid Prototyping machinery which is usually used in the Automobile Industry. The structure was developed with a software, created by Arup specifically for this project, which allowed for highly complex analysis and optimization. In this way specific sizes, shapes, profiles and weights could be assigned to each of the tubes individually by testing the whole space frame in various conditions. The collected data was transformed into a 3D model from which all necessary structural drawings could be extracted. This digitally driven, automated planning process ensured precision, accuracy and high time efficiency which enabled the team to produce detailed plans for an optimized structure in less than one week.

The first case study is the Aquatic Centre in Beijing. The structure consists of 22 000 steel tubes which are connected through 12 000 joints. Within this space frame are simple circular tubes which are welded to spherical nodes manually on site. All members are framed into the nodes, creating a perfect structure for seismically active areas, such as Beijing..

3 DIFFERENT TYPES OF STRUCTURAL JOINTS

88

FA B R I C AT I O N

CASE STUDY: INVESTMENT CASTING - JOINTS THE QUANTUM CLOUD, LONDON ANTHONY GORMLEY AND LUSAS (STRUCTURAL ENGINEERING)

The structure of the 30m high x 16m x 10m oval cloud sculpture was generated by a custom fractal growth software and consists of 1.5m long, randomly oriented steel sections. The centre forms the structural core and visually appears as a human body which diffuses towards the edges.

The investment casting uses a wax positive of the joint (the investment) to create a mould, where this wax is then melted to obtain the mould and cast repetitive elements in it. The specifically developed software for this project automatically generates files which were the basis for the SolidWorks software in which the 3D fabrication documents were created.

In total are 325 tetrahedral steel units, each made of four hollow steel sections that are welded together. The Neighbouring units are connected through individually investment cast joints and are initially connected with steel pins which are removed after the joints are welded together.

CONNECTION NODES: CAST JOINT, TETRAHEDRAL PART AND SYSTEM OF WELDED METAL PROFILES Fig. 3.46 - Quantam Cloud by Antony Gormley, London

GEOMETRICAL DEVELOPMENT

CASE STUDY: CUSTOM 3D-PRINTED JOINTS DOUBLY CURVED CANOPY SCREEN, LONDON ARCHITECTURAL ASSOCIATION, EMTECH STUDENTS, 2012 This case study focuses on the importance of joints within differentiated structural systems, as well as various methods of how to feasibly create and manufacture those. In general the combination of small customized elements with larger, standardized elements can be considered as an efficient fabrication strategy. When looking deeper into complex structures it becomes clear that the current challenge is to utilize digital fabrication where it becomes effective and necessary.

They were digitally developed, allowing the joints to be accurately placed into the simple straight timber struts within the desired curved position.

The connection between the wood struts was critical due to the double-miter joint, which has the wood angled in two directions. These different angles are illustrated below for the different tiers/levels of the canopy. Due to the sharp angle between the wood struts, mechanical connections such as bolts were not possible due to limited length and the inability to accurately predrill or place bolts at the repetitive corner conditions.

The EmTech canopy is a project we were involved in that combined both customized and standardized elements to achieve a double curvature in geometry. We revisited this project as a precedent for this research.

The double curvature of the canopy is induced by the customized 3D Printed joints which therefore form the key elements in this project.

THE STANDARDIZED WOOD ELEMENTS FOR EACH TIER OF THE CANOPY

TIER 01

85.5°

40.4°

TIER 02

85.5°

49.6°

85.5°

85.5°

49.6°

426.8

40.4°

85.5°

85.5°

40.3°

426.8

50.0°

85.5°

50.0°

416.2

40.3°

41.6°

90

85.5°

48.9°

85.5°

85.5°

48.9°

426.8

40.8°

85.5°

85.5°

40.8°

426.8

49.8°

85.5°

85.5°

49.8°

416.2

40.8°

416.2

TIER 04

85.5°

47.9°

426.8

40.8°

416.2

TIER 03

85.6°

85.5°

85.5°

85.5°

85.6°

47.9°

41.6°

426.8

85.6°

85.6°

41.6°

49.1°

416.2

85.6°

85.6°

49.1°

41.6°

85.6°

42.8°

46.6°

426.8

416.2

FA B R I C AT I O N

85.6°

85.6°

85.6°

46.6°

42.8°

426.8

85.6°

85.7°

42.8°

48.1°

416.2

85.7°

85.6°

48.1°

42.8°

416.2

Although the sophistication of this project lies in the joints, the struts as well have to be individually developed and cut in various angles in order to meet the precision in detail of the overall appearance. The struts could be cut with a simple table saw with the help of specifically designed guiding boxes. Each frame consists of 4 differently cut timber struts and 3 different joints. Each row of the installation is made of the same type of frame.

When considering this method for an architectural scale, properties of the materials available for the additive manufacturing process have to be tested against durability in outdoors space. Hence more and more materials are being developed for the 3D printing process, therefore it could be considered as a viable method.

GLOBAL GEOMETRY OF THE CANOPY, CUSTOM JOINTS ILLUSTRATED

04-top

04-side

04

04-bottom

03-top

03

03

03-side

03-bottom

02

02

02-top

02 02-side

01 01

02-bottom

01-top

01

01

01-side

01-bottom

CELLULAR COMPLEXITY

91

DEVELOPED HYBRID FABRICATION METHOD

The chosen fabricated method utilizes the geometry of the truncated cubes and octahedrons, where the truncated cube becomes the joint; and the octahedron is divided into several plates or struts based on the offset network.

At an architectural scale application, it would consist of non-standardized elements which are customized, and standardized elements which are typically available. The joint is the customized element and would be produced through casting or additive manufacturing methods, where a variety of structural materials are available within this method including metals.

The space-packing concept of this geometry utilizes the truncated cube to fill the voids in the octahedron, completing its structural spacepacking capabilities. Therefore, in this case the joints are well suited for this purpose.

As for the standardized elements, a range of sheet materials are available, ranging from transparent glass, to opaque metals and wood.

Furthermore, for the areas where struts are needed, wood, metal and acrylic profiles are abundant, and would be used based on the performative aspects of the specified area. Furthermore, extruded profiles could be readily customized in aluminium and other materials for the strut elements.

The advantage of this system is the ability to create a transition or gradient not only in the porosity, but also in the type of cell, by switching from plates to struts, the system changes from closes cells to open cells.

NON-STANDARDIZED ELEMENTS

ADDITIVE MANUFACTURING MOULD PRODUCTION CASTING

92

STANDARDIZED ELEMENTS

LASERCUTTING WATER-JET

MACHINING

LIQUID MATERIAL

SHEETMATERIAL

PROFILES

JOINTS

PLATES

STRUTS

3D PRINTED METAL CAST METAL

WOOD METAL GLASS

WOOD METAL ACRYLIC

FA B R I C AT I O N

PLATES AND STRUTS MODEL

VARIATION IN POROSITY AND CELL TYPE: CUSTOMIZED JOINTS, STANDARDIZED PLATES AND STRUTS

image references

Fig. 3.1 to 3.45 - Taken or Created by Cellular Complexity authors: Kais Al-Rawi, Julia Koerner or Marie Boltenstern.

Fig. 3.46

- http://2.bp.blogspot.com/-JIn1nVF-jmc/TjU v8PEqMUI/AAAAAAAAB4w/8wXdDjk0jUc/ s1600/19+Firmament+-+Antony+Gormley.JPG

94

FA B R I C AT I O N

FA B R I C AT I O N overview The variety of tested methods contributed towards an understanding of the fabrication of complex geometrical systems, revealing limitations and opportunities concerning materiality and possible scaling of the structure. The fabrication explorations on a model scale included techniques which could be eventually scaled up to an architectural scale.

Throughout the experiments it became clear that the sophistication of such a complex systems lies in the joint, if the structural efficiency of the packing structure is to remain. This encouraged the decision of developing a combination of customized joints with planar standardized plate and strut elements. Another reason for choosing a plates and struts system is that it allows for the required combination of open and closed cells, while allowing for porosity changes.

This chosen method allows for the integration of plates, including a variation of opaque and translucent plates, which means that the integration of glass plates could be possible within the architectural system. Further, the shape of the plates and struts can change gradually, so there can be a porosity gradient throughout the system. The available digital fabrication methods, including laser-cutting and water-jet cutting allow for precise cutting of plates in the desired degree of porosity.

The joints can be precisely produced in any desired geometry, thus combining complex angles, through the use of additive manufacturing for making the mould or for producing the joint itself with 3D printing.

A study of the number of repetitive joints would be required to determine the feasibility of printing in relation to casting. From an economical point of view, this means that 3D printing is more efficient for joints which occur in a small amount only and from a certain amount onwards, it is viable to produce a mould - but here again it has to be taken into consideration that a mould is only usable a limited number of times.

As a result, the decision is to further develop the system based on the truncated cube and octahedron geometry, with a combination of custom joints, and standard plates and struts. The potential of this geometry and its development architecturally and performatively is to be investigated.

CELLULAR COMPLEXITY

95

96

THE SYSTEM In the previous section, fabrication methods were investigated and evaluated. The results determined that a hybrid fabrication method is best suited for the architectural application of this system. Based on this fabrication method, there are certain limits implied on the system, this includes the planar property of standardized elements within the system. In terms of scale, the abundance of sheet material and profiles in various sizes facilitate the scaling of elements.

Therefrom this section investigates the computational development of this system on the digital platform, in order to define the parameters behind the geometry and the opportunities and limitations they imply. The system will be generated through an algorithm where we as designers have control of the various parameters affecting the porosity and scale of the system. Furthermore, the structural effects with these changing parameters are tested to investigate efficient structural strategies.

The computational application provides further potential in the application of geometry. Due to the surface-based algorithmic approach, the system can be tested on planar, single curved and double curved surfaces. The architectural potential of this approach is investigated through typologies, which are then tied back to the fabrication research in order to understand what effects will these morphological changes imply on fabrication.

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97

POROSITY GRADIENTS

Within the system, several possibilities of how to control the required porosity gradients were developed. One of the gradients is the material gradient which creates variation in the size of the opening and the strut thickness - it defines how much material is used in single cells. For the opening size, the cell is offset in its centre to a certain scale-number and then subtracted from the initial cell. A bigger opening means more porosity when keeping the other factors the same. When changing the strut thickness, material is added or subtracted on the outer parts of the cell; where the porosity can be reduced by increasing the strut thickness.

MATERIAL GRADIENT OPENING SIZE 0.0

0.5

1.0 1.0

The geometrical gradient deals with cell size, number of cells and the shape of the cell. Increasing the cell size and keeping the used material the same, means a higher degree of porosity for the single cell. Increasing the number of cells while keeping the overall volume of the structure the same means lower porosity.

Adding layers of cells has an effect on the porosity when the dimensional layering axis is not directly perpendicular to the orthogonal system. The shape and proportion of each cells can be changed, to address morphological or structural requirements which are concerned with directionality.

The surface-based programming of this method within the surface co-ordinates allows for the use of planar, single curved and also double curved surfaces. This allows for the production of double curved geometries in a global scale, which are fabricated through linear and planar elements.

All the developed tools for varying porosity can be used for smooth transitions throughout the system. This includes: changing cell size, number of layers, adding or reducing material, as well as changing the shape of the cell. What changes however is the structural performance of the cells when changing those factors. The ability of getting a very specific porosity through different parameters unviels a range of possibilities of how to deal with controversial requirements on structural, day lighting and visual needs without heavily compromising on the qualities of each. The cell is able to change its shape according to local requirements, such as programmatic needs and according to global requirements which is an adaptation the overall global form.

0.0

STRUT THICKNESS 0.0

1.0

0.0

The performative aspects including structure and day lighting require testing through analysis software workbenches. The results from these tests, and possible tests of site conditions will define the precise application of the system architecturally.

1.0

98

0.5

THE SYSTEM

GEOMETRICAL GRADIENT CELL SIZE

0.0

NUMBER OF CELLS

0.5

1.0

CELL SHAPE based on local requirement

1.0

2.0

CELL SHAPE based on global requirement

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POROSITY RANGE: CATALOGUE

The two main parameters that are affecting the porosity of the system in a planar application are the Strut Thickness and the Openings. The effect these two parameters create are catalogued below for single cells. For this purpose, the cells catalogued have a maximum porosity of about 50%. The cells within higher range porosity are left out. This is due to the nature of porous systems and their characteristic of having about 30% porosity or lower.

The ratio of solid to void is displayed at the four extremes presented, Thick and Closed, Thick and Open, Thin and Closed & Thin and Open. The porosity is also displayed at these four extremes within the catalogue, the porosity ranges from 48.44% to 99.73%, this means that only 51.56% and 0.27% material volume is used within the overall cell volume, respectively.

POROSITY RANGE SINGLE CELL 5 x 5m

0.5156 (48.44%)

0.0027 (99.73%)

0.1231 (87.69%)

STRUT THICKNESS

0.0123 (87.7%)

OPENINGS

100

THE SYSTEM

Similarly, the porosity is catalogued however in this case for an aggregation of 8 cells in two levels each containing two by two cells.

In this case the porosity and ratia are exactly the same as those of the single cell. This is due to fact that the cells in the aggregation are identical to those shown individually. Since porosity is a ratio, the ratio will remain the same because both parameters of volume will increase at the same rate.

However if the aggregation contains cells that are not arranged in a planar manner, or not space-packed, or contain certain elongation or deformation in any direction, the porosity will then become different.

POROSITY RANGE 8 CELLS 5 x 5m

0.5156 (48.44%)

0.0027 (99.73%)

0.1231 (87.69%)

STRUT THICKNESS

0.0123 (87.7%)

OPENINGS

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101

FINITE ELEMENT ANALYSIS

most efficient one as it has a high structural performance while keeping the used material to an efficient minimum. The stronger the cell has to be, the smaller the opening and the larger the strut thickness should be. Through the efficient arrangement of material in the closest-packing system, the material volume can be kept low, even in areas which require a high structural efficiency.

Finite Element Analysis software was used to examine the effect of changing the various gradients on the structural efficiency. In test 01, the effect of the geometrical gradient was tested by filling up a Volume with first one big cell and then eight smaller cells while keeping the material and overall volume the same. Through that, the size of the cell decreases and the number of layers increases.

As mentioned in earlier results within the Geometrical Development chapter, by increasing the number of cells and layers, and keeping the same material and overall volume, the structural performance can be increased - in this case the displacement can be reduced up to 50% and the mean stress up to 70%.

The test results serve as a basis on understanding the effect of parameters which becomes particularly useful when combining structural and visual requirements. Often, controversial properties such as high structural performance and high porosity have to be combined within the structure, therefore the balance of the various gradients have to be studied in detail in order to maintain the structural capabilities of the cell aggregations.

In the following test 02, the changes in the material gradient were analysed. Various combinations of different strut thicknesses and openings were tested in comparison. Economically speaking, the example which has a small strut thickness and a small opening is the

TEST 01 - GEOMETRICAL GRADIENT

DISPLACEMENT (Y)

Material Volume: 1.5m³ Dimension: 5 x 5 x 5 m

SINGLE CELL

biggest displacement: 0.07 mm

STRESS (MEAN)

biggest stress: 2.5 MPa average stress: 0.16 MPa

10 kN

5m 5m

8 CELLS biggest displacement: 0.03mm

10 kN

5m 5m

102

THE SYSTEM

biggest stress: 0.27MPa average stress: 0.045MPa

TEST 02 - MATERIAL GRADIENT

DISPLACEMENT (Y)

STRESS (MEAN)

LARGE OPENING - SMALL STRUT THICKNESS

biggest displacement: 0.001 mm

biggest stress: 0.02 MPa average stress: 0.005 MPa

LARGE OPENING - LARGE STRUT THICKNESS

biggest displacement: 0.0004 mm

biggest stress: 0.03 MPa average stress: 0.0004 MPa

SMALL OPENING - SMALL STRUT THICKNESS

biggest displacement: 0.0006 mm

biggest stress: 0.004 MPa average stress: 0.01 MPa

SMALL OPENING - LARGE STRUT THICKNESS

biggest displacement: 0.0002 mm

biggest stress: 0.02 MPa average stress: 0.002 MPa

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103

FINITE ELEMENT ANALYSIS SETUP

A structural analysis was carried out to test the effect of various gradients on cells in an aggregation. The test results provided a basic understanding of which gradient-aggregations are structurally efficient and used for certain requirements in the design process. Each case was tested in terms of displacement (x,y,z) and mean stress. For each example, 5 cells were stacked in an overall dimension of 1 x 1 x 5 meters and loaded with 10kN. The overall material volume was 0.6m² in every aggregation, this guaranteed that the test results were comparable. In each of the three tests, first an aggregation which included variation in the geometrical gradient - a change in cell size - was set out. In the next step, to each of these initial test aggregations, a material gradient was added - first a change in opening, then a change in strut thickness, again in both directions.

TEST 01 GEOMETRICAL GRADIENT

For tests which involve a geometrical gradient, the results displayed that arge cells on the bottom and small cells on the top (close to the load) have the most efficient aggregation. In this formation, the displacement could be reduced by 50% and the stress which was now almost even throughout the structure could be reduced by almost 70% compared to the example without any material gradient. This effectiveness could be increased by adding material gradients to the structure. The strongest aggregation is the one with a large strut thickness on the bottom, growing smaller to the top - in this aggregation, the stress is almost evenly distributed throughout the structure. When considering material efficiency in the evaluation, the aggregation which operates with opening gradient is the most effective one. In the following pages, the results will be discussed in more detail.

TEST 02 none

TEST 03 small - large

large - small

MATERIAL GRADIENT OPENING

small - large

large - small

small - large

large - small

small - large

large - small

MATERIAL GRADIENT STRUT THICKNESS

large - small

small - large

large - small

small - large

large - small

small - large

104

THE SYSTEM

POROSITY GRADIENT

FINITE ELEMENT ANALYSIS TEST 01

biggest displacement: 0.015 mm average displacement: 0.0008 mm

biggest stress: 0.05 MPa average stress: 0.06 MPa

biggest displacement: 0.008 mm average displacement: 0.006 mm

biggest stress: average stress:

In this first test, no geometrical gradient was applied, which means all aggregated cells are the same size. The results of this tests show, that adding material - no matter if through the openings gradient or the struts thickness gradient ,and if on bottom or top, the structural performance of the aggregation can be improved. The largest effect is achieved when adding more strut-thickness on the bottom rather than on the top.

0.02 MPa 0.12 MPa

GEOMETRICAL GRADIENT biggest displacement: 0.014 mm average displacement: 0.006 mm

biggest stress: 0.2 MPa average stress: 1.2 MPa

THICKNESS GRADIENT biggest displacement: 0.003 mm average displacement: 0.0001 mm

biggest stress: 0.01 MPa average stress: 0.003 MPa

biggest displacement: 0.003 mm average displacement: 0.002 mm

biggest stress: 0.07 MPa average stress: 0.005 MPa

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FINITE ELEMENT ANALYSIS TEST 02

POROSITY GRADIENT biggest displacement: 0.013 mm average displacement: 0.0008 mm

biggest stress: 0.06 MPa average stress: 0.02 MPa

biggest displacement: 0.009 mm average displacement: 0.006 mm

biggest stress: 0.1 MPa average stress: 0.02 MPa

In the second test, the gradient which involved large cells on the bottom and small cells on the top. As discussed earlier, this produced the most efficient arrangement of cells in terms of displacement and mean stress. What this test displayed is that the most effective arrangement was the one with a material gradient as in this example, which on the bottom has a large strut thickness to take all the loads and on the top has a small opening in order to resist the directly applied loads better.

GEOMETRICAL GRADIENT biggest displacement: 0.009 mm average displacement: 0.004 mm

biggest stress: 0.05 MPa average stress: 0.04 MPa

THICKNESS GRADIENT

106

biggest displacement: 0.07 mm average displacement: 0.0004mm

biggest stress: 0.04 MPa average stress: 0.0003 MPa

biggest displacement: 0.004 mm average displacement: 0.002 mm

biggest stress: 0.07 MPa average stress: 0.004 MPa

THE SYSTEM

POROSITY GRADIENT

FINITE ELEMENT ANALYSIS TEST 03

biggest displacement: 0.01 mm average displacement: 0.0007 mm

biggest stress: 0.07 MPa average stress: 0.006 MPa

biggest displacement: 0.012 mm average displacement: 0.008 mm

biggest stress: 0.09 MPa average stress: 0.004 MPa

In test 03, the geometrical gradient grows from small cells on the bottom to big cells on the top. This arrangement showed an improvement in comparison to test 01 which had no geometrical gradient at all and is comparable in effectiveness to the previous test. In this example, the biggest cell is on the top and therefore directly takes all the loads, the material-efficient aggregation which includes change of opening size was the most efficient one. In general it can be stated, that in reducing the opening size, a material efficient as well as structurally efficient aggregation can be formed.

GEOMETRICAL GRADIENT biggest displacement: 0.008 mm average displacement: 0.004 mm

biggest stress: average stress:

0.07 MPa 0.03 MPa

THICKNESS GRADIENT biggest displacement: 0.003 mm average displacement: 0.0002 mm

biggest displacement: 0.004 mm average displacement: 0.003 mm

CELLULAR COMPLEXITY

biggest stress: 0.04 MPa average stress: 0.01 MPa

biggest stress: 0.1 MPa average stress: 0.02 MPa

107

PARAMETRIC DESIGN TOOL

In a first typological study, the developed tools to create porosity gradients were tested on different examples of transitions from horizontal to vertical surfaces.

In the example of TYPE A, the surfaces are prepared from a regular, horizontal surface where no change in cell size and shape will take place to a transition surface in which the cells are shaped by the global form of the surface to the vertical surface, in which the cells are shaped by a local change in order to generate a differentiated wall.

Digitally, the developed system is applied on generated surfaces, which define the global shape of the design. Through manipulation of the iso-curves on the surfaces, the cell shape and size can be varied to the desired amount. The examples below, TYPE A, TYPE B and TYPE C show various preparations of surfaces in order to achieve different conditions, which will be presented in the next pages. While the size variation is controlled by the input surface, the material gradient is controlled through the algorithm.

In example TYPE B, the horizontal surface is shaped with the goal to create a gradually increasing opening for a possible open roof structure, the transition surface again will shape the cells and the vertical surface is regular and will have variation through changes in the material gradient.

In example TYPE C, the horizontal and the transition surface will have porosity differentiation through the material gradient, whereas the vertical surface’s cells will gradually change in size, controlled by the iso-curves of the surface.

The balance between the geometrical and material gradient, and number of cells layers would be driven by performance and fabrication cost within an actual design development phase. These typologies demonstrate the possibility of producing highly complex configurations and transitions which include double-curvature and twisting.

SURFACE AND ISO-CURVES

CELL GRID

TYPE A

TYPE A

TYPE B

TYPE B

TYPE C

TYPE C

108

THE SYSTEM

TYPOLOGY STUDY - TYPE A

TYPE A is a typology of a spatial conditions where a roof changes into a facade. The parameters for the roof are set to have closed cells in order to have a walkable surface. Throughout the middle transition surface the cellular system increases the porosity level to achieve an open cellular system for the facade. This typology displays the possibility of various gradients within one system. Further it shows gradients from regularity to irregularity within one system.

base surface and isocurves

base surface and isocurves

grid on surface POROSITY GRADIENT TRANSITION VERTICAL TO HORIZONTAL

grid on surface

POROSITY GRADIENT TRANSITION VERTICAL TO HORIZONTAL

GRADIENT IN CELL SIZE

GRADIENT IN OPENINGS

GRADIENT IN PLATE THICKNESS

SIDE VIEW

GRADIENT IN CELL SIZE

GRADIENT IN OPENINGS

GRADIENT IN PLATE THICKNESS

SIDE VIEW

TOP VIEW

TOP VIEW

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109

TYPOLOGY STUDY - TYPE B

In TYPE B the parameters for the roof are set to have open and large cells in order to have light transmitting ceiling. Throughout the middle transition surface the porosity level stays the same though the regularity of cell size is given. Throughout the third surface the cells get less porous do work as enclosed facade system. This typology displays gradients varying regularity to irregularity within one system as well cell size differentiation.

base surface and isocurves

base surface and isocurves

grid on surface POROSITY GRADIENT TRANSITION VERTICAL TO HORIZONTAL

grid on surface

POROSITY GRADIENT TRANSITION VERTICAL TO HORIZONTAL

GRADIENT IN OPENINGS

GRADIENT IN STRUT THICKNESS

GRADIENT IN STRUT THICKNESS

GRADIENT IN CELL SIZE

SIDE VIEW

GRADIENT IN CELL SIZE

SIDE VIEW

TOP VIEW

TOP VIEW

11 0

THE SYSTEM

GRADIENT IN OPENINGS

TYPOLOGY STUDY - TYPE C

In TYPE C the parameters for the roof are set to have regular and open cells in order to have a light transmitting roof structure. Throughout the middle transition surface the cellular system decreases the porosity level to achieve enclosed cellular system for the facade. What is displayed in this typology is a thickness change in struts and that an enclosed cellular facade system can be achieved either this way or by altering the value of inside boolean geometry - which is the opening size.

base surface and isocurves

base surface and isocurves

grid on surface POROSITY GRADIENT TRANSITION VERTICAL TO HORIZONTAL

grid on surface

POROSITY GRADIENT TRANSITION VERTICAL TO HORIZONTAL

GRADIENT IN PLATE THICKNESS

GRADIENT IN OPENINGS

GRADIENT IN STRUT THICKNESS

SIDE VIEW

GRADIENT IN PLATE THICKNESS

GRADIENT IN OPENINGS

GRADIENT IN STRUT THICKNESS

SIDE VIEW

TOP VIEW

TOP VIEW

CELLULAR COMPLEXITY

111

3D PRINTED STUDY MODEL OF TYPOLOGY - TYPE A

ROOF PATCH

11 2

TRANSITION PATCH

THE SYSTEM

FACADE PATCH

CELLULAR COMPLEXITY

11 3

JOINTS FABRICATION EFFICIENCY

The typologies generated earlier were analysed for the viability in terms of the relation of additive manufactured joints to cast joints. Five patches from the typologies, with varying geometrical and material gradients were compared. The physical possibility and economic feasibility of fabrication was taken into account and lead to an understanding of the amount of additive manufactured joints, moulds and cast joints.

size followed the material thickness while in the second patch the joint size did not follow the material thickness. This resulted in a reduction of additive manufactured joints followed by a reduction in moulds, while the number of cast joints per mould increased. Dependant on the manufacturing method, the mould the feasibility and number of cast joints from one mould would affect the decision of chosing one method over the other.

The first two patches contained a material gradient only. The difference in joint size adaptability was compared. In both examples the strut thickness increases throughout the system. In the first patch the joint

PATCH 1

PATCH 2

MATERIAL CHANGE IN STRUT THICKNESS

MATERIAL CHANGE IN STRUT THICKNESS

JOINT SIZE FOLLOWS MATERIAL THICKNESS

JOINT SIZE DOES NOT FOLLOW MATERIAL THICKNESS

72 9 9 15 135 144

11 4

CELLS 3D PRINTED JOINTS MOULDS JOINTS PER MOULD CAST JOINTS JOINTS IN TOTAL

72 1 1 143 143 144

THE SYSTEM

CELLS 3D PRINTED JOINT MOULD JOINTS PER MOULD CAST JOINTS JOINTS IN TOTAL

The third and the fourth patches contained both a material and a geometrical gradient. The difference between a regular and an irregular system is compared. The cell size change allowed the system to include variation. The number of additive manufactured joints for the moulds to cast joints has increased in comparison to the second patch.

In these examples the joint size did not follow material thickness, thus the change in number was not taken into account within this examples.

This comparison investigated the constraints of physical possibility and feasibility of irregularity throughout the system.

The main difference in the patches compared is the opportunity that joints would be additively manufactured for the fabrication of moulds as well as for joint variation in the system, by means of incorporating a parametric change to produce each joint slightly different from the other.

PATCH 3

PATCH 4

GEOMETRY CHANGE IN CELL SIZE

GEOMETRY CHANGE IN CELL SIZE

JOINT SIZE DOES NOT FOLLOW MATERIAL THICKNESS

JOINT SIZE DOES NOT FOLLOW MATERIAL THICKNESS

72 24 24 3 / 15 84 144

CELLS 3D PRINTED JOINTS MOULDS JOINTS PER MOULD CAST JOINTS JOINTS IN TOTAL

96 17 17 7 / 36 163 180

CELLULAR COMPLEXITY

CELLS 3D PRINTED JOINTS MOULDS JOINTS PER MOULD CAST JOINTS JOINTS IN TOTAL

11 5

JOINTS FABRICATION EFFICIENCY

This patch was analysed as a transition patch between a horizontal and a vertical surface. Because of the radical change within the geometry almost every single joint was categorised as an additive manufactured joint. This sets a discussion for the feasibility of such a radical change in geometry within the system in relation to the physical possibility of fabrication. The typology revealed that the system can achieve curvature and has no geometric constraints or physical constraints, however the feasibility of fabricating the system in such geometry would be questionable.

PATCH 5 MATERIAL CHANGE IN STRUT THICKNESS JOINT SIZE FOLLOWS MATERIAL THICKNESS

72 108 2 14 28 136

11 6

CELLS 3D PRINTED JOINTS MOULDS JOINTS PER MOULD CAST JOINTS JOINTS IN TOTAL

THE SYSTEM

OVERVIEW OF JOINT VARIATION

In terms of varying the joint size with material thickness, it is more efficient to maintain the joint size the same and develop it to a high level of detail, reducing complexity. Furthermore, the spatial effect of the joint would be unified and adaptable within spaces, where no substantially larger joints appear within a space.

The evaluation of this analyses reveals that in order to receive comparable results the number of cells need to be the same. This includes that the number of layers and rows in all patches can change as long as the number of cells stays the same. Those patches are made of three vertical and three horizontal layers and nine rows of cells. In this case this was the minimum amount of cells required to achieve an acceptable gradient.

Once the variation in geometry requires symmetry, one additional row of cells needs to be added such as in a patch four. The required symmetry results of a gradient variation which is mirrored. This has of course an effect on the final numbers of joints.

EVALUATION TABLE

PATCHES PATCH 1

PATCH 2

PATCH 3

PATCH 4

PATCH 5

STRUT THICKNESS

CHANGE

CHANGE

CHANGE

CHANGE

CHANGE

GEOMETRY

NO VARIATION

NO VARIATION

VARIATION

VARIATION

VARIATION

JOINT SIZE

FOLLOWS STRUT THICKNESS

DOES NOT FOLLOW STRUT THICKNESS

DOES NOT FOLLOW STRUT THICKNESS

DOES NOT FOLLOW STRUT THICKNESS

DOES NOT FOLLOW STRUT THICKNESS

SPECIFICS

AMOUNT CELLS

72

72

72

95

72

3D PRINTED JOINTS

9

1

24

17

108

MOULDS

9

1

24

17

2

JOINTS PER MOULD

15

143

3 / 15

7 / 36

14

CAST JOINTS

135

143

84

163

28

JOINTS IN TOTAL

144

144

144

180

136

CELLULAR COMPLEXITY

11 7

11 8

THE SYSTEM

THE SYSTEM overview Throughout the progression of the system development phase, the opportunities and limits of the digital design tools were explored and tested on specific examples. The ability to vary porosity became tied to a number of controlled parameters within the algorithm. This allow for a wide range of variations and combinations of how to meet potential performative aspects within the system and its architectural application. We further developed an understanding of a material gradient and a geometrical gradient.

In the realm of a material gradient the challenge becomes, how to combine the various gradients and the question comes up of where to use which tool in which intensity and what is the best way of how to generate a certain desired porosity in the most efficient way. The main ambition when actually applying the generated system and porosity levels is to always maintain a controlled and smooth porosity gradient in all directions. The parameters affecting structure have already been defined through a number of Finite Element Analysis tests.

The feasability and fabrication of these typologies was revisited. The fabrication method developed earlier allows for various ways of how to realize the generated typologies. The customized joints can either follow the strut thickness in size or stay the same size. Based on the frequency they occur throughout the structure. Certain cases require identical joints everywhere, others require several joints which are repeated, and finally cases that require customized joints at each node.

Therefore, it is important to consider the amount of joints, and the production limit of moulds, where an opportunity is already given to create variation.

This sets an initial limitation to the development of geometrical gradients and the amount they recur at.

These defining parameters of the system, their opportunities and constraints have set a foundation for the systems development, the next phase will examine its application at an architecture scale.

Within the geometrical gradient, the algorithmic approach allowed for the application of the system on complex surfaces. This was further tested through a range of typologies which include architectural transitions. These complex transitions were analysed geometrically and performatively.

CELLULAR COMPLEXITY

11 9

120

ARCHITECTURAL A P P L I C AT I O N Throughout the previous section, the system was investigated in further detail and the defining parameters for its application were established. This section will examine the application of the system at an architectural scale.

For the architectural application, we became particularly interested in the tower typology and the diverse programmatic uses involved in this type. The current state-of-the-art architecture in tower design creates limited variation within towers to address architectural and programmatic conditions. A case study is investigated for this purpose, and its relation to our system.

The case study leads us to selecting a site and range of programs to commence the application process.

Throughout our research we investigated architectural competitions and selected the suckerPUNCH international competition which involves the design of a convention, hotel and casino in Hudson Yards, New York.

The application of the system at this scale provided us with case study on how the system operates at a large scale and the opportunities and limitations which become apparent.

CELLULAR COMPLEXITY

121

TYPOLOGICAL CASE STUDY THE SHARD, LONDON RENZO PIANO BUILDING WORKSHOP

Throughout the dissertation, several typologies were considered for the architectural application of the system, of most interest was the tower typology. The large-scale of this typology and the lack of architectural systems which are able to address variation at this scale encouraged us to consider it for the dissertation.

The system would be able to address diverse programmatic changes, which would require continuous changes within the facade and the structural system. Throughout our system, they would be closely integrated.

Our choice of The Shard as a case study is due to its distinct urban condition which combines numerous programmatic functions in a high density node. As part of our research, we intend to examine the variation in the architecture of The Shard in terms of its facade and overall structure and how they vary with the urban and programmatic conditions. The levels below and at ground combine multiple transportation nodes. The tower itself includes offices at the lower levels, a hotel and restaurants at mid levels, residences and an observatory at the upper levels of the tower.

DISTINCT URBAN / ARCHITECTURAL CONDITION Mixed-Use Tower:

STRUCTURE INVESTIGATE VARIATION IN

- OFFICES - HOTEL - RESIDENCES

Public Transportation

FACADE

- BUS STATION - RAILWAY STATION - UNDERGROUND: - NORTHERN LINE - JUBILEE LINE

residences

underground and railway station

hotel

mixed use tower

offices bus station

offices

offices

railway station

underground northern line

122

A R C H I T E C T U R A L A P P L I C AT I O N

bus station

underground jubilee line

THE STRUCTURE

The structure of skyscrapers typically depends on two main loads: -Dead and Live Loads: These are the loads from the structure of the building and its furnishings and occupants, the direction of this load is the gravities direction, they increase at lower floors of the building.

-Lateral Loads: These are loads due to environmental elements such as wind. The direction of these loads is perpendicular to gravity and increases at the higher floors of the building.

OBSERVATORY LEVELS 68-72

The design of The Shard demonstrates a degree of variation that responds to the structural loads outlined. In terms of Dead and Live Loads, the core area of the structure decreases as the structure becomes higher and reaches its peak, with changing intervals as programs change. Although cores are typically used to resist lateral loads, the decrease in core size does optimize the structure for both efficiency in material and space. As for lateral loads, the tapered design of the building reacts to the lateral loads. The smaller the floor plate of the building, the less lateral wind loads it needs to resist.

Conventional Typical Plan Tower

CORE AREA

5.2%

DECREASE IN DEAD AND LIVE LOADS WITHIN THE STRUCTURE LESS STRUCTURE IS REQUIRED AT THE TOP

RESIDENCES LEVELS 53-65

CORE AREA

29.5%

INCREASE IN LATERAL WIND LOADS SMALLER FLOOR PLATE PROVIDES MORE STABLE STRUCTURE

HOTEL

LEVELS 34-52

ELEVATION

SHEAR

MOMENT

DEFLECTION

MOMENT

DEFLECTION

(ESTIMATED FROM REFERENCE 1)

CORE AREA

53.9%

Tapered Plan Tower eg. The Shard

OFFICES LEVELS 2-28

CORE AREA

100%

RESTAURANTS LEVELS 31-33

ELEVATION

SHEAR

(ESTIMATED FROM REFERENCE 1)

CELLULAR COMPLEXITY

123

THE FACADE

The design of the building consists of eight shards of glass leaning towards each other. The entire facade is a ventilated double skin facade. The system is consistent throughout the structure and does not vary between the different programmatic and urban conditions. The two skins with a cavity in between provide enhanced thermal performance, and contain a shading element in the cavity to reduce heat gain from sunlight. The ventilation aspect of the facade was designed to operate at several levels. First, ventilation within the same floor for cooling during summer, where cold air enters from the outside to the cavity, into the spaces at low points. Warm air escape at high points of the space through stack effect to higher points in the cavity, further to the outside.

The second performative ventilation level is to have openings closed between the cavity and exterior. During winter, excess heat from office spaces can rise through the stack effect within the cavity towards the residential and hotel floors where it is needed. If excess heat exists within all floors, heat will rise towards the top of the building and exit the cavity. These ventilation strategies were part of the original design scheme, however during construction the facade was changed to become a non ventilated double skin facade.

ORIGINAL SCHEME: Ventilation within same floor

RESIDENCES Fig. 5.2 Cross-Ventilation within the same floor or space: - Cold air into building through cross ventilation t hrough l ow openings i n the facade at each floor.

HOTEL

- Warm air out of the building through stack e ffect and h igher openings i n the facade at each floor.

Ventilation through building

OFFICES

Fig. 5.1 Fig. 5.3 Double Skin Facade Section with R oller Blinds

Excess Heat form Office floors: - Through stack effect rises to Hotel and Residential floors where heat is needed.

- Rise of heat from all floors towards the top of the tower.

124

A R C H I T E C T U R A L A P P L I C AT I O N

CASE STUDY SYNTHESIS

The Shard presents an urban condition that integrates multiple distinct programmatic functions. The variation in structure attempts to achieve an efficient structure through a continuously decreasing floor plate towards higher floors, and decreasing core size with programmatic changes. The facade and ventilation systems are consistent throughout the structure with no variation; however attempts to address different programs ventilation in one system by stack effect. The various elements within the design are treated as separated performative elements and layers and not part of an integrated system that is inherent to the design.

URBAN / ARCHITECTURAL CONDITION MIXED-USE TOWER:

In terms of application within the context of the dissertation, the structural analysis suggest the use of more porous cells at the higher parts of the building. This is due to their material efficiency and lower structural needs, in addition the porosity allows wind to pass through where lateral loads are high. Furthermore, the use of low porosity cells at lower parts of the building where higher structural capacities are needed and lower wind loads are present. In general, the Shard does contain variation however does not attempt to create variation with specific programs and orientations.

VARIATION ACROSS BUILDING

RESPONDING TO CONDITION

CORE STRUCTURE

DECREASE IN DEAD AND LIVE LOADS AT HIGHER FLOORS

APPLICATION IN CELLULAR CONTEXT

STRUCTURE

- OFFICES - HOTEL - RESIDENCES

LEVEL 68-72

5% AREA

30% AREA

LOW POROSITY CELLS NEAR BASE OF BUILDING

LEVEL 34-52

54% AREA

- BUS STATION - RAILWAY STATION - UNDERGROUND:

LEVEL 2-33

higher structural capacity cells at lower parts of the building

100% AREA

- NORTHERN LINE - JUBILEE LINE

FLOOR PLATES LEVEL 2: 100% AREA LEVEL 40: ~50% AREA LEVEL 72: ~11% AREA

HIGH POROSITY CELLS AT HIGHER FLOORS

allow wind to pass through and not apply lateral forces onto the building

LEVEL 53-67

TRANSPORTATION:

USE OF:

DECREASE IN WIND LATERAL LOADS WITH SMALLER FLOOR-PLATES

DOUBLE SKIN FACADE NON-CHANGING THROUGHOUT BUILDING

FACADE/ VENTILATION

-STACK EFFECT for excess heat

features throughout:

-SOLAR GAIN

-openings to exterior at each level in both low and high points

-VENTILATION

-opening at the top of building at facade cavity

-NATURAL DAY LIGHTING

-roller blinds in facade cavity

CELLULAR COMPLEXITY

STACK EFFECT: CONTINUOUS VERTICAL VOIDS IN STRUCTURE

transfer excess heat between programmes

VOIDS BETWEEN CAVITY AND INSIDE AND OUTSIDE

transfer heat outside of the building cross ventilation

125

ARCHITECTURAL APPLICATION

Subsequent to our research into the tower typology, which investigated the case study of an existing tower in London, we investigated possible opportunities for application. We selected to define our application through an architectural ideas competition, this would define a site and SUCKERPUNCH COMPETITION / www.suckerpunchdaily.com rangeYork of programmatic uses for ourCenter system.

New City Casino/Convention

This would provide us with a case study for application and allow us to develop the project further based on our findings. The competition brief and requirements are shown below and on the page to the left, including jury members.

The interest in the tower typology lead us to the context of Manhattan in New York, the suckerPUNCH competition Recently, Newwhere York’s we statefound government has been trying architectural to legalize non-Indian casinos throughout the state.

Current are asking for the of sevenManhattan.

“Vegas”-sized for a casino, hotel andproposals convention centre in construction Hudson Yards, casinos throughout New York. Although lawmakers have pushed to keep the casinos out of This competition was well suited to our system due to its involvement in New York City, this ideas competition aims to investigate what a casino would do to New York a large urban site, the City requirements a diverse range of programs.

City and, likewise, what and New York would do to a of casino.

The New York casinos are being pitched by their supporters as “regional tools. Although is arguably in Furthermore, the time line ofrevitalization” the competition was Manhattan well suited to our no need of revitalization, it does have one clear zone that could use rethinking—Hudson Yards dissertation, where the submission of our entry would be more than a and the area around its neighbouring convention centre. The existing Jacob Javits Centre month an prior to the completion of by the dissertation. remains isolated structure surrounded a no-man’s-land of parking and train tracks. Cut off from restaurants, hotels, and entertainment, it is hardly an inviting location for a large convention, nor does it allow for or engender connection to the city at-large. You might as well have your convention in Secaucus. There is talk of relocating the Centre to Queens, to be sited next to the recently opened “racino” at Aqueduct Racetrack—a major financial success thus far, and example of the excitement people in the five boroughs have for gambling. The proposed convention centre would be the largest in the United States. This competition asks entrants to leave the convention centre at its current location on Manhattan’s West Side, but replace it and add a hotel and casino to the complex.

Entrants are asked to rethink this zone so as to create a dynamic destination in the city for tourists, residents, and convention-goers alike. At the same time, the complex should become a draw for non convention-goers.

COMPETITION BRIEF BY SUCKERPUNCH:

COMPETITION OUTLINES:

Recently, New York’s state government has been trying to legalize nonIndian casinos throughout the state. Current proposals are asking for

This is an open, international ideas competition hosted by suckerPUNCH to generate the construction of seven “Vegas”-sized casinos throughout New York. progressive contemporary designs.

There are no plans for the Casino/Convention Center to be built at this time. The sitehave is not owned by or withcasinos suckerPUNCH. Although lawmakers pushed toaffiliated keep the out of New York

City, this ideas competition aims to investigate what a casino would do to New York City and, likewise, what New York City would do to a casino. The New York casinos are being pitched by their supporters ///jury/AWARDS as “regional revitalization” tools. Although Manhattan is arguably in no need revitalization, kutan AYATAof (YOUNG & AYATA) it does have one clear zone that could use rethinking—Hudson Yards and the area around its neighbouring ezio BLASETTI (Ahylo Studio) david ERDMANcentre. (davidclovers) convention The existing Jacob Javits Centre remains an isolated marc FORNES (THEVERYMANY) structure surrounded by a no-man’s-land of parking and train tracks. ferda KOLATAN (su11 Architecture & Design) craig SCOTT (IwamotoScott Architecture) marcelo Cut offSPINA from(P-A-T-T-E-R-N-S) restaurants, hotels, and entertainment, it is hardly an mike SZIVOS (SOFTlab) inviting location for a large convention, nor does it allow for or engender abigail COOVER (hume coover studio, suckerPUNCH) connection to thecoover city at-large.

You might as well have your convention nathan HUME (hume studio, suckerPUNCH)

in Secaucus. There is talk of relocating the Centre to Queens, to be

$2500 prizestowillthe be awarded andopened the winning designs will be published on suckerPUNCH. sited innext recently “racino” at Aqueduct Racetrack—a

If a Vegas-style themed casino clearly wouldn’t work in New York City, then what would bring New Yorkers out to gamble? Is it a family focused zone for tourists or an adults-only retreat?

The proposed building should incorporate state-of-the-art facilities for both modern gambling and high- tech conventions. The convention centre should be unique while remaining flexible, and the casino should shake off both cheesy Vegas aesthetics and the dry desperation of Atlantic City to strive for something architecturally rich and complex—while simultaneously entertaining. The complex should also find a way to reconnect to Manhattan’s nearby entertainment districts. Madison Square Garden, Times Square, and the High Line seem cut off, despite their proximity. This complex should aim to recharge its surroundings in the same way the High Line did the Meatpacking District, bringing in pedestrians and cleaning up the area. On the western, waters edge of Manhattan, the site also includes a large pier that can be used for a portion of the program or turned into outdoor parks and recreation areas. The site includes the land the current convention centre lies on, the space over the West Side Yard train yard, and the aforementioned waterfront pier. The West Side Yard was designed to accommodate an overbuild in its air rights, and space was left between the tracks for columns to support a platform above the tracks. The history of proposals for the very same site includes the ongoing Hudson Yards Redevelopment and the IFCCA “Competition for Manhattan’s West Side.” (COMPETITION BRIEF BY SUCKERPUNCH)

CELLULAR COMPLEXITY ENTRY WAS AWARDED SECOND PLACE

entertaining. The complex should also find a way to reconnect to Manhattan’s nearby entertainment districts. Madison Square Garden, Times Square, and the High Line seem cut off, despite their proximity.

This complex should aim to recharge its surroundings in the same way the High Line did the Meatpacking District, bringing in pedestrians and cleaning up the area. On the western, waters edge of Manhattan, the site also includes a large pier that can be used for a portion of the program or turned into outdoor parks and recreation areas.

The site includes the land the current convention centre lies on, the space over the West Side Yard train yard, and the aforementioned waterfront pier. The West Side Yard was designed to accommodate an overbuild in its air rights, and space was left between the tracks for columns to support a platform above the tracks. The history of proposals for the very same site includes the ongoing Hudson Yards Redevelopment and the IFCCA “Competition for Manhattan’s West Side.”

major financial success thus far, and example of the excitement people in the five boroughs have for gambling. The proposed convention centre would be the largest in the United States. This competition ///entryREQUIREMENTS asks entrants to leave the convention centre at its current location on Manhattan’s West Side, but replace it required and add a hotel andtwo casino to This is an open ideas competition. entrants will be to digitally submit [2] boards at 18”complex. high x 24”wide and 150dpi in tiff format with the provided 5 digit code in a 1”x1” square the

This is an open, international ideas competition hosted by suckerPUNCH to generate progressive contemporary designs. There are no plans for the Casino/Convention Center to be built at this time. The site is not owned by or affiliated with suckerPUNCH.

Entrants are asked to rethink this zone so as to create a dynamic PLANS all necessary site floor plans to describe the residents, project including at minimum a ground level destination inand the city for tourists, and convention-goers plan describing the form, integration of program, and relationship to the site alike.

At the same time, the complex should become a draw for non *scale is at the discretion of the entrant convention-goers.

SECTIONS one [1] north/south section one [1] east/west section If a Vegas-style themed casino clearly wouldn’t work in New York City, *scale is at the discretion of the entrant then what would bring New Yorkers out to gamble? Is it a family focused RENDERINGS one [1] aerial view zone for tourists or an adults-only retreat? The proposed building one [1] street level view state-of-the-art facilities for both modern gambling should incorporate one [1] interior view and rendering high- tech The and convention centre should be unique *one bestconventions. describing the formal atmospheric intent of the project must be while remaining and150dpi the casino should shake offbeboth cheesy rendered at 10” high xflexible, 13” wide and in tiff format.

This image is to included on the boards one of the above Vegasasaesthetics andviews. the dry desperation of Atlantic City to strive for

THE JURY

in the lower right hand corner of each board. Image requirements are as follows:

something architecturally rich and complex—while simultaneously

///competitionSCHEDULE 126 27 April 2012 competition launch 11 June 2012 deadline for questions

kutan AYATA (YOUNG & AYATA) ezio BLASETTI (Ahylo Studio) david ERDMAN (davidclovers) marc FORNES (THEVERYMANY) ferda KOLATAN (su11 Architecture & Design) craig SCOTT (IwamotoScott Architecture) marcelo SPINA (P-A-T-T-E-R-N-S) mike SZIVOS (SOFTlab) abigail COOVER (hume coover studio, suckerPUNCH) nathan HUME (hume coover studio, suckerPUNCH)

A R C H I T E C T U R A L A P P L I C AT I O N

thus far, and example of the excitement people in the five boroughs have for gambling. The and the area around its neighbouring convention centre. The existing Jacob Javits Centre proposed centre be the largest in the United This competition asks Recently,anconvention New York’s state would government has been trying toofStates. legalize non-Indian casinos remains isolated structure surrounded by a no-man’s-land parking and train tracks.

Cut entrants to the leave the Current convention centre are at its current location on Manhattan’s West Side, but throughout state. asking construction of seven “Vegas”-sized off from restaurants, hotels, proposals and entertainment, itfor isthe hardly an inviting location for a large replace it and add a hotel and casino to the complex. casinos throughout York. lawmakers havetopushed keep the out of convention, nor doesNew it allow forAlthough or engender connection the city to at-large.

Youcasinos might as well Entrants are asked to rethink this zone soto as to create awhat dynamic destination intothe cityYork for New York this ideas aims casino would New have yourCity, convention in competition Secaucus. There is investigate talk of relocatinga the Centre to do Queens, to be tourists, residents, what and convention-goers alike. same time, should become City and, York “racino” City would doAttothe a casino.

The the Newcomplex York casinos being sited nextlikewise, to the recentlyNew opened at Aqueduct Racetrack—a major financialare success a draw for non convention-goers. pitched their supporters asexcitement “regional revitalization” is arguably in thus far,by and example of the people in thetools. five Although boroughsManhattan have for gambling.

The ///entryREQUIREMENTS no need ofconvention revitalization, it does have zone thatUnited could use rethinking—Hudson proposed centre would beone theclear largest in the States.

This competitionYards asks and the area around its neighbouring centre.

Theonexisting JacobWest Javits Centre entrants to leave the convention centreconvention at its current location Manhattan’s Side, but remains isolated surrounded by a no-man’s-land of parking tracks.toCut replace itan and add a structure hotel andopen casino to the complex.

This is an ideas competition. entrants willand be train required digitally off from restaurants, entertainment, it is hardly an inviting location large Entrants are asked tohotels, rethink thisboards zone soatas18” to create dynamic destination ininfor the for with submit two and [2] high xa24”wide and 150dpi tiffacity format convention, nor does it convention-goers allow for or engender connection to the city at-large.

You mightbecome as well tourists, residents, and alike.

At the same time, the complex should the provided 5 digit code in a 1”x1” square in the lower right hand corner have convention in Secaucus. There is talk of relocating the Centre to Queens, to be a drawyour for non convention-goers. of each board.

Image requirements are as follows: sited next to the recently opened “racino” at Aqueduct Racetrack—a major financial success thus far, and example of the excitement people in the five boroughs have for gambling. The proposed convention centre would be the largest in the United States. This competition asks PLANS entrants to leaveall thenecessary convention centre at its floor currentplans location Manhattan’s Side, including but site and toondescribe theWest project replace it and add a hotel and casino to the complex. at minimum a ground level plan describing the form, integration of Entrants are asked to rethink this zone so as to create a dynamic destination in the city for COMPETITION OUTLINES: program, and relationship tothe thesame site time, the complex should become tourists, residents, and convention-goers alike. At *scale is at the discretion of the entrant a draw for non convention-goers.

SECTIONS This is an open, international ideas competition hosted by suckerPUNCH to generate progressive contemporary designs. There are no plans for the Casino/Convention Center to one [1] north/south section be built at this time. is not owned by or affiliated with suckerPUNCH. oneThe [1]site east/west section

train yard, and the aforementioned waterfront pier. The West Side Yard was designed to entertainment districts. Madison Square Garden, Times Square, and the High Line seem cut accommodate an overbuild in itsclearly air rights, and space in was leftYork between the for columns If adespite Vegas-style casino wouldn’t New thentracks what in would bring off, their themed proximity.

This complex should work aim to recharge itsCity, surroundings the same to support a platform above the Thefocused history of proposals for the same site includes New Yorkers todid gamble?

Is tracks. it a family zone for or very anand adults-only way the High out Line the Meatpacking District, bringing in tourists pedestrians cleaningretreat? up the the ongoing Hudson Yards Redevelopment and the IFCCA “Competition for Manhattan’s West The proposed building waters should edge incorporate state-of-the-art for both modern area.

On the western, of Manhattan, the site facilities also includes a large piergambling that can Side.”

(COMPETITION BRIEF BY SUCKERPUNCH) andused hightech conventions. convention centre beparks unique while remaining flexible, be for a portion of the The program or turned intoshould outdoor and recreation areas.

The and the casino offconvention both cheesy Vegas andover the the dry West desperation of site includes theshould land theshake current centre liesaesthetics on, the space Side Yard Atlantic Cityand to strive for something architecturally complex—while simultaneously train yard, the aforementioned waterfront pier.rich Theand West Side Yard was designed to entertaining. complex inshould also find way was to reconnect tothe Manhattan’s nearby accommodateThe an overbuild its air rights, and a space left between tracks for columns entertainment districts.

Madison Square Garden, Square, Line cut to support a platform above the tracks.

The historyTimes of proposals forand the the veryHigh same siteseem includes off, despite their proximity.

This complex should aimIFCCA to recharge its surroundings in the same the ongoing Hudson Yards Redevelopment and the “Competition for Manhattan’s West way High Line did the Meatpacking District, bringing in pedestrians and cleaning up the Side.”the (COMPETITION BRIEF

BY SUCKERPUNCH) area. On the western, waters edge of Manhattan, the site also includes a large pier that can be used for a portion of the program or turned into outdoor parks and recreation areas. The site includes the land the current convention centre lies on, the space over the West Side Yard train yard, and the aforementioned waterfront pier. The West Side Yard was designed to accommodate an overbuild in its air rights, and space was left between the tracks for columns to support a platform above the tracks. The history of proposals for the very same site includes the ongoing Hudson Yards Redevelopment and the IFCCA “Competition for Manhattan’s West Side.” (COMPETITION BRIEF BY SUCKERPUNCH)

COMPETITION OUTLINES: *scale is at the discretion of the entrant

RENDERINGS one [1] aerial view

This is an open, international ideas competition hosted by suckerPUNCH to generate ///jury/AWARDS one [1] street level view progressive contemporary designs. There are no plans for the Casino/Convention Center to oneThe [1]site interior be built at this time. is notview owned by or affiliated with suckerPUNCH. kutan AYATA (YOUNG & AYATA) best describing the formal and atmospheric intent of the *one rendering ezio BLASETTI (Ahylo Studio) project must be rendered at 10” high x 13” wide and 150dpi in tiff format. david ERDMAN OUTLINES: (davidclovers) COMPETITION This image is to be included on the boards as one of the above views. marc FORNES (THEVERYMANY) ferda KOLATAN (su11 Architecture & Design) ///jury/AWARDS craig SCOTT (IwamotoScott Architecture) This is an open, international ideas competition hosted by suckerPUNCH to generate marcelo SPINA (P-A-T-T-E-R-N-S) ///competitionSCHEDULE progressive designs. There are no plans for the Casino/Convention Center to kutan AYATAcontemporary (YOUNG & AYATA) mike SZIVOS be at this (SOFTlab) time.

TheStudio) site is not owned by or affiliated with suckerPUNCH. eziobuilt BLASETTI (Ahylo abigail COOVER (hume coover studio, suckerPUNCH) david ERDMAN 27 (davidclovers) April 2012 competition launch nathan HUME (hume coover studio, suckerPUNCH) marc FORNES (THEVERYMANY) 11 June 2012 deadline for questions ferda KOLATAN (su11 Architecture & Design) 18 be June 2012and answers to questions postedonon suckerPUNCH $2500 in prizes will awarded the winning designs willwill be be published suckerPUNCH. craig SCOTT (IwamotoScott Architecture) 25 June 2012 early registration deadline ///jury/AWARDS marcelo SPINA (P-A-T-T-E-R-N-S) 13 August 2012 project submission deadline mike SZIVOS (SOFTlab) kutan (YOUNG & coover AYATA)studio, abigailAYATA COOVER suckerPUNCH) 3(hume September 2012 winners will be posted on suckerPUNCH ezio BLASETTI (Ahylocoover Studio)studio, suckerPUNCH) nathan HUME (hume ///entryREQUIREMENTS david ERDMAN (davidclovers) ///awards marc $2500FORNES in prizes (THEVERYMANY) will be awarded and the winning designs will be published on suckerPUNCH. This an open ideas will be required to digitally submit two [2] boards ferdaisKOLATAN (su11 competition.

Architecture entrants & Design) at 18”SCOTT high x 24”wide andin 150dpi in tiffwill format the provided digit code in a 1”x1” square $2500 prizes bewith awarded and5 the winning designs will be craig (IwamotoScott Architecture) in the lower right(P-A-T-T-E-R-N-S) hand corner of each board. Image requirements are as follows: marcelo SPINA published on suckerPUNCH. mike SZIVOS (SOFTlab) PLANS abigail COOVER (hume coover studio, suckerPUNCH) ///entryREQUIREMENTS all necessary and coover floor plans to describe the project including at minimum a ground level ///program nathan HUMEsite (hume studio, suckerPUNCH) plan describing the form, integration of program, and relationship to the site This is an open ideas competition. entrants will be required to digitally submit two [2] boards *scale is the discretion of the entrant $2500 in at prizes will beand awarded and theformat winning designs will be 5published at 18” high x 24”wide 150dpi in tiff with the provided digit codeon insuckerPUNCH. a 1”x1” square Exhibition / Convention Space SECTIONS in the lower right 2,000,000 hand corner square of each board. feet Image requirements are as follows: one [1] north/south section one [1] east/west section PLANS MeetingofRoom Square Footage *scale is at the discretion the entrant all necessary site and floor plans to describe the project including at minimum a ground level 200,000 square feet / 50 rooms RENDERINGS ///entryREQUIREMENTS plan describing the form, integration of program, and relationship to the site one [1] aerial view *scale is at the discretion of the entrant one street level view Ballroom This [1] is an open ideas competition. entrants will be required to digitally submit two [2] boards SECTIONS one [1]high interior view 30,000 squareinfeet at 18” x 24”wide and 150dpi tiff format with the provided 5 digit code in a 1”x1” square one [1] north/south section *one rendering describing the formal atmospheric intent project must be in the[1] lower rightbest hand corner of each board. and Image requirements are of as the follows: one east/west section rendered at 10” high x 13” wide and 150dpi in tiff format. This image is to be included on the *scale is at the discretion Hotel of the entrant boards as one of the above views.

PLANS RENDERINGS 4000 suites all site and floor plans to describe the project including at minimum a ground level onenecessary [1] aerial view plan describing the view form, integration of program, and relationship to the site one [1] street level Theater *scale at the view discretion of the entrant one [1]isinterior 1500 seats SECTIONS *one rendering best describing the formal and atmospheric intent of the project must be one [1] north/south rendered at 10” highsection x 13” wide and 150dpi in tiff format. This image is to be included on the ///competitionSCHEDULE Hall one [1] as east/west section boards one ofLecture the above views.

200 seats *scale is at the discretion of the entrant 27 April 2012 competition launch RENDERINGS 11 2012 view deadline for questions oneJune [1] aerial Cafeteria / Restaurant / Lounge / Retail 18 2012 level answers will be posted on suckerPUNCH oneJune [1] street viewto questions 60,000 square feet or 20 restaurants and 70 shops 25 June 2012 early registration deadline one [1] interior view 13 August 2012 best project submission *one rendering describing thedeadline formal and atmospheric intent of the project must be ///competitionSCHEDULE Entertainment Area 3 September 2012 winners will be posted over theformat. courseThis of the weekison rendered at 10” high x 13” wide and 150dpi in tiff image to suckerPUNCH be included on the 40,000 square feet or 4 clubs and 1 large showroom boards onecompetition of the above views.

27 Aprilas 2012 launch 11 June 2012 deadline for questions Gambling floor will be posted on suckerPUNCH 18 June 2012 answers to questions 120,000 square feet 25 June 2012 early registration deadline 13 August 2012 project submission deadline 3 September 2012 winners will Facilities be posted over the course of the week on suckerPUNCH Operational ///competitionSCHEDULE 200,000 square feet

Above and Below: Site Aerial Images from Google Earth

27 April 2012 competition launch Loading Docks 11 June 2012 deadline for questions 50 truck bays will be posted on suckerPUNCH 18 June 2012 answers to questions 25 June 2012 early registration deadline 13 August 2012 project submission deadline Service, Circulation and Support programs as required. This program 3 September 2012 winners to willbe be open postedand over flexible. the courseIt ofshould the week suckerPUNCH is meant beon used as a guideline but

changes can be made at the discretion of each entrant.

CELLULAR COMPLEXITY

127

Site Aerial Image from Google Earth

128

A R C H I T E C T U R A L A P P L I C AT I O N

CELLULAR COMPLEXITY

129

COMPETITION SITE PANORAMAS Images from Google Street View

The Site is located between 10th -12th Avenue and 30-39th Street. The Pier, the Convention Centre site and the site between the Convention Centre and the Hudson yards are built areas. While the Hudson Yards consist mainly of train tracks and stored trains. On the west side of the overall site there is 12th Avenue, highly used traffic connection between north and south of Manhattan’s West side.

2

3

1

VIEW TOWARDS THE PIER

2 3

12th AVENUE LOOKING SOUTH 1 EXISTING CONVENTION CENTRE

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EXISTING CONVENTION CENTRE

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11th AVENUE LOOKING NORTH

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12th AVENUE LOOKING NORTH

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12th AVENUE & west 34th STREET

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12th AVENUE & west 33th STREET

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10th AVENUE & west 30th STREET

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10th AVENUE & west 34th STREET

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VIEW TOWARDS THE PIER

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12th AVENUE LOOKING SOUTH

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EXISTING CONVENTION CENTRE

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EXISTING CONVENTION CENTRE

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11th AVENUE LOOKING NORTH

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12th AVENUE LOOKING NORTH

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12th AVENUE & west 34th STREET

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12th AVENUE & west 33th STREET

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10th AVENUE & west 30th STREET

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10th AVENUE & west 34th STREET

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A R C H I T E C T U R A L A P P L I C AT I O N

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CELLULAR COMPLEXITY

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PROGRAMMATIC REQUIREMENTS

The Site is in total 262 569 square meters and the total area of program PROGRAM is 258 463 square meters. The program consists of a huge exhibition space and an even larger Hotel area. These two programs make up the biggest area of the building. Further there are several medium scale programs rooms,- PROGRAM operation facilities, the casino and the loading BUILDINGmeeting - TYPOLOGY docks. Finally there are several individual programs such as Cafés and restaurants, entertainment area, ballroom, theatre and lecture hall.

Twenty percent of the total program area is set out for circulation and SUCKERPUNCH COMPETITION support programs.

The GUIDELINE: program mainly consists of a combination of The site includes the land the current convention centre lies on, the space over the West Side residential commercial asThe well asSide entertainment program.

Yard train yard, and and the aforementioned facilities waterfront pier.

West Yard was designed to

Site Areas in Square Meters: Train yards right: 57 800 sqm Train yards left: 58 124 sqm Lower convention: 18 090 sqm Convention centre: 79 247 sqm Pier: 19 223 sqm

PROGRAM RELATION: The Site is in total 262 569 square meters and the total area of program is 258 463 square 262 569ofsqm meters. TOTAL: The program consists a huge exhibition space and an even larger Hotel area.

These two programs make up the biggest area of the building. Further there are several medium scale programs meeting rooms, operation facilities, the casino and the loading docks.

Finally there are several individual programs such as Cafés and restaurants, entertainment area, ballroom, theatre and lecture hall. Twenty percent of the total program area is set out for circulation and support programs. The program mainly consists of a combination of residential and commercial facilities as well as entertainment program.

accommodate an overbuild in its air rights, and space was left between the tracks for columns to support a platform above the tracks. The history of proposals for the very same site includes the ongoing Hudson Yards Redevelopment and the IFCCA “Competition for Manhattan’s West Side.”

SITE SPECIFICS AND SITUATION The Site is situated on the west side of Manhattan Mid Town close to the River edge. It is well connected to the City Centre through public and private transport. The whole area is divided into five pieces of land which are possible building zones. The land is disconnected through main and side streets. Above the Train yards the building area starts on top of the existing train tracks while on the convention centre’s Site building below zero level is possible.

350.00m

///SITE Train yards right: 57 800 sqm Train yards left: 58 124 sqm

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Btw yards /convention: 18 090 sqm

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Convention centre: 79 247 sqm

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///PROGRAM:

Hotel Hotel 400 /000 / 4000 suites 400 000 sqm 4000sqm suites / Convention Space ExhibitionExhibition / Convention Space 185 806 sqm 185 806 sqm Meeting Rooms Meeting Rooms 18581 sqm / 50 rooms 18581 sqm / 50 rooms Operational Operational Facilities Facilities 18581 sqm 18581 sqm floor GamblingGambling floor 11148 sqm 11148 sqm Loading Docks Loading Docks 10000 sqmbays / 50 truck bays 10000 sqm / 50 truck Cafeteria / Restaurant / Lounge / Retail

Cafeteria / Restaurant / Lounge / Retail sqm / 20 restaurants 5574 sqm5574 / 20 restaurants / 70 shops / 70 shops

Entertainment Area

Entertainment Area 40,000 square feet or 4 clubs and 1 large showroom = 12192 sqm = 5x (50 m x 50 m) 40,000 square feet or 4 clubs and 1 large showroom = 12192 sqm = 5x (50 m x 50 m)

Ballroom

Ballroom 30,000 square feet = 9144 square meters = 95.6 m x 95.6 m 30,000 square feet = 9144 square meters = 95.6 m x 95.6 m

Theater

Theater 1500 seats ~ 2000 sqm = 45 m x 45 m 1500 seats ~ 2000 sqm = 45 m x 45 m

Lecture Hall

Lecture Hall 200 seats ~ 270 sqm = 16.3 m x 16.3 m 200 seats ~ 270 sqm = 16.3 m x 16.3 m

20% service / circulation / support programs

20% service / circulation / support programs

132

A R C H I T E C T U R A L A P P L I C AT I O N

INFRASTRUCTURE SITE ANALYSIS

TRANSPORTATION AND GREEN ZONES The Hudson Yards is a good accessible site within Manhattan’s west side shore. It has good public transport connections, such as the The Hudson Yards a good accessible site within Manhattan's side shore. good connection to isthe Metro North, LIRR, Amtraktwest Transit andIt has subway public transport connections on a macro scale as well on the micro scale, such as the system of Lower Manhattan. Currently there are about 1300 parking connection to the Metro North, LIRR, Amtrakt Transit and subway system of Lower spaces on site and to spaces Pennon train station, the closest Manhattan.

Currently therewalking are aboutdistance 1300 parking site and walking distance to Penn station and closest is less then minutes the main airports of New ferrytrain port is less than ferry five port minutes andfivethe mainandairports of New York York City are within a 16 miles radius. Because the Lincoln Tunnel entrance is close to the site City are within a 16 miles radius. Because the Lincoln Tunnel entrance there is immediate access to the West Side Highway. An extension of the subway line Nr.7 is is closewith toathe there immediate access to the West Side Highway. planned localsite subway stopisnext to the existing convention centre; completion is planned for 2013.

Bus line service withisbus stops close to existing AnDecember extension of Furthermore the subway Nr.7 planned with a localconvention subway centre provides additional potentials from the public transportation system. Near the pier there stop next to the existing convention centre; completion is planned for are multiple Helicopter platforms.

December 2013. Furthermore Bus service with stops close to existing The site provides easy access throughout all transportation services, public and private, convention centre provides additional public transport.

Close to the and pier leaves space for further developments such as a new water taxi stop on the pier. there are multiple Helicopter platforms.

line Project. There is an extension planned to reach over the left side of the Hudson Yards.

This rises the possibility to extend the High line even further in the direction of the Times

Further of the site are the location to the current Square, benefits to state a connectivity between the districts.

Theclose shoreline next to the mainend streetofis partNew of theYork existing Hudson side of West Manhattan. area could be extended the City Highpark line Project.

There is This an park extension planned to on the pier and connected to the High line extension. reach over the left side of the Hudson Yards. This rises the possibility to extend the High line even further in the direction of the Times Square, to state a connectivity between the districts. The shoreline next to the main street is part of the existing Hudson park side of West Manhattan.

This park area could be extended on the pier and connected to the High line extension.

Green Zones

12

th

Av e

nu

e

Building area

The site provides easy access throughout all transportation services, public and private, and leaves space for further developments such as benefitstaxi of the site are a Further new water stop on the thelocation pier. close to the current end of the New York City High

41

st

40

th

Pie

r

th

Str

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41

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th

36

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co

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ya

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existing green zone and planned high line high line

ee

t

30

th

29

th

Str

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suggested green zone extension connection to TIMES SQUARE

ee

t

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Streets

Public Traffic

N Pie

N Pie

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r

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nv

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centre of public transport subway stops subway Line 7 (completed by 2013) bus line

main streets

bus stops

secondary streets

helicopter platforms

Lincoln tunnel

ferry port

CELLULAR COMPLEXITY

133

INFRASTRUCTURE TRANSPORTATION

TRANSPORTATION NODES The main transportation nodes that exist around the site are: Bus Lines: M11 running north-south, M42, M50 and M34-SBS running The main transportation towards east river.nodes that exist around the site are: Bus Lines: M11 running north-south, M42, M50 and M34-SBS running towards east river.

Subway Lines: 7, A, C7, andA, E connecting Queens Bronx.

Subway Lines: C and Eto Brooklyn, connecting toand Brooklyn, Queens and Pennsylvania Rail Station with services on more than 18 lines.

Bronx.

Ferry running to seven different destinations in Union and Jersey City.

For each mean of transportation, a relevant walking distance radius was assigned which would determine the connectivity of each site. For Bus Lines, a radius of 150m equivalent to 2 minute walk was set. For subway, ferry and rail, distances of 250m, 600m and 800m were set respectively.

2

0m Walkin 15 g

m 50

king Radiu Wal s

SUBW AY

S

dius Ra

BU

For each mean of Rail transportation, relevant walkingon distance assigned which Pennsylvania Station awith services moreradius than was 18 lines. would of each site.

For Bus Lines, radius ofand 150m equivalent to Ferrydetermine runningthetoconnectivity seven different destinations inaUnion Jersey City.

2 minute walk was set. For subway, ferry and rail, distances of 250m, 600m and 800m were set respectively.

Bus Stops - 2 minute walking radius (150m)

Subway - 3 minute walking radius (250m)

FERRY

600m Wa lk i n gR ad i

NN PE

us Ferry - 6 minute walking radius (600m)

134

Walking Radius 800m ON ATI T S

Rail Station - 10 minute walking radius (800m)

A R C H I T E C T U R A L A P P L I C AT I O N

PROGRAM ALLOCATION PROGRAM ALLOCATION

TRANSPORTATION AND WATER PROXIMITY The data for the allocation of programs was based on the transportation nodes and water proximity. Each program was evaluated for its need The datanear for thespecific allocation transportation of programs was based on the transportation and waterof to be nodes, based on thenodes relevance proximity. Each program was evaluated for its need to be near specific transportation nodes, the mode transport tomode the programs functional usage.functional Similarly the based on the of relevance of the of transportation to the programs usage.

Similarly the importance of the water proximity each program program was evaluated.

The importance of the water proximity to toeach was evaluated. evaluations for each program were recorded and input to our data spreadsheets are The evaluations for each program were recorded and input to which our data part of an overall program characteristics catalogue. spreadsheets which are part of an overall program characteristics For each site, an evaluation was set based on the analysed transportation nodes and their catalogue.

The evaluations of each program and each site were compared where the programs that have similar evaluation to a site were assigned to The evaluations of each program and site werewith compared where the that have that site. Some programs areeach assigned a choice of programs more than one similar evaluation to a site were assigned to that site. Some programs are assigned with a site.

This sets the constraint on constraint programs distribution on site. choice of more than oneinitial site. This sets the initial on programs distribution on site.

The developed architectural system exhibits potential were multiple programs stacked The developed architectural system exhibits potential werearemultiple together in tower conditions. Therefore, most programs would be located in one position on programs are stacked the studied tower typology. site. The area which is foundtogether to be most in connected would suit the most amountTherefore, of programs.

The siteprograms in between the West Rail and the Javits Centre high degree most would be Yards located in current one position ondisplay site.a The area of connectivity; rendering suitableconnected for multiple programs. which is found to beit most and would suit the most amount of programs. The site in between the West Rail Yards and the current Javits Centre display a high degree of connectivity; rendering it suitable for multiple programs.

proximity to each of the 5 different sites. Similarly the water proximity was evaluated for each site.

Walking Radi us 0m 15

m Walking Rad 250 ius AY W B U

PENN STATION 800m Walk ing R adiu s

S

00m Walking Radius RY 6 FER

BU S

For each site, an evaluation was set based on the analysed transportation nodes and their proximity to each of the 5 different sites.

Similarly the water proximity was evaluated for each site.

no PROGRAM

PROGRAM OVERALL TYPE AREA m2

1 Hotel

2 Exhibition / Convention 3 Meeting Rooms 4 Operational Facilities 5 Gambling Floor 6 Loading Docks Cafeteria/ Restaurant/ 7 Retail / Lounge 8 Entertainment Area 9 Ballroom 10 Theatre 11 Lecture Hall

400000 Hotel suites High gallery Exhibition1 185806 Exhibition2 18581 Meeting rooms 18581 variable 11148 Gambling Area 10000 Loading Bays Shops 5574 Restaurants Clubs 3716 Large show room 2787 Ballroom 2000 Theatre 270 Lecture Hall

subway stops bus stops ferry port

PROGRAM SITE - LOCATION

SITE - PROGRAM EVALUATION

w ater proximity 0-2 0-2 0-2 0-2 0-2 0 - not important 1 - somew hat important 2 - very important Bus

Metro

Ferry

Rail

0

1

1

2

2

2

2

2

2

1

2 N 1 N 1 2 2 2 1 2 1

2 N 1 N 1 2 2 2 1 2 1

1 N 1 N 0 1 0 0 0 1 0

1 N 1 N 0 0 0 1 1 1 1

0 N 1 N 2 0 1 1 0 1 0

CELLULAR COMPLEXITY

No.

SITE

1

CONVENTION

2 LOW CONVENTION 3 RAIL EAST 4 RAIL WEST 5 PIER

BUS

SUBWAY

FERRY

TRAIN

WATER

2

2

2

0

2

2 2 1 1

2 1 1 0

1 0 1 2

1 2 1 0

2 1 2 2

Above: Evaluation of sites in terms of transportation and water proximity Left: Evaluation of programs in terms of transportation and water proximity Below: Approximate matching choices between programs and site

SITE 1 CONVENTION 2 LOW CONVENTION 3 RAIL EAST 4 RAIL WEST 5 PIER

PROGRAM CONVENTION, CLUBS HOTEL, MEETING ROOMS, CLUBS,SHOPS, THEATRE SHOWROOM, LECTURE HALL GAMBLING, HOTEL, RESTAURANTS, BALLROOM SHOPS, RESTAURANTS

135

PROGRAM CATALOGUE

PROGRAM CATALOGUE

PROGRAM CATALOGUE PROGRAM DATA CATALOGUE

PROGRAM

SITE - PROGRAM

A programme catalogue was created in order to document the characteristics of each program and any criteria it holds that informs part of the system or the architecture.

The programs are listed with the areas, type and unit size. For The programme data catalogue was created in order to document theeach PROGRAM programme ranges are set for its desired dimensions the informs type of use. characteristics of each program and any criteria itbased holdsonthat Furthermore a heightorrange for the is programs also documented.

In with terms of A programme catalogue was in program order to document the characteristics of part of the system thecreated architecture.

The are listed allocation within the building, ranges are also set for minimum and maximum each program and any criteria it holds that informs part of the system or the the areas, type and unit size. For each programme ranges are set floor locations; number floors. architecture.

Thealongside programs the are listed withofthe areas, type and unit size. For each

Another section of the catalogue documents the Based relation means of on towards the programmes relations to nodes o in relation these nodes.

The outputs of both transport and the desire of the programme to be located near atospecific transporbe inof which site. tation which couldthat contribute thesystem use the programme.

There are alsonode, characteristics directlypositively relate totothe such asThis provides a reference for p

also considered a factor that can contribute tow

structure, lighting and enclosure. For each of these characteristics the There are of also that directly relate to the system suchofas structure, Another section the catalogue documents thespan relation towards relevant information ischaracteristics documented including widths, andmeans natural lighting and enclosure.

For each of these characteristics the relevant information transport and the desire of the programme to be located near a specific transporlighting needs.

for its desired dimensions based on the type of use. Furthermore a programme ranges are set for its desired dimensions based on the type of use. height range for the program is also documented. In terms of allocation Furthermore a height range for the program is also documented. In terms of within thewithin building, ranges are alsoare setalso for minimum and maximum floor allocation the building, ranges set for minimum and maximum locations; alongside thethenumber floor locations; alongside numberof of floors. floors.

is documented. tation node, which could contribute positively to the use of the programme.

There are also characteristics that directly relate to the system such as structure, lighting and enclosure. For each of these characteristics the relevant information is documented.

AREA m2 ENTIRE SITE

SITE 1 CONVENTION 2 LOW CONVENTION 3 RAIL EAST 4 RAIL WEST 5 PIER

262569

AREA m2

57800

1 train yards right

ENTIRE SITE

262569

58124

2 train yards left

1 train yards right

57800

2 train yards left

58124

3 betw een yards and convention

18090

4 convention centre

79247

No.

SITE

19223

1

CONVENTION

18090

3 betw een yards and convention

79247

4 convention centre

5 pier

no PROGRAM

OVERALL AREA m2

OVERALL AREA m2

PROGRAM TYPE AMOUNT

PROGRAM TYPE AMOUNT

AVG UNIT SIZE

AVG UNIT SIZE

PROGRAM Width Width

min

1 Hotel

2 Exhibition / Convention

2 Exhibition / Convention

3 Meeting Rooms

3 Meeting Rooms

4 Operational Facilities

4 Operational Facilities

5 Gambling Floor

4000 hotel suites

400000

4000 hotel suites

40000 m2 high gallery

400000

40000 m2 high 92903 m2 gallery exhibition1 92903 m2 exhibition1 92903 m2 exhibition2 92903 m2 exhibition2

185806

185806

50 meeting rooms

18581

50 meeting rooms

18581

18581

18581 11148

LoadingDocks Docks 66 Loading

10000 10000 5574 5574 0.5 0.5

88 Entertainment EntertainmentArea Area

3716 0.5 0.5 3716

99 Ballroom Ballroom

2787 2787

10 10 Theatre Theatre

2000 2000

11 Lecture Hall

270

11 Lecture Hall

136

270

variable

variable

11148

5 Gambling Floor

Cafeteria/Restaurant/ Restaurant/ Retail Cafeteria/ Retail / / Lounge 77 Lounge

2 2 1 1

PROGRAM

variable

variable

100

min

max

m

floor

floor

level

level

4

9

max

40

80

20

25 10 15

1 3 1

8 8 3

1 1 1

1 1 1

3

4

3

6

1

2

3

4

min

max

min

max

max

m

m

m

m

m

m

100

20

32

3

20

32

3

4

60

20 60 760 10

25 7 10 10 15

180

3

4

371.62

100

100

variable

max

min

30 40 50 60 50

variable

min

min

min

40000

N

N

N

40

180 N

3

Level allocation

Number of Floors/Levels

max

min

m

40000 92903 30 92903 92903 50 92903 50 371.62

Floor Height

Floor Height

SUB 2

PROGRAM

min

1 Hotel

BUS

2 LOW CONVENTION 3 RAIL EAST 4 RAIL WEST 5 PIER

PROGRAM no PROGRAM PROGRAM

GAMB

SITE - PROGRA

19223

5 pier

HOTEL,

4

11148

55

75

8

10

8

10

-1

2

1

1

200 48

48 52

552

85

8

-1

1

1

1

20 restuarants 20 restuarants 139.35139.357 70 shops 39.814286 70 shops 39.814286 16 4 clubs 4 clubs 464.5 464.5 18 1 large showshow room room 1858 1858 45 1 large

710 16 18 18 22 60 45

410 418 822 860

54 54 8 10 15 8

5 5 10 15

1 1 min 1

max 2 max 2

4 2 2 1

6 3 4 1

1 Ballroom 1 Ballroom

2787 2787 30

40 30

10 40

12 10

12

min

3

1

1

1 Theatre 1 Theatre

2000 2000 40

48 40

18 48

22 18

22

min

5

1

3

1 Lecture Hall

270

12

15

4

6

6

3

6

1

1

1 Gambling Area

1 Gambling Area

11148

50 Loading 50 Loading Bays Bays

200

1 Lecture Hall

A R C H I T E C T U R A L A P P L I C AT I O N

55

12

270

75

15

4

PROGRAM CATALOGUE PROGRAM CATALOGUE

SITE - PROGRAM Based on the programmesSITE relations to nodes of transportation, the sites were also evaluated - PROGRAM in relation to these nodes. The outputs of both evaluations inform which programs are likely to be in which site. This provides a reference for programme allocation. The proximity to water is Based the programmes to nodes transportation, the sites were also evaluated also considered a factor that can on contribute towards relations the allocation of aofprogramme. in relation to these nodes. The outputs of both evaluations inform which programs are likely to be in which site. This provides a reference for programme allocation. The proximity to water is also considered a factor that can contribute towards the allocation of a programme.

1 2 3 4 5

SITE PROGRAM SITE CONVENTION CONVENTION, CLUBSPROGRAM 1 CONVENTION CONVENTION, CLUBS LOW CONVENTION HOTEL, MEETING ROOMS, CLUBS,SHOPS, THEATRE HOTEL, MEETING ROOMS, RAIL EAST 2 LOW CONVENTION SHOWROOM, LECTURE HALL CLUBS,SHOPS, THEATRE RAIL EAST SHOWROOM,BALLROOM LECTURE HALL RAIL WEST 3 GAMBLING, HOTEL, RESTAURANTS, 4 RAIL WEST GAMBLING, HOTEL, RESTAURANTS, BALLROOM PIER SHOPS, RESTAURANTS 5

PIER

SHOPS, RESTAURANTS

SITE - PROGRAM EVALUATION

SITE - PROGRAM EVALUATION

No.

SITE

1

CONVENTION

BUS

No.

SITE

SUBWAY

2

1

CONVENTION

2 LOW CONVENTION 2 2 LOW CONVENTION 3 RAIL EAST 2 3 RAIL EAST 4 RAIL WEST 1 4 RAIL WEST 5 PIER 1 5 PIER

2 2 1 1 0

BUS

2

TRAIN

SUBWAY

2

1

2 20 11 12

2

WATER

0

FERRY

2

1

2 12 11 00

Number of PROGRAM Bus Bus Metro Ferry Floors/Levels

Metro Rail

min 0-2

0-2 0-2

max

minmin

max max

floor

floor

floor floor level level

9

max

40

1 3 1

8 8 3

1 1 1

3

6

1

min

max

min

-1

2

1

-1

1

1

max 0-2

0-2 0-2

max

40

80

1 3 1

8 81 31

1 1 12

1 1 21

3

6

1

2

2

2

min

max

min

max

max

N

N

2

1

1

1

1

1

1

-1

1 2

WATER 0

2

1 2 1 0

2 1 2 2

0

1

w ater in min Area w ith w ater columns in mincolumns Area w ith Ferry Rail Width Span Width Span Lighting Req Lighting Req Enclosure Enclosure proximityopen space? open span proximity space? span 0-2 0-2

0-2 0 or 0-2 1

2 1

0 2 2 N

N

1

2

2

2

2

2

1

1 N

2 1

2 1

0

N

N

N

N

1

1

1

1

1

1

N

N

1 1 4 min 2 1

4N

N6

N1

N1

N 0

26 max 3 2

21 2 2 1

13 4 2 1

0 11

1 2 0 0 0

0 0 0 1

12

0 01

02 2 0 2

31

2 21

02 2 1 2

0 1

1

1

min

3

1

min

5

1

3

6

1

4

1

2

min

5

1

1

1

0

3

63

12

21

1

1

1

3

2

1

0

2

N

2

1

1

11

11

1 0

1

0

1

0

0 or avg m21

avg avgm2 m

0 - none m2yes 1-

m2

0

40

5

0

40000 35 92903 55 92903

35 55 2 55 1

2 1 0

0

371

8

1

N

40

0 1 0 0

40000 0 92903 0 92903

0

371

0

N

1

1 max

2 1 min

0

N

1

max 2 max 2

N

1

2

-1

1 1 min 1

1

1

SPACE QUALITIES SPACE QUALITIES

STRUCTURE STRUCTURE

0 - not important 1 - somew hat important 0level - not important 0 - none level 1 - somew hat important 2 - very important 2 - very important 1- yes

9

80

2

1 0 1 1 2 2 2

Number of Level allocation Floors/Levels

min

TRAIN

2

PROGRAM PROGRAM SITE - LOCATION PROGRAM SITE - LOCATION

PROGRAM Level allocation

FERRY

N

5

55 8

N

N

N

N

0

11148

11148

60

1

0

m

avg 0 m- 2

0-2 0-2

0 -fully enclosed lightenclosed -fully 0 - no light 0 -0no light 1 -some enclosed m 1 -some light 1 -some 1 -some enclosed 2 -lots of light 2 -open air space 2 -lots of light 2 -open air space

2

0

1

2

60

1600

8

8 140

8.5 N

0 0 1 0 1

0 140 0 40 0

40 8.5 465 4 1858

4 2 20 1 35

2 1 0 2

9144 35

35 2

0

0

9144

1

35

0

0

0

2000

45

0 0

2000 0

45 270

13.5 0

0

270

13.5

1

CELLULAR COMPLEXITY

2

1 2 2 2 N

0

0

0

20

1 2 2

2

N

1600 0

465 0 1858

2

N

N

0 2

0 0 0

0-2

N

0 1

1

1 1 1 1 1 1 2 2

1 1 1 1 1 2 2 2

2

137

STRUCTURE STRUCTURE - PROGRAM SPAN VARIATION

PROGRAM SPAN VARIATION Through the use of simple structural logics, a set of conditions where generated where various conditions relating to program spans can be Through the use of simple structural logics, a set of conditions whereisgenerated where various comparatively analysed and evaluated.

The aim to investigate the conditions relating to program spans can be comparatively analysed and evaluated. The aim variations that occur within structural members due to programmatic is to investigate the variations that occur within structural members due to programmatic variations which theThe spans.

The first condition variations which affectaffect the spans. first condition explores identicalexplores spans overidentical repetitive floors, the second condition examines spans that are decreasing building height, the third spans over repetitive floors, the second conditionwith examines spans that is the opposite where the span increases with building height. The final two cases explore are decreasing with building height, the third is the opposite where the either short spans over a long span, or a long span over short spans. span increases with building height. The final two cases explore either short spans over a long span, or a long span over short spans.

SPAN VARIATION

VERTICAL LOADS

The various conditions presented set general consideration for the sizing and type of elements - the cells within the system. Additionally various conditions presented general consideration for building. the sizing and type theThe allocation of program withinsetthe vertical axis of the Each of of - the cells within the system. Each of the conditions becomes relevant at a specific theelements conditions becomes relevant at a specific part of the building. For part of the building. For example, the base of the building can have a situation similar to the example, the base the building have situation similar spans to the second condition with of large spans at publiccan areas at thealower parts, repetitive and programs can occur with abovelarge this portion where spans continue.

Theselower short spans second condition spans at short public areas at the parts,can then become larger at the top of the building where dead and live loads are low; similar the repetitive spans and programs can occur above this portion where short third condition. spans continue. These short spans can then become larger at the top of the building where dead and live loads are low; similar the third condition.

VERTICAL & HORIZONTAL LOADS

LOADS

vertical members (columns): slight size decrease with height horizontal members (beams): slight size decrease with height

vertical members (columns): size decrease with height horizontal members (beams): size decrease with height

vertical members (columns): size can be relatively the same horizontal members (beams): size can be relatively the same

vertical members (columns): size decrease with height horizontal members (beams): size decrease with height

vertical members (columns): size increase with height horizontal members (beams): size relatively the same

138

A R C H I T E C T U R A L A P P L I C AT I O N

CELL POROSITY

STRUCTURE STRUCTURE - PROGRAM IN TOWER

PROGRAM-SYSTEM DEVELOPMENT Based on the previous structural study, the conditions were allocated in the relevant positions within an overall tower context. The tower starts Based the previous structural study, the conditions were placed in the relevant positions with aonlow span structural transition to handle the loads from the large within an overall tower context. The tower starts with a low span structural transition to handle span public areas.

This large span breaks into the loads from the large span public areas.

This large spandown breaks gradually down gradually intosmaller smaller spansto to reach an area the areAt repetitive. thethere topmost spans reach an area where where the spans arespans repetitive. the topmost At parts, is an opportunity to increase spans and benefit from specific programmatic conditions. parts, there is anthe opportunity to increase the spans and benefit from specific programmatic This distribution is consideredconditions. to display the opportunities within gradients and the efficient use of a cellular system due to the ability to vary the cells gradually and create an efficient structure through a gradient.

This distribution is considered to display the opportunities within

The spatial qualities of the resultant spaces are evaluated where they can be related to the programmatic spaces and address their The spatial qualities of the resultant spaces are evaluated they can spaces be related need to the requirements.

For example, the lower publicwhere exhibition programmatic spaces and address their requirements. For example, the lower public aexhibition heavy spaces structure to structure the location and loads, do do not need due a heavy due to the location andtherefore loads, therefore nothave have gain natural haveto possibility to be gain natural light,light, yet stillyet havestill possibility be semi-enclosed.

Thesemi-enclosed. topmost spaces haveThe low loads and can benefit have from natural andand viewscan in programs such as restaurants and events topmost spaces low light loads benefit from natural light and spaces. Similarly other programs fall within this overall gradient of the tower. views in programs such as restaurants and events spaces. Similarly other programs fall within this overall gradient of the tower.

gradients and the efficient use of a cellular system due to the ability to vary the cells gradually and create an efficient structure through a gradient.

VARIATION

STRUCTURE

STRUCTURAL OUTLINE

SPATIAL QUALITIES

SUITABLE PROGRAMS

LIGHT

ENCLOSURE

MEDIUM LIGHT

ENCLOSED PRIVATE GAMBLING / EVENTS

LONG SPANS LOW DEAD AND LIVE LOADS HIGH LATERAL LOADS

RESTAURANTS HIGH NATURAL LIGHT LARGE SUITES

STRUCTURE

SHORT SPANS MID RANGE DEAD AND LIVE LOADS

HOTEL SUITES

MID RANGE LATERAL LOADS

LOW TO MID NATURAL LIGHT

MEETING ROOMS

BALLROOM / THEATRE

LONG SPANS HIGH RANGE DEAD AND LIVE LOADS

GAMBLING

LOW RANGE LATERAL LOADS

SEMI-ENCLOSED CONVENTION

SHORT SPANS

NO REQUIRED NATURAL LIGHT

OPEN

TRANSITION EXISTING TRAINS

VERY HIGH DEAD AND LIVE LOADS LOW RANGE LATERAL LOADS

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PROGRAM ALLOCATION

The strategy taken to develop the tower combines characteristics of the programs, their relation to the site, with characteristics of the overall system and how it works on an urban and architectural scale.

The intent is to illustrate the performance of the system in addressing variable architectural and programmatic conditions. The variation within the system would occur through gradients for structure and light requirements, with variations for additional environmental criteria such as rain and wind. The programmatic spaces were arranged with the idea of a tower and podium, where the podium contains exhibition and convention spaces alongside services with variation at a large scale which is based on macro-scale variations for urban design elements concerning structure, enclosure and light.

The regular span spaces are in the central part of the building and would still have a variation even though spans are repetitive, there is variation due to changing dead, live and lateral loads across the height of the building. The larger spans are either located at the top or bottom of the structure, at the bottom a heavy and solid structure with low natural light conditions exists. Whereas the top spaces have a light structure that is deep allowing for good views and natural light.

The exploded axonometric illustrates the assemblage of programs within the tower and how the spaces are arranged to achieve a gradient of structure, yet correspond to the lighting conditions within the spaces.

Private Gambling / Events Space Entertainment: Restaurants and Clubs Large Hotel Suites Hotel Suites

Meeting Rooms Hotel Amenities & Entertainment Ballroom Hotel Lobby & Entrance

Theatre Gambling Floor / Casino

Showroom Convention Centre Halls

Shops Operational Facilities Structural Transition Loading Docks High Line Park Gallery

Site Boundaries Programmatic Exploded Axonometric

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A R C H I T E C T U R A L A P P L I C AT I O N

SITE INTEGRATION

PROGRAM ALLOCATION

SITE INTEGRATION The tower which houses most programs is allocated on the area of the site with the best connection to the transportation nodes. However the current condition of the site and its interaction with the rest of The tower which most programs theproposal area of thethe siteextension with the bestof Manhattan is houses considered weak. is Asallocated part ofon our connection to the transportation nodes. However the current condition of the site and its the High Line Park is integrated into the building.

This would begin from interaction with the rest of Manhattan is considered weak. As part of our proposal the the gallery convention halls and This ending street-level extension of theadjacent High Line to Parkthe is integrated into the building. wouldat begin from the gallery adjacent to the convention halls and ending at street-level where the shops and where the shops and showroom area. The intent is to establish a link showroom area. The intent is to establish a link diagonally from this point towards Times diagonally from this point towards Times Square.

Square.

The of the HighHigh Line Line opensopens opportunities for direct connection the Theintegration integration of the opportunities for direct between connection convention spaces, the tower and the public realm. The Gallery itself in which the High Line between the convention spaces, the tower and the public realm.

The would run through becomes an extension of the exhibition and convention spaces, creating a Gallery itselfspace. in which the ofHigh run throughto becomes an public exhibition This type spaceLine wouldwould have semi-enclosure environmental conditions, yet of variations for light and structure. extension the exhibition and convention spaces, creating a public

exhibition space. This type of space would have semi-enclosure to environmental conditions, yet variations for light and structure.

As a research investigation into the application of the system and its potentials, the morphology of the tower is kept simple and is able to integrate within orthogonal planning grid of Manhattan. The complexity The morphology of the tower is kept simple to integrate withinoforthogonal planning grid of within the architecture would emerge as part the variations and Manhattan. The complexity within the architecture would emerge as part of the variations and gradients that correspond to the various programmatic conditions and gradients that correspond to the various programmatic conditions and shifts in program, shifts in and program, structure and enclosure. structure enclosure.

Site characteristics and data will inform various aspects within the application of the system,

Site characteristics data inform various within the this includes performative and aspects suchwill as natural light, based onaspects latitude and orientation. application of including the system, this includes aspects such Structural criteria site specific lateral loads, andperformative wind data for ventilation orientations andnatural strengths.light, based on latitude and orientation. Structural criteria as including site specific lateral loads, and wind data for ventilation orientations and strengths.

As a case study, we tested the system application for the competition entry which is shown in the next pages.

Programmatic Layouts on Site

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SUCKERPUNCH COMPETITION ENTRY BOARDS 13TH AUGUST 2012 BOARD ONE

BOARD TWO

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A R C H I T E C T U R A L A P P L I C AT I O N

SUCKERPUNCH COMPETITION ENTRY BOARDS 13TH AUGUST 2012 Descriptive text of project, from competition boards:

The current High Line Park is integrated into the building where it runs through Gallery and splits into two main paths. The first path goes lower and continues to street level through the shops. The second path goes to a higher level - at the roof of the convention centre where it continues diagonally towards Times Square. The programs are arranged in a co-ordinated manner with the way the cellular system operates in terms of structure and natural lighting. The programs with high spans and low natural light requirements are at the base of the tower such as the exhibition, theatre, ballroom and others. The programs that require low spans and natural light are placed at the upper parts of the tower such as the Hotel and Meeting Rooms. Through a hierarchy, the cellular building system contains low porosity cells at the base of the building for strong structure and no light, while being more porous at the top were loads are less and light is required. The porosity is also used to provide an efficient and optimized structure for the various span transformations and changes in loads throughout the programmatic shifts.

The programs were allocated in a tower-like fashion to create the density at the best connected area of the site. The central area between the current convention centre and west rail yards has the best access in terms of overall walking proximity to: Bus, Ferry, Subway and Rail. The developed cellular system would demonstrate the ability to respond to various programmatic conditions through a unified system which fits into the orthogonal urban planning of Manhattan and its grid blocks at one scale, while at a finer scale develop diverse detail to react to conditions each program requires. The programs were distributed within a tower computationaly through an evolutionary solver, were a range is set for each programs height, width, orientation, number of floors and floor allocation. The resultant allocation. As part of the design development, the connectivity of the site to the rest of Manhattan was a crucial aspect of the design.

FLOOR PLANS

Ground Floor: Street Access through Gallery, connection towards High Line Programs: Loading, Services, Shops and Showroom - Structural Transition

Convention Floor: Access through High Line into Gallery and Convention Spaces.

Programs: Convention / Exhibition Spaces

Theatre Floor: Connection from High Line towards Exhibition Roof - walkable connection to Times Square. Programs: Theatre and Casino

VARIATION

SECTION N/S

CASINO PROGRAMS

STRUCTURAL OUTLINE

STRUCTURE

LIGHT

ENCLOSURE

CELLS

CASINO POROSITY: mid-high

PRIVATE GAMBLING / EVENTS LONG SPANS

RESTUARANTS

DEPTH: Medium

HIGH LATERAL LOADS

Depth required between floors and not necessarly heavy or solid structure

SHORT SPANS

HOTEL SUITES

SIZE: small-mid

LOW DEAD AND LIVE LOADS TRANSFER CONDITIONS

LARGE SUITES

LAYERS: many

MEDIUM LIGHT

VARIATION The dead, live and lateral loads vary between the lower and higher parts of the tower and therefore require different thicknesses.

HIGH LIGHT ENCLOSED

MID RANGE DEAD AND LIVE LOADS

POROSITY: high LAYERS: few SIZE: large

MID RANGE LATERAL LOADS

DEPTH: low

LONG SPANS

MEETING ROOMS

HIGH RANGE DEAD AND LIVE LOADS LOW RANGE LATERAL LOADS

BALLROOM / THEATRE

NO LIGHT

NO / LOW LIGHT

LOW LIGHT

SEMI-ENCLOSED

GAMBLING

POROSITY: low SHORT SPANS VERY HIGH DEAD AND LIVE LOADS

CONVENTION

LOW RANGE LATERAL LOADS

TRANSITION

LAYERS: many NO LIGHT REQ

OPEN

SIZE: small DEPTH: high

EXISTING TRAINS

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SUCKERPUNCH COMPETITION ENTRY BOARDS 13TH AUGUST 2012 AREAL VIEW

12TH AVENUE BIRDS EYE PERSPECTIVE

144

A R C H I T E C T U R A L A P P L I C AT I O N

SUCKERPUNCH COMPETITION ENTRY BOARDS 13TH AUGUST 2012 PERSPECTIVE VIEW TOWARDS MIDTOWN

INTERIOR PERSPECTIVE OF EXHIBITION SPACE

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references

image references

1 - The web-based Java App by UOregeon was used to diagrammatically

Diagrams and Images not referenced were taken or created by Cellular

estimate the effects of basic building morphology on structure loads.

Complexity authors: Kais Al-Rawi, Julia Koerner or Marie Boltenstern.

http://darkwing.uoregon.edu/~struct/courseware/461/461_lectures/461_

Fig. 5.1 - http://highrise.bk.tudelft.nl/pdf/Shard_London_Bridge_web.pdf

lecture18/461_lecture18.html

Fig. 5.2 - Ibid Fig. 5.3 - Ibid (minor editing was done to the diagrams)

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A R C H I T E C T U R A L A P P L I C AT I O N

ARCHITECTURAL A P P L I C AT I O N overview Throughout the architectural application process, the scope was defined through typological case studies concluding with the decision of developing a tower application. The site and program were defined through a international ideas competition.

Since the tower extends over more than 70 floors about 200 meters in height, the cell size becomes critical factor. When the cells become over a few meters height, they require deformation in the horizontal axis to avoid over-thickening the facade.

The approach towards the application involved comprehensive site analysis towards the architectural requirements to be able to develop a successful entry. The goal was to be able to test the system on a tower application and develop understanding of the application of the system.

Furthermore, the development of a gradient over the height of the building became particularly challenging and requires additional investigation. The further development would require investigation into structural gradient typologies at a local and global scale, and the parameters that may influence this gradient.

The central aspect to applying the system was the allocation of programs. This process was based on studying basic structural typologies and the effect of changing program spans on structural members.

Based on this study, the assemblage of programs was defined, in conjunction with their natural lighting requirements.

The cellular complexity entry was awarded second place and gained recognition from an international jury of architects and designers. In terms of our research, the competition has become a case study for the application of the system. The initial concern that developed throughout the application is the matter of scale.

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147

148

SYSTEM DEVELOPMENT Throughout the previous section, the system was investigated in further detail and the defining parameters for its application were established. This section will examine the application of the system at an architectural scale.

For the architectural application, we became particularly interested in the tower typology and the diverse programmatic uses involved in this type. The current state-of-the-art architecture in tower design creates limited variation within towers to address architectural and programmatic conditions. A case study is investigated for this purpose, and its relation to our system.

The case study leads us to selecting a site and range of programs to commence the application process.

Throughout our research we investigated architectural competitions and selected the suckerPUNCH international competition which involves the design of a convention, hotel and casino in Hudson Yards, New York.

The application of the system at this scale provided us with case study on how the system operates at a large scale and the opportunities and limitations which become apparent.

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SITE PROGRAMS SITE PROGRAMS PROGRAM AND STRUCTURE PROGRAM AND STRUCTURE PROGRAM AND STRUCTURE The diagrams below illustrate in section therange diverse rangethat of are programs The diagrams below illustrate through section the diverse of programs included withinare the included tower, the within uses range public semi-public exhibition andand convention that the from tower, theand uses range from public semispaces, towards entertainment facilities including theatre, ballroom and casino above the The diagrams below illustrate section the diverse range of programs that are included public exhibition and through convention spaces, to entertainment facilities public areas, and within the top part the private hotel rooms and restaurant facilities in addition within the tower, the uses range from public and semi-public exhibition and convention including theatre, ballroom and including casino,theatre, directly above the public. The to a private events space at the topmost spaces, towards entertainment facilitiesfloor. ballroom and casino above the tower combines private androoms restaurant facilities in in addition public areas, and within the top hotel part therooms private hotel and restaurant facilities addition The are notand only arranged in the manner of public, semi-public to a a spaces private events space at the topmost floor. to gambling events space at the topmost floor.and private but are also based on how the architectural system operates which is based on structure, where the structure alsoare provides which are relatedoftopublic, natural lighting due to private the cellsbut geometriThe spaces not onlyqualities arranged in the manner semi-public and are also cal qualities when porosities appear. second diagram illustrates the variation within based on how thehigh architectural system The operates which is based on structure, where the spans involved for the allocated Note that the spans run throughout the tower in a structure also provides qualities programs. which are related to natural lighting due to the cells geometrigradient manner with noporosities direct shifts. cal qualities when high appear. The second diagram illustrates the variation within spans involved for the allocated programs. Note that the spans run throughout the tower in a gradient manner with no direct shifts.

The spaces are based on how the architectural system operates, where the structure also provides qualities which are related to natural lighting due to the cells geometrical qualities when high porosities appear. The second diagram illustrates the variation within spans involved for the allocated programs. Note that the spans run throughout the tower in a gradient manner with no sudden and direct shifts.

Program Variation

Private Gambling / Events Space Entertainment: Restaurants and Clubs Private Gambling / Events Space Large Hotel Suites Entertainment: Restaurants and Clubs Large Hotel Suites

Hotel Suites Hotel Suites

Meeting Rooms Hotel Amenities & Entertainment Meeting Rooms Ballroom Hotel Amenities & Entertainment Gambling Floor / Casino Ballroom Convention Centre Halls Gambling Floor / Casino

Theatre Gallery Theatre

Shops Operational Facilities, Loading Docks Gallery Convention Centre Halls Structural Transition Shops Operational Facilities, Loading Docks West Rail Yards Structural Transition West Rail Yards

Structural Variation span ~ 45m span ~ 30m span ~ 45m span span ~~ 15m 30m span ~ 15m

span ~ 5m span ~ 5m

span ~ 10m span ~ 15m span span ~~ 45m 10m span ~ 15m span ~ 45m span ~ 75m span ~ 7m span span ~~ 4m 75m span ~ 7m span ~ 4m

150

SYSTEM DEVELOPMENT

STRUCTURE PROGRAMMATIC STRUCTURAL TYPOLOGIES

STRUCTURE WITHIN BUILDING The further development of the system involved a range of programmatic structural typologies, where specific parts of the tower are chosen The conditionsatvary throughout the building, the base the dead live loads are andstructural investigated a local scale.

Theseattypologies set and a comparative very high, at the top the lateral loads are high. In general the base of the tower requires the geometrical and architectural most structure. The transformations in spans occur in a gradient manner where there are multiple transfer conditions which occur gradually.

The large public and semi-public spaces within the lower parts of the tower require a heavy and dense structure to allow for the large spans and at the same time transfer the dead loads from above towards the ground. The large span spaces at the top of the tower do not require such a heavy structure as they are mostly resisting lateral forces which are perpendicular to the low dead and live loads.

The two main conditions in which variations occur are either the transfer conditions where there is a change from one span to another or a condition of variation where there is a repetitive span over a large number of floors.

The transfer conditions are where loads from one span and set of columns need to be transferred to another. This situation typically requires a transfer beam which is deep, the depth provides the ability to transfer the loads from one area to another. Such conditions are outlined below with increased depth for this condition. The cellular system becomes of particular use to the ability to use low porosity cells which provide depth with low amount of material.

When a span occurs repetitively over multiple floors, a variation would still occur because the loads on the first few of these floors is not the same as the last few. There would be a change in dead, live and lateral loads which suggest change throughout the structure through slight variation. In this case, the porosity of the cellular system can be varied to address any variations within the structure at both local and global scales.

STRUCTURAL TYPOLOGIES

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151

PROGRAM-STRUCTURAL TYPOLOGY: THEATRE

The theatre is located in the top portion of the tower, above the restuarants and hotel suites. It has a long span, and high floor height.

The typology used to address this programmatic condition is presented, it aims to satisfy both the structural requirements and the lighting conditions; in a manner which works with the system and its gradients which attempt to efficiently create spatial conditions.

PROGRAM

SPAN WIDTH

HEIGHT

LOCATION

PROGRAM ABOVE

PROGRAM BELOW

Convention

45m

15m

Tower Top

Restaurants

Open

CONDITIONS

RESULTANT ORGANIZATION

Span: - high span, no transfer condition from above, transfer condition to spaces below

Vertical Members:

Location: - dead loads only from self weight, low live loads.

- high lateral loads with direction at walls, perpendicular to gravity.

Program: - the private events and gambling space requires views towards the outside due to its location on a high floor.

- ground surface can be resurfaced or staged for particular activities

structural condition example

The vertical members require multiple layers to achieve structural rigidity, furthermore several cells for the possibility of a gradient. The cells start very dense to allow for transfer of loads towards the ground members, however gradients towards very porous cells to allow for views, particularly within the outer layer. Near the corner where the ceiling and wall members meet, medium porosity cells are used to resist loads.

Horizontal Ground Members: The horizontal ground members are made up of two layers which are dense to allow for the transfer of loads towards the members within the floor below.

Horizontal Ceiling Members: The horizontal ceiling members are made up of two layers for additional strength, however both layers are of very porous to allow for views to the outside. They become less porous towards the edges due to higher loads and connection to vertical members.

The cell size is approximately 2 meters in this condition.

152

SYSTEM DEVELOPMENT

PROGRAM-STRUCTURAL TYPOLOGY: CASINO

The theatre is located in the lower portion of the tower, between the convention centre and the entertainment floor. It has a long span, and high floor height. The typology used to address this programmatic condition is presented, it aims to satisfy both the structural requirements and the lighting conditions; in a manner which works with the system and its gradients which attempt to efficiently create spatial conditions.

PROGRAM

SPAN WIDTH

HEIGHT

LOCATION

PROGRAM ABOVE

PROGRAM BELOW

Theatre

35m

15m

Tower Low

Entertainment

Convention

CONDITIONS

RESULTANT ORGANIZATION

Span: - high span, requires distribution of all loads above to only two parts, due to theatre above the transfer condition is not big and loads are already running through.

Vertical Members:

Location: - very high dead and live loads from all floors above, transfer of loads from above, full structural transition under this floor to handle these loads towards the ground.

- low lateral loads.

The vertical members require multiple layers to achieve structural rigidity, furthermore several cells for the possibility of a gradient. The gradient occurs vertically and horizontally.

-vertically cells become denser near the connection to the ceiling members.

-horizontally the cells become less dense towards the exterior as the they are away from the integral structural members

structural condition example

Horizontal Ground Members: The horizontal ground members are placed in one layer which is relatively dense, with slight variation where the cells are less dense towards the centre due to less loads transferred from the centre.

Horizontal Ceiling Members: The horizontal ceiling members are made up three layers due to the transfer condition occurring where the space above have a different span and need to transfer loads to the condition within this floor. The first layer provides a slab condition for the upper spaces, the second and third layer facilitate the transfer of loads. Very porous cells are used towards the centre due to the need of a depth more than strength as a path for loads. Near the edges where the horizontal members meet the vertical members the cells are dense and are less porous.

Program: - the theatre does not require natural lighting and will depend mainly on artificial lighting which is specified by the performance.

- at certain areas high floor height may be desirable.

- floors need not to be flat, resurfacing or platforms would be used, therefore surface permeability is not a concern.

The cell size is approximately 2 meters in this condition.

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PROGRAM-STRUCTURAL TYPOLOGY: MEETING

The meeting rooms are located in the middle portion of the tower, between the Entertainment floors and hotel suites, and consist of 2 floors. It has a medium span, and low floor height. The typology used to address this programmatic condition is presented, it aims to satisfy both the structural requirements and the lighting conditions; in a manner which works with the system and its gradients which attempt to efficiently create spatial conditions.

PROGRAM

SPAN WIDTH

HEIGHT

LOCATION

PROGRAM ABOVE

PROGRAM BELOW

Meeting Rooms

10m

4m

Tower Mid

Hotel

Meeting

CONDITIONS

RESULTANT ORGANIZATION

Span: - short to medium span, between hotel and amenities, theatre and ballroom. Transfer condition to hotel above.

Vertical Members:

Location: - high dead and live loads from all floors above - low lateral loads Program: - natural light requirements are not important, no or low natural light is acceptable.

- low floor height and flat floors are required.

The vertical members consist of two layers to achieve structural rigidity, these layers are enclosed to provide seperation between spaces. The members start with more porous and end with less porous cells near the connection with the transfer condition. The gradient is very slight and targets material efficiency. structural condition example

Horizontal Ground Members: The horizontal ground members are made up a single layer which is dense and allows for walkability.

Horizontal Ceiling Members: The horizontal ceiling members are made up of two layers for additional strength. They become less porous towards the edges due to higher loads and connection to vertical members.

The cell size is approximately 1 meter in this condition.

154

SYSTEM DEVELOPMENT

PROGRAM-STRUCTURAL TYPOLOGY: HOTEL

The hotel suites is located in the middle portion of the tower, between the meeting rooms and top restuarants / entertainment floors. It has a short span, and low floor height. The typology used to address this programmatic condition is presented, it aims to satisfy both the structural requirements and the lighting conditions; in a manner which works with the system and its gradients which attempt to efficiently create spatial conditions.

PROGRAM

SPAN WIDTH

HEIGHT

LOCATION

PROGRAM ABOVE

Hotel Level 5

5m

3m

Tower Mid-High

Hotel

CONDITIONS

RESULTANT ORGANIZATION

Span: - short span, repetitive throughout the tower for hotel rooms.

Vertical Members:

Location: - high dead and live loads from all floors above - low to medium lateral loads Program: - natural light requirements are important, medium to high natural lighting conditions are necessary.

- low floor height and flat floors are required.

PROGRAM BELOW Hotel

The vertical members consist of two layers to achieve structural rigidity, these layers are enclosed to provide seperation between spaces. The members start with more porous and end with less porous cells near the connection with the transfer condition. The gradient is very slight and targets material efficiency. structural condition example

Horizontal Ground Members: The horizontal ground members are made up a single layer which is dense and allows for walkability.

Horizontal Ceiling Members: The horizontal ceiling members are made up of two layers for additional strength. They become less porous towards the edges due to higher loads and connection to vertical members.

The cell size is approximately 1 meter in this condition.

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155

SOLAR EXPOSUREANALYSIS ANALYSIS SITE: ENVIRONMENTAL

SOLAR EXPOSURE ANALYSIS The secondary parameters towards applying the system architecturally is day lighting. The diverse programmatic requirements require variable lighting conditions andCentre therefore analysis would required on how The case study of the Aquatic in Beijing was chosen for itsbe structural performance andto building envelope. structural system had to respond to the seismic conditions on site as achieve theseThe conditions. well large span structural properties. The combination of geometrical non directional space frame structure and lightweight pneumatic ETFE facade skin system made it possible to The first analysis a solar analysisin of theof site, where the reduce gravity loads andis lateral loads. exposure The large dimensions depth the walls and roof provide possibility of largebuilding spanning structure and on highsite, interior ceilings. the threeof overallthemassing ofathe is placed and the Further percentage dimensional orthotropic loading bearing structure is an extremely efficient form of construction light on the surfaces is examined. that requires roughly 30% less steel than a column-and-beam system on a span of hundred meters and height of seven meters.

The ETFE pockets act as a protecting cover for the structure from the corrosive properties of the pool water and the polluted air of Beijing as well the facade acts as a mediating climate control system within the interior spaces of the building. Geometries from nature which have such performative aspects have been an inspiration to the PTW’s team.

In this test it is evident that the roof surfaces achieve the most solar exposure, followed by southern surfaces, while north surfaces obtain theThe least.

Thisofstudy provides initial input for towards theperformance design of case study the Aquatic Centre inan Beijing was chosen its structural and building envelope.

The structural to respond to the seismic conditions on site openings within the system,system and had how they could vary to achieve theas well large span structural properties. The combination of geometrical non directional space desired amount of day light at each program. frame structure and lightweight pneumatic ETFE facade skin system made it possible to reduce gravity loads and lateral loads. The large dimensions in depth of the walls and roof provide the possibility of a large spanning structure and high interior ceilings. Further the three dimensional orthotropic loading bearing structure is an extremely efficient form of construction that requires roughly 30% less steel than a column-and-beam system on a span of hundred meters and height of seven meters.

The ETFE pockets act as a protecting cover for the structure from the corrosive properties of the pool water and the polluted air of Beijing as well the facade acts as a mediating climate control system within the interior spaces of the building. Geometries from nature which have such performative aspects have been an inspiration to the PTW’s team.

SOLAR EXPOSURE ANALYSIS

156

SYSTEM DEVELOPMENT

SHADOW RANGE ANALYSIS SHADOW RANGE ANALYSIS

Furthermore, a shadow range analysis was performed for 4 different The facade of the Telus Headquarters in Vancouver is used to diagram the current state of times of the year.

The of skin thisfacade test is to investigate the parts of the double skin facade design.

Theaim double system is based on a multilayer principle, a combination of external layer, intermediate space and inneritself layer. Different layers contribute building that are self shaded by the building at different times of to different performative aspects, such as the external layer protects against weather and the year. This can become a further input towards creating variation improves the acoustic insulation against external noise. Within the external layer there are within program orventilation. single surface, whereinone part is more than openingsawhich allow for The air exchange the intermediate layershaded is activated by the solar induced thermalabuoyancy differentwithin wind effects. the other, creating further and gradient the system.

The intermediate layer is controlled by dampers on the top and fans on the bottom of the cavity to ensure a good airflow within both layers. In summer the exterior windows are open and let the air inside the cavity, it heats up and rises to the top of the cavity and exits through the dampers, while the interior windows stay closed to keep the heat outside of the spaces. In winter the dampers are closed and the fan is turned off as well the exterior and interior windows stay closed. This provides a thermal buffer zone which prevents the cold air from outside to enter the building.

AsInthe results show, the roof of the convention centre becomes shaded comparison to the double skin facade the Aquatic Centre has a three dimensional facade through different partssystem. of theTheyear, the extent thisofshading is also with integrated structural combination of twoof layers ETFE pockets with in-betweentherefore cavities used for seasonality the structural system similar to the skin variable, the and acts useperformative of program can bedouble utilized facade. It is designed for different seasonal conditions. In summer, when external weather within the design criteria. conditions are hot and humid, the internal layer is sealed. Through an opening on the bottom

edge air, cooled by passing over water around the building perimeter, enters the cavity between both layers and heats up, rises and is exhausted by roof vents.

Both layers are sealed during the winter months to minimise heat loss and in order to maximise the thermal performance of the envelope. Further the thermal mass of the water and concrete inside the building capture the heat collected during the day and release it in the evenings.

The three dimensional structural envelope is inaccessible, though can be entered for maintenance reasons. There is no geometrical differentiation between roof and wall within the whole system.

SPRING EQUINOX - 21 MARCH

SUMMER SOLSTICE - 21 JUNE

FALL EQUINOX - 21 SEPTEMBER

WINTER SOLSTICE - 21 DECEMBER

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157

SOLAR RADIATION ANALYSIS SITE: ENVIRONMENTAL ANALYSIS

SOLAR EXPOSURE ANALYSIS In a further step, a solar radiation analysis was performed, this analysis provides the solar intensity based on direct solar radiation and diffused solar radiation. direct solar radiation displays the intensity of light The case study of theThe Aquatic Centre in Beijing was chosen for its structural performance and building envelope.

Thetostructural system hadhitting to respond the seismic conditions on site as on surfaces due direct sunlight thetosurface.

The diffused solar well large span structural properties. The combination of geometrical non directional space radiation displays the intensity achieved through radiation, the measure frame structure and lightweight pneumatic ETFE facade skin system made it possible to is alsogravity related thislarge is transferred through the reduce loadsto andheat, lateralsince loads. The dimensions in depth of theradiation walls and roof provide the possibilityhigher of a largethan spanning andradiation. high interior ceilings. Further the three values become thatstructure of direct

The analysis shows that there is an intensity on all surfaces including the North Facades. This use of this analysis within the design would require further on the albedo of surfaces heat gainperformance within theand The case study study of the Aquatic Centre in Beijing was chosenand for its structural building envelope. The structural system had to respond to the seismic conditions on site as building.

dimensional orthotropic loading bearing structure is an extremely efficient form of construction that requires roughly 30% less steel than a column-and-beam system on a span of hundred meters and height of seven meters.

well large span structural properties. The combination of geometrical non directional space frame structure and lightweight pneumatic ETFE facade skin system made it possible to reduce gravity loads and lateral loads. The large dimensions in depth of the walls and roof provide the possibility of a large spanning structure and high interior ceilings. Further the three dimensional orthotropic loading bearing structure is an extremely efficient form of construction that requires roughly 30% less steel than a column-and-beam system on a span of hundred meters and height of seven meters.

The ETFE pockets act as a protecting cover for the structure from the corrosive properties of the pool water and the polluted air of Beijing as well the facade acts as a mediating climate control system within the interior spaces of the building. Geometries from nature which have such performative aspects have been an inspiration to the PTW’s team.

The ETFE pockets act as a protecting cover for the structure from the corrosive properties of the pool water and the polluted air of Beijing as well the facade acts as a mediating climate control system within the interior spaces of the building. Geometries from nature which have such performative aspects have been an inspiration to the PTW’s team.

Direct Solar Radiation / Daily Values

Diffused Solar Radiation / Daily Values

158

SYSTEM DEVELOPMENT

SOLAR ANALYSIS SHADOW RADIATION RANGE ANALYSIS

The facade of the Telus Headquarters in Vancouver is used to diagram the current state of double skin facade design. The double skin facade system is based on a multilayer principle, a combination of external layer, intermediate and inner Different layers contribute The average solar radiation, whichspace is based onlayer. both diffused and direct to different performative aspects, such as the external layer protects against weather and is displayed below.

The average results of this are somewhat improves the acoustic insulation against external noise.

Withinanalysis the external layer there are openings which allow for The air exchange inanalysis. the intermediate layer iscases, activated the by similar to those ofventilation. the solar exposure In both the solar induced buoyancy and different effects. program surfaces may production of thermal a detailed mesh for thewind required

enhance the resolution of the analysis provide which are The intermediate layer is controlled by dampers on and the top and fansresults on the bottom of the cavity to ensureata good both layers.

In summer the exterior are open applicable localairflow andwithin specific scales.

However in windows this case, the and let the air inside the cavity, itdue heatsto up and of the cavity and exits through resolution is sufficient the rises lackto the of top external factors affecting the dampers, while the interior windows stay closed to keep the heat outside of the spaces. In the exposure; only this is winteroverall the dampers are closed and self-shading the fan is turnedbecomes off as well a thefactor exteriorand and interior windows stay closed.

This provides a thermal buffer zone which prevents the cold air from investigated in detail separately outside to enter the building.

In comparison to the double skin facade the Aquatic Centre has a three dimensional facade with integrated structural system. The combination of two layers of ETFE pockets with in-between cavities used for the structural system acts performative similar to the double skin facade. It is designed for different seasonal conditions. In summer, when external weather conditions are hot and humid, the internal layer is sealed. Through an opening on the bottom edge air, cooled by passing over water around the building perimeter, enters the cavity between both layers and heats up, rises and is exhausted by roof vents.

Both layers are sealed during the winter months to minimise heat loss and in order to maximise the thermal performance of the envelope. Further the thermal mass of the water and concrete inside the building capture the heat collected during the day and release it in the evenings.

The three dimensional structural envelope is inaccessible, though can be entered for maintenance reasons. There is no geometrical differentiation between roof and wall within the whole system.

Average Solar Radiation / Daily Values

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DAY LIGHTING FACADE DAYANALYSIS LIGHTING ANALYSIS DAY LIGHTING ANALYSIS As part of the geometrical analysis a series of day light tests were executed to investigate the effect of different porosities and orientation. Throughout the tests three different porosities were chosen, for each porosity the test was carried out with the geometry once facing south In part continuation of analysis the analysis for of daylighting, an and once rotated fromenvironmental south. tests evaluate the amount daylight hitting a As of 45 thedegrees geometrical a seriesThe of day light tests were executed to investigate the surface geometries. effect ofbehind different porosities andwas orientation.

Throughout the tests threewith different analysis of the the system undertaken to be paired the porosities analysis were chosen, for each porosity the test was carried out with the geometry once facing south of the site.

Aanalysis series offrom day light tests were executed to investigate the The day sets a value for illuminance based onthe the amount location.ofFor New York City and oncelighting 45 degrees rotated south.

The tests evaluate daylight hitting a effect of6500 different porosities and within orientation.

Throughout the three a value of lux geometries. is set.

To set this value a comparative context, 0.27 lux tests is estimated surface behind the as the illuminance at a clear sky with full moon, and daylight between 5,000 25,000 lux, while different porosities were chosen, for each porosity the test was carried directday sunlight is analysis estimated as a30,000 - 100,000 lux. The results illustrate that the three tested The lighting sets value for illuminance based on the location.

For New York City out with the reasonable geometry once facing south and once 45 degrees rotated models lighting with higher porosity doisachieve a a value ofobtain 6500 lux is set. To day set this value values, within a cells comparative context, 0.27 lux estimated from south.

The testssky evaluate the amount daylight surface percentage of area the dayfull light criteria. as the illuminance atsatisfying a clear with moon, and daylightof between 5,000hitting - 25,000alux, while direct sunlight estimated as 30,000 - 100,000 lux. The results illustrate that the three tested behind the isgeometries. models obtain reasonable day lighting values, cells with higher porosity do achieve a percentage of area satisfying the day light criteria.

Daylight Factor : 50 - 100%

The day lighting analysis sets a value for illuminance based on the location. For New York City a value of 6500 lux is set. To set this value within a comparative context, 0.27 lux is estimated as the illuminance at a clear sky with full moon, and daylight between 5,000 - 25,000 lux, while direct sunlight is estimated as 30,000 - 100,000 lux. The results illustrate that the three tested models obtain reasonable day lighting values, cells with higher porosity do achieve a percentage of area satisfying the day light criteria.

Daylight factor mapped on an analysis grid.

Daylight Factor : 50 - 100%

Daylight factor mapped on an analysis grid.

N N Porosity : 0.14 Cell Aggregation prototype 01-

Cell Aggregation prototype 02- Porosity : 0.23

Cell Aggregation prototype 03- Porosity : 0.32

Cell Aggregation prototype 01- Porosity : 0.14 45.degree orientation

Cell Aggregation prototype 02- Porosity : 0.23

Cell Aggregation prototype 03- Porosity : 0.32

Cell Aggregation prototype 01- Porosity : 0.14

Cell Aggregation prototype 02- Porosity : 0.23

Cell Aggregation prototype 03- Porosity : 0.32

Cell Aggregation prototype 01- Porosity : 0.14

Cell Aggregation prototype 02- Porosity : 0.23

Cell Aggregation prototype 03- Porosity : 0.32

Daylight Factor : 50 - 100%

45.degree orientation

Daylight Factor : 50 - 100%

N N

Note :

All analysis based on recorded exterior Lux

value in New York City - 6500 Lux. Daylight factor mapped on analysis analysis based grid in on percentage in Lux Note : All recorded(%) exterior comparison the exterior daylight.

Results indicate value in NewtoYork City - 6500 Lux. Daylight factor that all daylight factors are desirable mapped on analysis grid in within percentage (%) limits. in

comparison to the exterior daylight. Results indicate that all daylight factors are within desirable limits.

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SYSTEM DEVELOPMENT

DAY LIGHTING ANALYSIS DAY LIGHTING ANALYSIS As part of the geometrical analysis a series of day light tests were executed to investigate the effect of different porosities and orientation. Throughout the tests three different porosities were chosen, for each porosity the test was carried out with the geometry once facing south The were further bylight analysing theamount effect of layering andtests 45 degrees rotatedcontinued from south.

The tests evaluate the daylight hitting As part ofonce the geometrical analysis a series of day tests were executed to of investigate the a surface behind the geometries. effect of different porosities and orientation.

Throughout the obtained tests three different porosities a specific patch multiple times. The results were also quite were chosen, for each porosity the test was carried out with the geometry once facing south predictable, where thefrom increase inilluminance layers resulting in a of decrease in day asouth. value for based onamount the location.

For New Yorka City and The onceday 45 lighting degreesanalysis rotated sets The tests evaluate the daylight hitting lighting.

However degree of this decrease is not substantial when a value of 6500 lux is the set. To set this value within a comparative context, 0.27 lux is estimated surface behind the geometries. as the illuminance at a clear skyas withthose full moon, and very daylighthigh between 5,000 - 25,000 while comparing patches such with porosity.

The lux, factor sunlight is estimated 30,000 - 100,000 lux.

Theonresults illustrate that theYork three tested The direct day lighting analysis sets a as value for illuminance based the location.

For New City that should be kept in mind that the amount of day lighting increases models obtain dayvalue lighting values, cells withcontext, higher0.27 porosity achieve a a value of 6500 lux isreasonable set. To set this within a comparative lux is do estimated with the opening sizeskyofwith the cells, therefore a low porosity celllux, can still percentage of at area satisfying thefull day light and criteria. as the illuminance a clear moon, daylight between 5,000 - 25,000 while direct sunlight as purposes 30,000 - 100,000 The results that the three be used foris estimated structural andlux. satisfy lightillustrate requirements if ittested has a models obtain reasonable day lighting values, cells with higher porosity do achieve a suitable opening size. percentage of area satisfying the day light criteria.

Daylight Factor : 50 - 100%

The effect on orientation is not significant and was not tested in the second patch. The reason behind this is that due to the rotation of the sun throughout the day, the total amount of day light will not be affected if the cell is slightly tilted, since the spaces will still gain day light when the sun is at a slightly different angle.

However, the accuracy and resolution of the Ecotect software was not very high, in some cases the results were conflicting and some adjustments were required.

Daylight factor mapped on an analysis grid.

Daylight Factor : 50 - 100%

Daylight factor mapped on an analysis grid.

N Cell Aggregation prototypeN01- Porosity : 0.14

Cell Aggregation prototype 02- Porosity : 0.23

Cell Aggregation prototype 01- Porosity : 0.14 45.degree orientation

Cell Aggregation prototype 02- Porosity : 0.23

Cell Aggregation prototype 03- Porosity : 0.32 Cell Aggregation prototype 03- Porosity : 0.32

Daylight Factor : 50 - 100%

45.degree orientation

Daylight Factor : 50 - 100%

N N Cell Aggregation prototype 01- Porosity : 0.14 Cell Aggregation prototype 01- Porosity : 0.14

Note :

Cell Aggregation prototype 02- Porosity : 0.23 Cell Aggregation prototype 02- Porosity : 0.23

Cell Aggregation prototype 03- Porosity : 0.32 Cell Aggregation prototype 03- Porosity : 0.32

All analysis based on recorded exterior Lux

value in New York City - 6500 Lux. Daylight factor on analysis grid percentage (%) in Notemapped : All analysis based oninrecorded exterior Lux comparison to City the exterior daylight.

Results indicate value in New York - 6500 Lux. Daylight factor that all within desirable mapped on daylight analysisfactors grid in are percentage (%) in limits. comparison to the exterior daylight. Results indicate that all daylight factors are within desirable limits.

CELLULAR COMPLEXITY

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STRUCTURAL DEVELOPMENT

In parallel to the lighting analysis, the structure was investigated in further detail. Based on the allocated programs and morphology, a range of structural conditions was developed. These conditions are divided into transfer conditions and gradient conditions. In reality both conditions contain porosity gradients, the difference is in intensity and scale.

CHARACTERISTICS

DESCRIPTION

GRADIENT SCALE estimate

CELLULAR ORGANIZATION

Transfer Type A

-Transfer between two spans -One span Above 20m -Transfer Ratio above 2

This condition occurs where there is transfer between a large span and a span that is atleast 2 times smaller.

~4m to ~8m

Transfer Type B

-Transfer between two spans -One span Above 20m -Transfer Ratio below 2

-deep structure -dense at corners -dense at the top -very porous n ear bottom

This condition occurs where there is transfer between a large span and a span that is similar.

~3m to ~6m

Transfer Type C

-Transfer between two spans -Spans Below 20m -Transfer Ratio above 2

This condition occurs where there i s transfer between a regular span and a span that is atleast 2 times smaller.

~1m to ~3m

Transfer Type D

-Transfer between two spans -Spans Below 20m -Transfer Ratio below 2

This condition occurs where there is transfer between a regular span and a span that is similar

~0.5m to ~2m

Gradient Local

Gradient r equired within program f loor f or v iew or l ocal structural optimization

This condition is where a g radient is needed as part of the program requirement and/or its s tructure, typically occurs at roof conditions

Program Floor Height

Gradient Global

Gradient across multipe f loors for optimization with g lobal structural loads

This condition is where a gradient is needed across multiple floors of similar span for structural optimization

Program Total Levels Height

STRUCTURAL CONDITION

LOADS: LATERAL DEAD

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Four different transfer conditions were devised, the variation between them is the span length and ratio between the two transfers. For the gradient conditions they can exist in a local area or in a global form.

The local gradient attempts to address programmatic conditions or to create efficient use of material. The global gradient connects multiple gradients within the structure.

FORCE: DIRECTION

High

Low

Horizontal

Mid

Mid

Horizontal & Vertical

Low

High

Vertical

CELL

SYSTEM DEVELOPMENT

-multi-layered -shallow structure -dense at corners -dense both at t he top and bottom

-multi-layered case specific

-elongated cells near bottom, -constained cells at top

STRUCTURAL CONDITIONS

The devised conditions are displayed on different locations of the building as shown in the section below. Transfer conditions occur whenever there is a change in span; the type becomes dependant on the span change. Local Gradients are outlined in locations such as the top floor casino and the roof of the convention centre. This is where detail is required for lighting, view or roof walkability.

Local Gradient

~ 45m

Transfer Type B

~ 30m

Transfer Type D

~ 15m

Transfer Type C

High Lateral Low Dead & Live

Medium Lateral Global Gradient

~ 5m

~ 10m ~ 15m ~ 45m

Transfer Type D

~ 75m ~ 7m ~ 4m

Local Gradient

Transfer Type D Transfer Type A

Medium Dead & Live

Low Lateral High Dead & Live

Transfer Type A

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SYSTEM ARCHITECTURAL APPLICATION

As a further study, a segment of the building was selected where the system is applied in finer detail illustrating various gradients and variations within the facade to address different properties. This segment includes a North-West Corner which contains convention halls, a theatre, hotel amenities, restuarants, meeting rooms and hotel suites.

The conditions are outlined besides each program, and the type of gradient or transfer condition is defined. Furthermore, the lighting conditions of the program are also defined, some data refers back to the initial program data catalogue. This gives firsthand information towards the application of the algorithm and the intensity and scale of gradient for each program surface.

hotel suites

meeting rooms

entertainment / amenities

STRUCTURAL CONDITIONS

LIGHT CONDITIONS

Global Gradient

High Natural Light

Transfer Type D Medium Natural Light

Transfer Type D

Low Natural Light

Transfer Type A

No Requirement

theatre

Transfer Type B exhibition / convention centre

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SYSTEM DEVELOPMENT

No Requirement

FACADE DAY LIGHTING ANALYSIS

An initial patch was developed for each of the programs, where the cell size corresponds to the requirements of this program structurally, visually and for day lighting. Furthermore, two additional patches are generated to examine the effect of a north or south oriented facade.

The north facade receives less day light and would therefore allow for bigger openings, and the south facade would have smaller openings to avoid solar heat gain.

WEST FACADE

NORTH FACADE east - west HOTEL

Hotel

HOTEL

MEETING

Meeting

MEETING

ENTERTAINMENT

SCHEMATIC 3D SECTION north

east - west

north

north

HOTEL HOTEL

HOTEL

HOTEL

HOTEL

HOTEL

HOTEL

MEETING MEETING

MEETING

MEETING

MEETING

MEETING

MEETING

ENTERTAINMENT ENTERTAINMENT

ENTERTAINMENT

ENTERTAINMENT

THEATRE THEATRE

THEATRE

THEATRE

THEATRE

THEATRE

THEATRE

CONVENTION CONVENTION

CONVENTION

CONVENTION

Amenities

ENTERTAINMENT

SOUTH FACADE east - west

A schematic 3D section was generated based on these programs to display the assemblage of programs and the cellular arrangement and variation within the various programs and transfer conditions, within an overall gradient.

THEATRE

Theatre

THEATRE

CONVENTION

Convention

CONVENTION

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GRADIENT CONDITIONS

The 3D section below alongside the corner perspective display the allocation of programs within the building, and the way the cells adapt to address each program differently. What is important is that a global gradient is still maintained in the system, and there are smooth transitions from one part to another. The architectural and spatial potential of this system are to be investigated further.

166

SYSTEM DEVELOPMENT

CELLULAR COMPLEXITY

167

FURTHER POTENTIALS OF THE SYSTEM

The developed system displayed various potential within the systematic and performative sides of architecture, where there are further potentials spatially and architecturally. Several spatial typologies were produced to examine some of these potentials The earlier study of how to integrate the facade and the program to make the façade inhabitable tests how the interaction of façade and program could work. This was carried out by changes in cell size and porosity according to specific programs, the result however was somewhat conventional. In the following typologies a number of conditions are investigated. The integration of accessible cells and the creation of intricate spaces are part of the possibilities of making the façade inhabitable in certain desired areas.

Terraced spaces can be created on the inside and on the outside of the building. In this case the aspect that requires further resolution ishas the transition from the floor plates to the façade. The aim should be not to simply use conventional floor plates but to integrate them in the cellular arrangement. The typologies allow for an adaption in the design process to spatial programs and their influences. The innovative aspect in this study, in comparison to the earlier developed example is the integration of a continuous - rather than an abrupt, pixelated change in thickness of layers.

The first spatial typology investigates the involvement of not only a gradient in cells, but also a spatial gradient. Therefore the spaces would be designed in a similar manner to the system, for its inputs.

SPATIAL GRADIENT IN ADDITION TO CELLULAR GRADIENT

168

INHABITABLE COURTYARD CONDITIONS

SYSTEM DEVELOPMENT

Furthermore, the second typology investigates the creation of light well or courtyard condition which is inhabitable, the potential is to generate this condition through substantially larger cells where this condition becomes part of the inhabitable cellular system. The design of this courtyard can be optimized to the natural lighting conditions of the site it is located in.

Finally, the last condition visualizes the effect of creating a direct change in program towards a courtyard condition, this is where the aspect of building up redundancies and additional material becomes of interest, returning to the natural cellular systems. This may include form-finding methods which utilize environmental criteria to generate a morphology.

The third typology considers branching of the cellular system, and the possibility of inhabiting spaces in between the branching of the system. The interest would lie in investigating branching logics and their efficiency towards structural parameters. In this case it is a downside branching that is illustrated, the opposite can also hold potential.

INHABITABLE FACADE CONDITIONS

FACADE VARIATION WITH SPATIAL VARIATION

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169

INHABITABLE FACADE GRADIENT

170

SYSTEM DEVELOPMENT

FACADE COURTYARD CONDITION

CELLULAR COMPLEXITY

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172

SYSTEM DEVELOPMENT

SYSTEM DEVELOPMENT overview The system development phase investigated performative aspects in higher details, the strategy was to set out a number of conditions for each performative property. Structurally, a range of conditions were defined, and for day lighting a number of levels where also defined.

Throughout this process we developed a North-West corner of the building which demonstrated the abilities of the system in responding to specific program, creating a gradient and being structurally coherent throughout. This was illustrated in patches, threedimensional sections and corner perspectives.

This process was further continued by utilizing environmental analysis software to obtain analysis data that is specific to the building and site, and furthermore to the system. This allowed us to link the system, to the proposed architecture at the given site.

However, throughout the application it was evident that the architectural and spatial potential of this system is very valuable, therefore we examined these aspects in a typological study. This study investigated a number of spatial conditions which were initially independent of performative aspects.

However, at further investigation of such conditions there are several opportunities to inherit them within the system. Most conditions refer to aspects within natural systems and their development of redundancy and excess material, which is still effective and not redundant in many situations.

At this stage, the application of the system was limited to a segment of the building, allowing us to develop a more refined resolution. The system was developed through program patches, where these patches directly corresponded to the specific program needs. The challenge was then to create a gradient between those patches. The parametric design tool and its use of direct numerical parameters aided this process. We were able to generate specific iso-curves for gradients on the surfaces. Furthermore, we can input the gradient ranges and therefore they become interlinked from one program to another. The ending gradient of one program becomes the starting gradient of another.

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JURY COMMENTS The research was presented at the Architectural Association in London to an international jury which included: The jury was held on the 20th of August 2012 at the Main Lecture Hall, 36 Bedford Square.

Francis Aish, Foster + Partners Selim Bayer, Flat C Jeroen Janssen, AKT II Tom Lea, Amanda Levete Architects Wolf Mangelsdorf, Buro Happold Theo Spyropoulos, AA DRL Jordi Truco, ELISAVA / HYBRIDa In addition to the EmTech Faculty: Michael Weinstock George Jeronimidis Evan Greenberg Mehran Gharleghi Furthermore, the competition entry for the suckerPUNCH competition, was reviewed by a panel of international jury members which included: The jury reviewed the entry which was submitted on the 13th of August 2012, an earlier stage of the research.

Kutan Ayata, YOUNG & AYATA Ezio Blasetti, Ahylo Studio David Erdman, davidclovers Marc Fornes, THEVERYMANY Ferda Kolatan, su11 Architecture & Design Craig Scott, IwamotoScott Architecture Marcelo Spina, P-A-T-T-E-R-N-S Mike Szivos, SOFTlab Abigail Coover, hume coover studio, suckerPUNCH Nathan Hume, hume coover studio, suckerPUNCH The suckerPUNCH jury awarded the Cellular Complexity competition entry Second Place.

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A R C H I T E C T U R A L A P P L I C AT I O N

Several topics set the discussion for the EmTech jury, this included the referencing of natural systems and the way in which they operate with material redundancies. The jury suggested a comparison of cost-efficiency between conventional building systems and what is being proposed by this research. Furthermore, the morphology within the architectural application was discussed, where the jury pointed out the potentials within the system of creating inhabitable cellular spaces and their continuation. This may include the inclusion of curved spaces within the system as part of both the potential and research into cellular systems. As part of our research we investigated the performative and definitive aspects of the system. The exploration of such spatial and architectural qualities are part of the intention and further development.

As for the suckerPUNCH competition. Feedback was received from two of the jury members as follows: Craig Scott (IwamotoScott Architecture): The underlying ideas regarding a responsive, scripted structural porosity are compelling, and the site strategy seems promising. Yet, the tower’s overly boxy form and the lack of specificity of the casino interior seem like missed opportunities. Curiously, the spacemaking potential of the designer’s “3-D sphere packing” and “3D voronoi based on pores” is not very present other than as a gradated space frame of sorts—particularly not as a habitable condition, at least not as it is currently rendered and drawn in section.

Marcelo Spina (P-A-T-T-E-R-N-S): This is a very interesting project at the level of the research that it presents. The approach at the problem of packing and cellular partition is very rigorous and deserves to be mentioned. However, given the manifest cellular interest on the part of the authors, the overall deployment of the project falls very much within the morphodynamic “flow”like genre, one which this site has seen before in excellent projects such as West Side Convergence by Reiser+Umemoto. It seems that if the research is pursued seriously, not only at the level of research but also in its architectural design application, one would have to seriously consider issues of scale of components in relation to size of the whole, apses of multi directionality very much found in any cellular system, and the reduction of linear flow as the main feature of the project.

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CONCLUSION This research first initiated through an interest in the coherence of natural systems, where cellular systems were found to be particularly interesting due to their efficient abilities in addressing a variety of performative properties, by integrating morphology with material and structure. The crucial aspect in cellular systems is their occurrence within a wide range of scales. This fact implies that such systems are able to adapt and perform within multiple scales and purposes. Therefore, the scalability of cellular systems and their geometries was viable within an architectural scale. The natural systems informed the research with the underlying principle of cellular geometries, from which two-dimensional and three-dimensional space-packing geometries were developed for an architectural application. The aspect of most interest within these systems was the ability to create variation and changes in porosity.

Eventually, the gradient condition where porosity changes gradually became a focus within the application and was investigated programmatically for an architectural context.

Throughout the development of the research and architectural application, the emergent technologies in design, analysis and fabrication were of particular use and influence towards the project. In terms of design, the parametric computational methods allowed for the underlying set-up of the system and the introduction of a range of variables to control different parts of the system using algorithms; this would otherwise be unachievable through traditional methods given the current level of control. As the process progressed, the algorithms and digital models became particularly heavy due to the large amount of data. Given this data dilemma, the integration of analysis workbenches within the process was computationally impossible.

Therefore, the analysis methods were used to generate comparative guidelines which inform the algorithmic parameters. These included testing site conditions, or a range of developed patches

176

which lead to assumptions on the performance of the system. In order to develop an accurate use of these analysis tools, comprehensive cataloguing and documentation would be required to precisely address performative properties. This would create an endless loop-hole for optimization and testing, in this context we limited our tests to extreme and median variations of the system. The aspect that is even more challenging within the analysis tools is the design for combinatory performance aspects, where more than one criteria is to be satisfied. The current approach to such challenges involves evolutionary computation, where multiple iterations are generated and evaluated for fitness in a number of criteria. This vwas an option within the system, though given the computational load of the geometries and algorithm, it would be particularly intensive.

The emergent digital fabrication methods including additive manufacturing were considered within the fabrication of the complex geometries. Due to the limitations in scale and costs, these technologies were found to be best combined with traditional fabrication methods. This involved the development of a hybrid fabrication method includes the use of customized joints and standardized elements.

This involves complex 3D printed or cast joints in combination with planar struts and plate elements.

The intent is to utilize the advanced technology where it is required within the system. Furthermore, materials which include structural composites and highly insulating translucent panels become of interest for further investigation. In parallel to the fabrication development, the systems geometrical development was in process, the results from the system were constantly evaluated with the given fabrication methods for viability. The synthesis was to develop the system while maintaining a viable ratio of customized joints to standardized joints. In a large scale application, the quantity of joints allow for the development of multiple variations at the same efficiency and feasibility of a single variable. These

limitations are particularly tied to the scale of the project, if the system was developed on a pavilion scale, both analysis and fabrication technologies would offer further opportunities within the design and procurement of the system.

The choice of the tower typology allowed for an architectural application at a large scale. This unveiled the opportunity of developing hierarchy within the system through the developed gradients.

This means that the tower is to operate at an urban scale through a global gradient, and at a programmatic scale through a local gradient; the challenge was to integrate these two together. The application of the system was tested architecturally on a portion of the tower. The intent was to examine the system on a given site and program, therefore these two parameters heavily influenced the architecture and system design. However, as a research application these parameters were conservatively manifested into a basic form, to test the potentials of the system in variation. The overall cell distribution resulted in a dense structure. Although the system targets material efficiency in structure, and the use of material where it is most required; the current optimization is based on structural assumptions from comparitive geometrical tests. Therefore, precise optimization simulations would be required to determine the redundancies within a refined material and structural strategy.

In terms of architectural design, the detailed development of the tower-core and circulation is an aspect to be further developed. The technical and mechanical aspects have potential for integration within the system. This includes the unavoidable cores, not due to structure, but also circulation and mechanical transport of water and waste.

The opportunity may develop through transition mechanical spaces which work within the gradient to shift between programs, and operate the tower.

Although the system was exploited at the level of the cell in the overall design, there are architectural and spatial qualities to be revealed. The potential of a smooth gradient would result in higher structural performance, thus helps to loosen the very dense aggregation of cells. Furthermore it creates spaces which are of high architectural and spatial quality. A higher variation in cell size could allow inhabitability of the facade which in a further step makes the dense aggregation of cells justifiable. It is also a step away from the current rectilinear appearance of the building if the mentioned smooth transitions in cell size are considered. Furthermore, a spatial gradient is an aspect for future development of the programmatic arrangements, where the program itself also operates in a gradient.

In Conclusion, this research develops an architectural system which ¬utilizes efficient geometries and develops variation through a cellular system to address a multitude of properties in different programmatic and environmental site conditions.

The research further utilizes emergent technologies in design, analysis and fabrication. The abstraction of underlying principles from natural systems has driven the coherence of the system and its hierarchy in addressing properties at different scales. The further development of this research and system would refer back to these natural systems and their potential to develop spatial and architectural qualities alongside the performative qualities currently displayed. This aspect would examine the concepts of redundancy and material build-up in relation to spaces and the development of a spatial gradient within the inputs for the system.

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SELECTED BIBLIOGRAPHY books

presentations

Addington, M., & Schodek, D. L. (2005). Smart materials and new technologies for the architecture and design professions. Oxford: Architectural.

Cox, S. Solid Cellular Materials. University of Wales Aberystwyth.

Carroll, S. B. (2005). Endless forms most beautiful: the new science of evo devo and the making of the animal kingdom. New York: Norton.

Jeronimidis, G. (2004). Biodynamics. Emergence: morphgenetic design strategies, London: Wiley-Academy.

Knaack, U., & Klein, T. (2008). Façades. Rotterdam: 010 Publishers.

Gibson, L. J., & Ashby, M. F. (1997). Cellular solids (Second ed.). Cambridge: Cambridge university press.

Hausladen, G., & Saldanha, M. d. (2007). Climate skin: concepts for building skins that can do more with less energy. Basel: Birkhäuser

Ju, J. Research Vision: Smart Cellular Materials, I )Energy Efficient Design, ii) Energy Harvesting Structures . Clemson University, Cedar - Clemson Engineering Design Applications and Research.

Rosa, M. E. (2007). Cellular Materials: Structure and Properties.

ICEMS-Instituto de Ciência e Engenharia de Materiais e Superfícies, Departamento de Engenharia de Materiais, Instituto Superior Técnico, Universidade Técnica de Lisboa.

Strauß, H. Additive Manufacturing in architecture and building construction. xx: TU Delft, Facade Research Group, Hochschule Ostwestfalen-Lippe, University of Applied Science.

dissertations

Hensel, M., Menges, A., & Weinstock, M. (2010). Emergent technologies and design. Oxon, [U.K.: Routledge.

McQuaid, M., & Beesley, P. (2005). Extreme textiles: designing for high performance. New York: Smithsonian Cooper-Hewitt, National Design Museum Pawlyn, M. (2011). Biomimicry in architecture. London, UK: Riba Publishing Pearce, P. (1990). Structure in nature is a strategy for design.

Cambridge: MIT Press. (Original work published 1978)

Ajdari, A. (2008). Mechanical behavior of cellular structures: a finite.

Boston: IRis Notheastern University, Department of Mechanical and Industrial Engineering.

Satira, R. (2010). Cellular Solid Morphologies, Inhabitable Cellular Structure. London, Architectural Association: Emergent Technologies and Design Tenu, V. (2009). Minimal surfaces as self organizing systems - A particle spring system simulation for generating triply. London: Bartlett School of Graduate Studies.

Reiser, J., & Umemoto, N. (2006). Atlas of novel tectonics. New York: Princeton Architectural Press.

Weinstock, M. (2006). Self-Organisation and Material Constructions. Techniques and technologies in morphogenetic design, London: Wiley-Academy.

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articles Colding, T. H., & Minicozzi, W. P. (2005). Shapes of embedded minimal surfaces. Cambridge: Department of Mathematics, Massachusetts Institute of Technology.

Stampfl, J., Wöß, A., Fratzl, P., & Seidler, S. (2002). Rapid prototyping of ceramic and polymeric cellular materials. Vienna: IFMBE Proceedings.

Ehrlich, H., & Worch, H. (2007). Sponges as natural composites: from biomimetic. Dresden: Max Bergmann Center of Biomaterials, Institute of Materials Science.

Tekoglu, C., & Onck, P. R. (2005). Size effects in the mechanical behavior of cellular. Groningen: Journal of materials science.

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Wadley, H. N. (2006). Multifunctional periodic cellular metals. xx: Philosophical Transactions of the royal society.

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web Algorithms in nature drive architecture research, parametric designs - YouTube. (n.d.). YouTube - Broadcast Yourself.. Retrieved April 29, 2012, from http://www.youtube.com/watch?v=Yn_Xarm6Rj8 American Cement Building – Los Angeles - Retrieved May 7, 2012, from http://populuxebooks.com/blog/index.php/american_cement_ building_los_angelesAmerican Cement Building – Los Angeles Biodegradable synthetic resin replaces vital body parts. (n.d.). Phys.

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SELECTED BIBLIOGRAPHY

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ReubenMiller . Retrieved April 29, 2012, from http://reubenmiller. typepad.com/my_weblog/2007/12/early-modern-co.html Soap Foam Cahir - video- Retrieved May 7, 2012, from http://vimeo.com/7261475 Shenzhen International Airport under construction - Massimiliano + Doriana Fuksa | Simbiosis News. (n.d.). Simbiosis News | Architecture, Design and Vanguard. Retrieved April 30, 2012, from http://simbiosisgroup.net/27870/shenzhen-airport-underconstruction-massimiliano-doriana-fuksa WertelOberfell. WertelOberfell. Retrieved April 30, 2012, from www. platform-net.com Ted Talk in Salzburg by Siavash Mahdavi - State of the Art in 3D printing - video Retrieved May 7, 2012, from http://www.youtube.com/ watch?v=MU3W-RrJDT4 Titanium Foam. (n.d.). x. Retrieved May 2, 2012, from medgadget. com/2010/09/titanium_foam_as 3dma_rock Primer. Stony Brook University - Department of Applied Mathematics & Statistics. Retrieved May 2, 2012, from http://www. ams.sunysb.edu/~lindquis/3dma/ Sea Urchin Blog - Retrieved May 26 2012, from http://echinoblog. blogspot.co.uk/2010_05_01_archive.html Structure-property relationships of a biological mesocrystal in the adult sea urchin spine, J. Seto, Y. Ma, S. Davis, F. Meldrum, A. Gourrier, Y.-Y. Kime, U. Schilde, M. Sztucki, M. Burghammer, S. Maltsev, C. Jäger, and H. Cölfen, PNAS 109, 3699–3704 (2012). - Retrieved May 26 2012, from http://www.pnas.org/ content/109/10/3699 systemicprocess + responsive skin by David Jaubert- Retrieved April 30, 2012, from http://www.core.form-ula.com/2008/04/08/systemicprocess/ and http://davidjaubert.com/projects/porous-wall/ Voronoi relaxation study - Retrieved May 7, 2012, from http:// livecomponents-ny.com/

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182

APPENDIX This appendix includes various parts of the research which are not presented earlier. This includes the computational algorithms used to generate the system with further explanation on how they operate.

Additionally a number of photographs of the 3D printed geometries have been included Furthermore, the appendix includes research which contributed towards the development of the research however did not become particularly relevant within the overall scheme presentation.

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FACADE PROPERTIES

Opposing to conventional facades, which consist of different layers to address various properties, the suggested system inherits the required structural and performative aspects within one single system. Instead of having several separate sub-systems, one intricate system, adaptable to given environmental conditions, in the design and planning phase is developed.

INSTEAD OF DIFFERENT LAYERS OF SEPERATE SYSTEMS

+

+

The studied properties of cellular systems were analyzed and in a further step related to the properties a façade has to address. This helped to understand how a structure in a cellular system looks like in order to address a certain property and how this can be abstracted for a façade system.

The properties which have to be addressed in the development of the façade include structure, insulation, ventilation, weather and climate protection, visual aspects as sunlight while respecting the difference between summer and winter. Often, requirements of façade systems are contractive - Enclosure and insulation has to be guaranteed but at the same time lots of light has to enter the building. A proper insulation glazing can improve the façade performance in this aspect significantly.

Also, the layer thickness is an important factor as insulation is not linearly proportional to the layer thickness. Another important factor is the solar control which often contradicts with the light requirements.

Further, a decision has to be take if the user has access to the system and control ventilation1. The structural building skin is an alternative suggestion to the internal building core1.

REQUIRED PROPERTIES INHERITED IN ONE SINGLE SYSTEM

The process of how to design the façade by use of the cellular system was developed. There are certain properties which are developed for the whole building - such as structure and visual aspects- and properties which are addressed on a smaller scale including ventilation and insulation. For each property a range of cell scales and porosities is defined.

PROPERTIES PROPERTIES CELLULAR CELLULAR SYSTEMS SYSTEMS

PARAMTERS PARAMTERS

FACADEFACADE PROPERTIES PROPERTIES

structural structural 2D + 3D structures 2D + 3D structures deformationsdeformations with forces: with forces: in-plane: shear deflection - bending and rotation and rotation in-plane: shear deflection - bending out-of plane out-of forces:plane generally extension orextension compression forces: generally or compression

thermalthermal low thermal lowconductivity thermal conductivity in foams in foams requires: requires: -small cell size -small cell size -high porosity -high porosity -low convection -lowand convection conduction andproperties conduction properties of material and of material gas used and gas used

acousticacoustic

geometry (optimized geometryor(optimized variable/random) or variable/random) cell properties cell(size, properties thickness, (size,etc.) thickness, etc.)

- material- material

(and properties: (andmodulus, properties: etc.) modulus, etc.)

thickness of thickness cellular system of cellular system temperature temperature difference across difference across

- cell size- cell size - porosity- porosity - material- material - gas in pores - gas in pores

- porosity- porosity - open cell - open not closed cell not cell closed cell

1- Hausladen, G., & Saldanha, M. d. (2007). Climate skin: concepts for building skins that can do more with less energy. Basel: Birkhäuser

184

cell shapecell shape cell packing cell packing porosity porosity density density

- for optimization - for optimization at scale at scale

sound absorbing sound absorbing

(that comes (that from comes within the from same within room/space) the same room/space) -porous materials -porous absorb materials sound absorb and sound and convert it to heat convert (negligable) it to heat (negligable) -must be open -must celled be open celled -must be open -must celled be open celled

STRUCTURAL STRUCTURAL

- arrangement - arrangement of cells and of cells structure: and structure:

APPENDIX

STRUCTURE STRUCTURE thicknessthickness material material ENVIRONMENT ENVIRONMENT site data site data temperatures temperatures

THERMAL THERMAL

ACOUSTIC ACOUSTIC

SPATIAL SPATIAL

VISUAL VISUAL

ENVIRONMENTAL ENVIRONMENTAL

FACADE DESIGN PROCESS

INPUTS

POSSIBLE OUTPUTS VARIATION

SITE INFO: -Latitude(sun) -Wind data(wind) INPUTS -Site Outline (perimeter) -Surrounding Buildings

TYPOLOGY: -Height -Programmes -Spatial Facade Areas -Structure

ATTRACTORS: -Light -Ventilation -Visual -Loads/Structure

BUILDING: FACADE: -Programme Plan -Voids in Facade/Spatial -Building Morphology POSSIBLE OUTPUTS -Lattice Size -Floor Heights -Gradients

CELLS: -Cell Size -Cell Geometry -Cell Porosity

SITE INFO: -Latitude(sun) -Wind data(wind) -Site Outline (perimeter) -Surrounding Buildings

TYPOLOGY: -Height -Programmes -Spatial Facade Areas -Structure

ATTRACTORS: -Light -Ventilation -Visual -Loads/Structure

BUILDING: -Programme Plan -Building Morphology -Floor Heights

CELLS: -Cell Size -Cell Geometry -Cell Porosity

PROPOSED PROCESS STEPS

STEP001

VARIATION

FACADE: -Voids in Facade/Spatial -Lattice Size -Gradients

re-evaluate / validate

STEP003a

STEP003b

STEP004

OVERALL LATTICE PROPOSED PROCESS STEPS STRUCTURE re-evaluate / validate

STEP002

SUN / LIGHT / VISUAL

WIND & VENTILATION

INSULATION, ETC.

Inputs:

Inputs:

Inputs:

Inputs:

Inputs:

STEP001 -Site Data -Building Programmes OVERALL LATTICE -Spatial Facade Areas

STEP002 -Overall Lattice -Structural Loads Gradient; STRUCTURE resulting in subdivision

STEP003a -Orientation, and surroundings -Site Latitude SUN / LIGHT / VISUAL -Overall Lattice and Structure

STEP003b and surroundings -Orientation, -Site Wind wind paths WIND & Data, VENTILATION -Overall Lattice and Structure

INSULATION, ETC.

Inputs: Outputs:

Inputs: Outputs:

Inputs: Outputs:

Inputs: Outputs:

Inputs: Outputs:

-Site Data -Overall Building Lattice -Building based on Programmes programme, with -Spatial Facade Areas spatial facade areas.

-Overall Lattice -Lattice Subdivision -Structural Loads Gradient; -Primary Cell Layout: resulting in subdivision size based on subdvision

-Orientation, and surroundings -Developed Lattice with: -Site Latitude variable thickness -Overall Lattice and Structure porosity

-Orientation, and surroundings -Developed Lattice with : -Sitevariable Wind Data, wind paths thickness -Overall Lattice and variable porosityStructure

Outputs: (multiple iterations)

Outputs: (multiple iterations)

-Developed Lattice with: variable thickness Combinatorial Optimization? porosity

-Developed Lattice with : variable thickness variable porosity

(multiple iterations) HEIRARCHY level ii

(multiple iterations)

porosity based on loads Outputs: Outputs: plan sections generated -Primary Hierarchy based on based on programme structural loads -Overall Building Lattice -Lattice Subdivision based on programme, with -Primary Cell Layout: VOID SIZE VOID vs SIZE CELL vs SIZE CELL SIZE (multiple iterations) (optimal iteration) spatial facade areas. size based on subdvision based on loads void within void system: within system:cell withinporosity system: cell within system: plan sections generated Hierarchy rooms - structural rooms -open structural spaceopen space varies-Primary within varies within based on HEIRARCHY level i based on programme structural loads visual openvisual parts open parts defined lattice defined lattice

continuous continuous voids for ventilation voids for guidance ventilation guidance iterations) insulation(multiple voids insulation (membrane voids (membrane possibility) possibility)

(optimal iteration)

tertiary parameters STEP004 tertiary parameters

Outputs:

HEIRARCHY level iii

Combinatorial Optimization?

HEIRARCHY level i

HEIRARCHY level ii

ENTIRE BUILDING ENTIRE BUILDING

HEIRARCHY level iii

PART OF FACADE PART OF FACADE

OVERALL OVERALL LATTICELATTICE STRUCTURE STRUCTURE

SUN / LIGHT SUN // VISUAL LIGHT / VISUAL WIND & VENTILATION WIND & VENTILATION INSULATION INSULATION global solution:global solution: increase thickness increase thickness of overall system of overall system

structural loads increase

structural

density loads increase

increase

change of change of density cell size cell size increase increase cell density increase cell density local solution: local solution: change of change of porosity % porosity % increase cell increase cell wall thickness wall thickness inside

inside

outside

outside

control of porosity control of porosity through acquired through site data acquired site data vectors according vectors according to sun movement to sun movement global solution:global solution: change of change of cell size cell size wind loads increase

porosity wind increase loads increase

porosity increase

more sun required: more sun required: increase of cellincrease porosity of cell porosity increase of cellincrease size of cell size decrease of system decrease thickness of system thickness

inside

inside

outside

outside inside

create continuous create continuous path of porous path cells of porous cells to ventilate to ventilate

inside

outside

continuous aggregation continuous aggregation of cells which fulfil of cells desired which fulfil desired insulation properties insulation properties

no need of change no need of change of cell size or porosity of cell size or porosity along defined path along defined path

local solution: local solution: change of change of porosity % porosity % at individual cells at individual cells

CELLULAR COMPLEXITY

outside

185

INITIAL SCALE STUDY OF CELL SIZE SCALE RANGE OF CELLULAR SYSTEM RELATED TO FACADE PROPERTIES PATCH OF 300.00 X 150.00 CM

2.00 cm

4.00 cm

8.00 cm

THERMAL

ACOUSTIC - insolation - LARGE SCALE: GEOMETRY CONTROLLED

VISUAL - POROSITY LOW 0.2 / POROSITY HIGH 0.9

VENTILATION - increases with porosity

STRUCTURAL - Material Scale Limitations apply

SPATIAL

186

APPENDIX

16.00 cm

32.00 cm

128.00 cm

64.00 cm

CELLULAR COMPLEXITY

256.00 cm

187

188

APPENDIX

CELLULAR COMPLEXITY

189

COMPUTATIONAL FLUID DYNAMICS

FORCE

DIRECTION

CELL

WIND

WIND INLET

GEOMETRY

hexagonal tesselation dual-network offset tetra decahedron

offset

porosity

0.234

cell size : 500x500mm

0’ hexagonal tesselation offset tetra decahedron

inlet:

offset

porosity

0.20

.232

cell size : 500x500mm

velocity

10ms-1 outlet: pressure

hexagonal tesselation dual-network offset

1Pa

tetra decahedron

offset

porosity

0.234

cell size : 500x500mm

45’ hexagonal tesselation offset tetra decahedron

offset

porosity

0.20

.232

cell size : 500x500mm

190

APPENDIX

CONTOUR

STREAMLINE FLOW

STREAMLINE FLOW

PRESSURE

CORONAL SECTION

TRANSVERSE SECTION

CELLULAR COMPLEXITY

191

COMPUTATIONAL FLUID DYNAMICS

FORCE

CELL

CELL

STREAMLINE FLOW

WIND

GEOMETRY

ORGANIZATION

CORONAL and TRANSVERSE SECTION

inlet: velocity

10ms-1

hexagonal tesselation dual-network offset tetra decahedron

offset

porosity

outlet: pressure

1Pa

0.234

cell size : 500x500mm

3x3x1

inlet: velocity

hexagonal tesselation offset

10ms-1

tetra decahedron

outlet: pressure

1Pa

192

offset

porosity

0.20

.232

cell size : 500x500mm

3x3x1

APPENDIX

SHADOW ANALYSIS

SHADOW DIAGRAMS

JANUARY 21st 3pm

APRIL 21st 3pm

JULY 21st 3pm

Cell Aggregation prototype 01- Porosity : 86%

N

Cell Aggregation prototype 02- Porosity : 77%

N

Cell Aggregation prototype 03- Porosity :68%

N

CELLULAR COMPLEXITY

193

194

THE SYSTEM

CELLULAR COMPLEXITY

195

196

THE SYSTEM

CELLULAR COMPLEXITY

197

198

Photo Studio AA

Photo Studio AA

CELLULAR COMPLEXITY

199

RHINO PYTHON SCRIPT OF STRUCTURE

A script was developed which builds up the cell according to an input surface. The surface can be planar, curved or doubly curved. The geometry of the cells develops along the surface and consists of planar parts only, even if the surface is curved. The points for each cell are defined by dividing the surface in a desired number of points in both, u and v direction. In each of those points, the surface normal is found in order to create the height of the cell. This height is added several times in an amount which is defined by the number of layers of the system. Through these basic points, each cell is built up by first creating the bounding box of the cell. The geometries which define the strut thickness and the opening are then booleaned out of this basic box in a defined range of scales towards an attractorpoint for each. This range is always a value between 0 and 1 as the distances to the attractor points are remapped. For each gradient, a minimum and a maximum value is entered, so the gradient is then generated between those numbers.

If the minimum and the maximum value are the same number, there is no gradient. In the corners of each cell, the joint is built up, following an average size of the defined strut thickness. The basic surface is modeled and the attractor are points set in Rhino. By editing the control lines of the surface, the shape and the size of the later built up cells can be defined. Variable values such as number of divisions in u and v direction - which define the number of cells in each layer - and the number of layers, which multiplies the number of before generated cells in the third direction are entered before running the script. Also, the minimum and maximum factor for strut thickness and opening gradient as well as the height of each layer is defined by the user. After entering those values, the script runs and builds up the structure. Often, a large number of data is created and in extremely twisting surfaces it can happen that some cells cannot be built up any more.

import rhinoscriptsyntax as rs points=[] pointsforcenter=[] rs.EnableRedraw(False) import rhinoscriptsyntax as rs points=[] pointsforcenter=[] #---------------------------------------------------------------------------------------------------------------------------------------------rs.EnableRedraw(False) #---------------------CHANGE CHANGE CHANGE CHANGE CHANGE CHANGE CHANGE CHANGE CHANGE CHANGE ---------------------------#--------------------------------------------------------------------------------------------------------------------------------#----------------------------------------------------------------------------------------------------------------------------------------------------------#---------------------CHANGE CHANGE CHANGE CHANGE CHANGE CHANGE CHANGE CHANGE CHANGE CHANGE ---------------intUdivisions =3 ------------- =35 intVdivisions ENTER VALUES FOR VARIABLES #---------------------------------------------------------------------------------------------------------------------------------------------numberoflayers=7 number of cells (defined by U+V divisions of surface) intUdivisions =3 #HEIGHT OF CELL: intVdivisions =35 #cellheightfactor=1 number of layers vectorfactor=2 numberoflayers=7 #SCALE OF INSIDE BOOL 0-1 (if both are the same, no gradient) thickness of layers #HEIGHT OF CELL: mininsidescalefactor=0.4 range of opening gradient #cellheightfactor=1 maxinsidescalefactor=0.9 vectorfactor=2 (0-closed,1-open) #SCALE OF THICKNESS INSIDE BOOL 0-1 (if both are the same, gradient) #MATERIAL 0-1 (if both are the same, nono gradient) range of strut thickness gradient mininsidescalefactor=0.4 minmaterialthicknessfactor=0 (0-closed,1-open) maxinsidescalefactor=0.9 maxmaterialthicknessfactor=0.3 #MATERIAL THICKNESS 0-1 (if both are the same, no gradient) jointthicknessfactor=1 minmaterialthicknessfactor=0 #--------------------------------------------------------------------------------------------------------------------------------maxmaterialthicknessfactor=0.3 -------------#--------------------------------------------------------------------------------------------------------------------------------jointthicknessfactor=1 -------------#--------------------------------------------------------------------------------------------------------------------------------#----------------------------------------------------------------------------------------------------------------------------------------------------------#---------------------------------------------------------------------------------------------------------------------------------------------overallthicknesschange=0 #---------------------------------------------------------------------------------------------------------------------------------------------actualmininsidescalefactor=(0.1+9.8*mininsidescalefactor) actualmaxinsidescalefactor=(0.1+9.8*maxinsidescalefactor) overallthicknesschange=0

actualmininsidescalefactor=(0.1+9.8*mininsidescalefactor) actualmaxinsidescalefactor=(0.1+9.8*maxinsidescalefactor) def samplesurface(cubesurface, cubeUdivisions,cubeVdivisions): listUdomain = rs.SurfaceDomain(strSrf,0) # list of 2 elements - starting and ending point of domain listVdomain = rs.SurfaceDomain(strSrf,1)

SAMPLE SURFACE divide surface in u and v points in the before entered number of points

def samplesurface(cubesurface, cubeUdivisions,cubeVdivisions): listUdomain==(listUdomain[1]-listUdomain[0])/intUdivisions rs.SurfaceDomain(strSrf,0) # list of 2 elements - starting and ending point of domain floatUstep listVdomain==(listVdomain[1]-listVdomain[0])/intVdivisions rs.SurfaceDomain(strSrf,1) floatVstep listofrows = [] floatUstep = (listUdomain[1]-listUdomain[0])/intUdivisions for i in rs.frange(listUdomain[0],listUdomain[1],floatUstep): floatVstep = (listVdomain[1]-listVdomain[0])/intVdivisions columnlist = [] for j in rs.frange(listVdomain[0],listVdomain[1],floatVstep): listofrows = [] columnlist.append(rs.EvaluateSurface(strSrf,i,j)) listofrows.append(columnlist) for i in rs.frange(listUdomain[0],listUdomain[1],floatUstep): columnlist = [] return listofrows #rs.AddPoints(listofrows[10][0]) take 10th element of list, which is a list - second number:take first j inlist rs.frange(listVdomain[0],listVdomain[1],floatVstep): element for of this in the list columnlist.append(rs.EvaluateSurface(strSrf,i,j)) listofrows.append(columnlist) return listofrows #rs.AddPoints(listofrows[10][0]) take 10th element of list, which is a list - second number:take first SELECT ATTRACTORPOINTS element of this list in the list materialthicknessattractors=rs.GetObjects('select materialthickness attractor point',1) AND SURFACE insidescaleattractors=rs.GetObjects('select inside bool attractor point',1) strSrf = rs.GetObject("select surface",8) listofpoints = samplesurface(strSrf,intUdivisions,intVdivisions) materialthicknessattractors=rs.GetObjects('select materialthickness attractor point',1) insidescaleattractors=rs.GetObjects('select inside bool attractor point',1) cells=[] strSrf = rs.GetObject("select surface",8) zpoints=[] 2centroids=[] 00 APPENDIX listofpoints = samplesurface(strSrf,intUdivisions,intVdivisions) surfacepointslist=[] jointsurfacelist=[] cells=[] listofsurfacecenterlists=[]

element of this list in the list

materialthicknessattractors=rs.GetObjects('select materialthickness attractor point',1) insidescaleattractors=rs.GetObjects('select inside bool attractor point',1) strSrf = rs.GetObject("select surface",8) listofpoints = samplesurface(strSrf,intUdivisions,intVdivisions)

DEFINE LISTS AND LOOP

cells=[] zpoints=[] centroids=[] surfacepointslist=[] jointsurfacelist=[] listofsurfacecenterlists=[]

for accessing all points for each cell in u,v and z direction

for i in range (0,len(listofpoints)-1): for j in range (0,len(listofpoints[i])-1): for k in range (0,numberoflayers): pyramidcentroidnormals=[] verybottompointlist=[listofpoints[i][j],listofpoints[i+1][j],listofpoints[i+1][j+1],listofpoints[i][j+1]] normalunilist=[] startlist=[] endlist=[] edgelist=[] surfacepoints=[] #vectorfactor=rs.Distance(listofpoints[0][0],listofpoints[1][0]) materialmax=(vectorfactor/2.1) materialmin=vectorfactor/25 actualminmaterialthickness=(materialmin+(materialmax-materialmin)*minmaterialthicknessfactor) actualmaxmaterialthickness=(materialmin+(materialmax-materialmin)*maxmaterialthicknessfactor)

CONVERT NUMBERS TO FACTOR

#jointthickness=((materialmin+(materialmaxmaterialmin)*(minmaterialthicknessfactor+maxmaterialthicknessfactor)/2))*jointthicknessfactor jointthickness=actualminmaterialthickness*jointthicknessfactor for h in range (0,len(verybottompointlist)): closest=rs.SurfaceClosestPoint(strSrf,verybottompointlist[h]) NORMALS IN Z DIRECTION normaldir=rs.SurfaceNormal(strSrf,closest) normaluni=rs.VectorUnitize(normaldir) #normalscale=rs.VectorScale(normaluni,cellheightfactor*vectorfactor*numberoflayers*(1+i*overallthicknesschange)) normalscale=rs.VectorScale(normaluni,vectorfactor*numberoflayers*(1+i*overallthicknesschange)) normal=rs.VectorAdd(verybottompointlist[h],normalscale) #verytoppoint=rs.AddPoint(normal) edge=rs.AddLine(verybottompointlist[h],normal) edgelist.append(edge) zpoints01=rs.DivideCurve(edgelist[0],numberoflayers) zpoints02=rs.DivideCurve(edgelist[1],numberoflayers) zpoints03=rs.DivideCurve(edgelist[2],numberoflayers) zpoints04=rs.DivideCurve(edgelist[3],numberoflayers) zpoints.extend(zpoints01)

GENERATE ALL POINTS OF CELL BOUNDING BOX

rs.DeleteObjects([edgelist[0],edgelist[1],edgelist[2],edgelist[3]]) start01=rs.AddPoint(zpoints01[k]) end01=rs.AddPoint(zpoints01[k+1]) smallnormaldir01=rs.VectorCreate(end01,start01) smallnormaluni01=rs.VectorUnitize(smallnormaldir01) pyramidnormal01=rs.VectorScale(smallnormaluni01,jointthickness)

start02=rs.AddPoint(zpoints02[k]) end02=rs.AddPoint(zpoints02[k+1]) smallnormaldir02=rs.VectorCreate(end02,start02) smallnormaluni02=rs.VectorUnitize(smallnormaldir02) pyramidnormal02=rs.VectorScale(smallnormaluni02,jointthickness)

start03=rs.AddPoint(zpoints03[k]) end03=rs.AddPoint(zpoints03[k+1]) smallnormaldir03=rs.VectorCreate(end03,start03) smallnormaluni03=rs.VectorUnitize(smallnormaldir03) pyramidnormal03=rs.VectorScale(smallnormaluni03,jointthickness)

start04=rs.AddPoint(zpoints04[k]) end04=rs.AddPoint(zpoints04[k+1]) smallnormaldir04=rs.VectorCreate(end04,start04) smallnormaluni04=rs.VectorUnitize(smallnormaldir04) pyramidnormal04=rs.VectorScale(smallnormaluni04,jointthickness) bottompointlist=[start01,start02,start03,start04] toppointlist=[end01,end02,end03,end04] normalunilist=[smallnormaluni01,smallnormaluni02,smallnormaluni03,smallnormaluni04] pyramidcentroidnormals=[pyramidnormal01,pyramidnormal02,pyramidnormal03,pyramidnormal04] srfnormal01scale=rs.VectorScale(normalunilist[0],vectorfactor) srfnormal02scale=rs.VectorScale(normalunilist[1],vectorfactor) srfnormal03scale=rs.VectorScale(normalunilist[2],vectorfactor) srfnormal04scale=rs.VectorScale(normalunilist[3],vectorfactor)

GENERATE ALL NECESSARY VECTORS

srfnormal01=rs.VectorAdd(bottompointlist[0],srfnormal01scale) srfnormal02=rs.VectorAdd(bottompointlist[1],srfnormal02scale) srfnormal03=rs.VectorAdd(bottompointlist[2],srfnormal03scale) srfnormal04=rs.VectorAdd(bottompointlist[3],srfnormal04scale)

#SURFACE POINTS - 6 CUBE SURFACES surface01points=[bottompointlist[0],bottompointlist[1],toppointlist[1],toppointlist[0]] surface02points=[bottompointlist[1],bottompointlist[2],toppointlist[2],toppointlist[1]] surface03points=[bottompointlist[2],bottompointlist[3],toppointlist[3],toppointlist[2]] surface04points=[bottompointlist[3],bottompointlist[0],toppointlist[0],toppointlist[3]] surface05points=[bottompointlist[0],bottompointlist[1],bottompointlist[2],bottompointlist[3]] surface06points=[toppointlist[2],toppointlist[3],toppointlist[0],toppointlist[1]] surfacepoints=[surface01points,surface02points,surface03points,surface04points,surface05points,surface06points] surfacepointslist.append(surfacepoints) surfacecenterlist=[] quadsurfacelist=[] #create quadsurfaces quadsurfaceface01part01=rs.AddSrfPt([surfacepoints[0][1],surfacepoints[0][2],surfacepoints[0][3]]) CELLULAR COMPLEXITY quadsurfaceface01part02=rs.AddSrfPt([surfacepoints[0][3],surfacepoints[0][0],surfacepoints[0][1]]) quadsurfaceface01=rs.JoinSurfaces([quadsurfaceface01part01,quadsurfaceface01part02],delete_input=True) quadsurfacecenterdirection=rs.VectorCreate(surfacepoints[0][1],surfacepoints[0][3]) quadsurfacecenterscale=rs.VectorScale(quadsurfacecenterdirection,0.5)

LIST ALL POINTS FOR EACH FACE OF CELL BOUNDING BOX

201

#quadsurfacecenter=rs.SurfaceAreaCentroid(quadsurface) quadsurfacecenter=rs.AddPoint(quadsurfacecenter) surfacecenterlist.append(quadsurfacecenter) quadsurfaceface02part01=rs.AddSrfPt([surfacepoints[1][1],surfacepoints[1][2],surfacepoints[1][3]]) quadsurfaceface02part02=rs.AddSrfPt([surfacepoints[1][3],surfacepoints[1][0],surfacepoints[1][1]]) quadsurfaceface02=rs.JoinSurfaces([quadsurfaceface02part01,quadsurfaceface02part02],delete_input=True) quadsurfacelist.append(quadsurfaceface01) quadsurfacelist.append(quadsurfaceface02) quadsurfacecenterdirection=rs.VectorCreate(surfacepoints[1][1],surfacepoints[1][3]) quadsurfacecenterscale=rs.VectorScale(quadsurfacecenterdirection,0.5) quadsurfacecenter=rs.VectorAdd(surfacepoints[1][3],quadsurfacecenterscale) #quadsurfacecenter=rs.SurfaceAreaCentroid(quadsurface) quadsurfacecenter=rs.AddPoint(quadsurfacecenter) surfacecenterlist.append(quadsurfacecenter) for a in range (2, len(surfacepoints)): quadsurfacepart01=rs.AddSrfPt([surfacepoints[a][0],surfacepoints[a][1],surfacepoints[a][2]]) quadsurfacepart02=rs.AddSrfPt([surfacepoints[a][2],surfacepoints[a][3],surfacepoints[a][0]]) quadsurface=rs.JoinSurfaces([quadsurfacepart01,quadsurfacepart02],delete_input=True) quadsurfacelist.append(quadsurface) #create surface centers quadsurfacecenterdirection=rs.VectorCreate(surfacepoints[a][0],surfacepoints[a][2]) quadsurfacecenterscale=rs.VectorScale(quadsurfacecenterdirection,0.5) quadsurfacecenter=rs.VectorAdd(surfacepoints[a][2],quadsurfacecenterscale) #quadsurfacecenter=rs.SurfaceAreaCentroid(quadsurface) quadsurfacecenter=rs.AddPoint(quadsurfacecenter) surfacecenterlist.append(quadsurfacecenter) listofsurfacecenterlists.append(surfacecenterlist)

CREATE CELL BOUNDING BOX SURFACES

#join quadsurfaces jointsrf01=rs.JoinSurfaces(quadsurfacelist,delete_input=True) jointsurfacelist.append(jointsrf01) #---------------------------- CENTROID ------------------------centroid_L01=rs.SurfaceVolumeCentroid(jointsrf01) #rs.AddPoint(centroid_L01[0]) centroids.append(centroid_L01[0])

CREATE CENTROID OF BOUNDING BOX

# # #----------------------------------------JOINTS JOINTS JOINTS JOINTS ------------------------------------------------# #---------------------------------------------------------------------------------------------------------------------------------# #---------------------------------------------------------------------------------------------------------------------------------# #VECTOR 01 bottom 1-2 VECTORS FOR JOINTS vector01=rs.VectorCreate(bottompointlist[0],bottompointlist[1]) vector01uni=rs.VectorUnitize(vector01) vector01=rs.VectorScale(vector01uni,jointthickness) #PYRAMID LAYER 01 - VECTOR 02 vector02=rs.VectorCreate(bottompointlist[1],bottompointlist[2]) vector02uni=rs.VectorUnitize(vector02) vector02=rs.VectorScale(vector02uni,jointthickness) #PYRAMID LAYER 01 - VECTOR 03 vector03=rs.VectorCreate(bottompointlist[2],bottompointlist[3]) vector03uni=rs.VectorUnitize(vector03) vector03=rs.VectorScale(vector03uni,jointthickness) #PYRAMID LAYER 01 - VECTOR 04 vector04=rs.VectorCreate(bottompointlist[3],bottompointlist[0]) vector04uni=rs.VectorUnitize(vector04) vector04=rs.VectorScale(vector04uni,jointthickness) #PYRAMID LAYER 01 - VECTOR 01A vector01A=rs.VectorCreate(toppointlist[0],toppointlist[1]) vector01Auni=rs.VectorUnitize(vector01A) vector01A=rs.VectorScale(vector01Auni,jointthickness) #PYRAMID LAYER 01 - VECTOR 02A vector02A=rs.VectorCreate(toppointlist[1],toppointlist[2]) vector02Auni=rs.VectorUnitize(vector02A) vector02A=rs.VectorScale(vector02Auni,jointthickness) #PYRAMID LAYER 01 - VECTOR 03A vector03A=rs.VectorCreate(toppointlist[2],toppointlist[3]) vector03Auni=rs.VectorUnitize(vector03A) vector03A=rs.VectorScale(vector03Auni,jointthickness) #PYRAMID LAYER 01 - VECTOR 04A vector04A=rs.VectorCreate(toppointlist[3],toppointlist[0]) vector04Auni=rs.VectorUnitize(vector04A) vector04A=rs.VectorScale(vector04Auni,jointthickness) booleanlist02=[] #PYRAMID LAYER 01 CORNER 01 #TOP-01 pyramidtop01=rs.VectorAdd(bottompointlist[0],pyramidcentroidnormals[0]) #pyramidtop01=rs.AddPoint(pyramidtop01) #VECTOR L01-C01-01 vector01_01=rs.VectorAdd(bottompointlist[0],vector01*-1) #rs.AddPoint(vector01_01) #VECTOR L01-C01-02 vector01_02=rs.VectorAdd(bottompointlist[0],vector04) #rs.AddPoint(vector01_02) #SURFACE curve01_01=rs.AddInterpCurve([bottompointlist[0],vector01_01,vector01_02,bottompointlist[0]],1) srf01_01=rs.ExtrudeCurvePoint(curve01_01,pyramidtop01) srf01_02=rs.AddSrfPt([bottompointlist[0],vector01_01,vector01_02]) jointsrfpyramid01=rs.JoinSurfaces([srf01_01,srf01_02],delete_input=True) scalepoint01=rs.SurfaceVolumeCentroid(jointsrfpyramid01) jointsrfpyramid01scaled=rs.ScaleObject(jointsrfpyramid01,scalepoint01[0],[1.1,1.1,1.1],copy=True) booleanlist02.append(jointsrfpyramid01scaled)

202

#BOTTOM-01 pyramidbottom01A=rs.VectorAdd(toppointlist[0],pyramidcentroidnormals[0]*-1) #pyramidbottom01=rs.AddPoint(pyramidbottom01) #VECTOR L01-C01-01 APPENDIX vector01A_01=rs.VectorAdd(toppointlist[0],vector01A*-1) #rs.AddPoint(vector01_01) #VECTOR L01-C01-02

SURFACES FOR JOINTS

#SURFACE curve01_01=rs.AddInterpCurve([bottompointlist[0],vector01_01,vector01_02,bottompointlist[0]],1) srf01_01=rs.ExtrudeCurvePoint(curve01_01,pyramidtop01) srf01_02=rs.AddSrfPt([bottompointlist[0],vector01_01,vector01_02]) jointsrfpyramid01=rs.JoinSurfaces([srf01_01,srf01_02],delete_input=True) scalepoint01=rs.SurfaceVolumeCentroid(jointsrfpyramid01) jointsrfpyramid01scaled=rs.ScaleObject(jointsrfpyramid01,scalepoint01[0],[1.1,1.1,1.1],copy=True) booleanlist02.append(jointsrfpyramid01scaled) #BOTTOM-01 pyramidbottom01A=rs.VectorAdd(toppointlist[0],pyramidcentroidnormals[0]*-1) #pyramidbottom01=rs.AddPoint(pyramidbottom01) #VECTOR L01-C01-01 vector01A_01=rs.VectorAdd(toppointlist[0],vector01A*-1) #rs.AddPoint(vector01_01) #VECTOR L01-C01-02 vector01A_02=rs.VectorAdd(toppointlist[0],vector04A) #rs.AddPoint(vector01_02) #SURFACE curve01A_01=rs.AddInterpCurve([toppointlist[0],vector01A_01,vector01A_02,toppointlist[0]],1) srf01A_01=rs.ExtrudeCurvePoint(curve01A_01,pyramidbottom01A) srf01A_02=rs.AddSrfPt([toppointlist[0],vector01A_01,vector01A_02]) jointsrfpyramid01A=rs.JoinSurfaces([srf01A_01,srf01A_02],delete_input=True) scalepoint01A=rs.SurfaceVolumeCentroid(jointsrfpyramid01A) jointsrfpyramid01Ascaled=rs.ScaleObject(jointsrfpyramid01A,scalepoint01A[0],[1.1,1.1,1.1],copy=True) booleanlist02.append(jointsrfpyramid01Ascaled)

SURFACES FOR JOINTS (OCTAHEDRONS) IN EVERY CORNER

#PYRAMID LAYER 01 CORNER 02 #TOP pyramidtop02=rs.VectorAdd(bottompointlist[1],pyramidcentroidnormals[1]) #pyramidtop02=rs.AddPoint(pyramidtop02) #VECTOR L01-C02-01 vector02_01=rs.VectorAdd(bottompointlist[1],vector01) #rs.AddPoint(vector02_01) #VECTOR L01-C02-02 vector02_02=rs.VectorAdd(bottompointlist[1],vector02*-1) #rs.AddPoint(vector02_02) curve02_01=rs.AddInterpCurve([bottompointlist[1],vector02_01,vector02_02,bottompointlist[1]],1) srf02_01=rs.ExtrudeCurvePoint(curve02_01,pyramidtop02) srf02_02=rs.AddSrfPt([bottompointlist[1],vector02_01,vector02_02]) jointsrfpyramid02=rs.JoinSurfaces([srf02_01,srf02_02],delete_input=True) scalepoint02=rs.SurfaceVolumeCentroid(jointsrfpyramid02) jointsrfpyramid02scaled=rs.ScaleObject(jointsrfpyramid02,scalepoint02[0],[1.1,1.1,1.1],copy=True) booleanlist02.append(jointsrfpyramid02scaled) #BOTTOM-02 pyramidbottom02A=rs.VectorAdd(toppointlist[1],pyramidcentroidnormals[1]*-1) #pyramidbottom02=rs.AddPoint(pyramidbottom02) #VECTOR L01-C02-01 vector02A_01=rs.VectorAdd(toppointlist[1],vector01A) #rs.AddPoint(vector02_01) #VECTOR L01-C02-02 vector02A_02=rs.VectorAdd(toppointlist[1],vector02A*-1) #rs.AddPoint(vector02_02) curve02A_01=rs.AddInterpCurve([toppointlist[1],vector02A_01,vector02A_02,toppointlist[1]],1) srf02A_01=rs.ExtrudeCurvePoint(curve02A_01,pyramidbottom02A) srf02A_02=rs.AddSrfPt([toppointlist[1],vector02A_01,vector02A_02]) jointsrfpyramid02A=rs.JoinSurfaces([srf02A_01,srf02A_02],delete_input=True) scalepoint02A=rs.SurfaceVolumeCentroid(jointsrfpyramid02A) jointsrfpyramid02Ascaled=rs.ScaleObject(jointsrfpyramid02A,scalepoint02A[0],[1.1,1.1,1.1],copy=True) booleanlist02.append(jointsrfpyramid02Ascaled)

#PYRAMID LAYER 01 CORNER 03 #TOP pyramidtop03=rs.VectorAdd(bottompointlist[2],pyramidcentroidnormals[2]) #pyramidtop03=rs.AddPoint(pyramidtop03) #VECTOR L01-C03-01 vector03_01=rs.VectorAdd(bottompointlist[2],vector02) #rs.AddPoint(vector03_01) #VECTOR L01-C03-02 vector03_02=rs.VectorAdd(bottompointlist[2],vector03*-1) #rs.AddPoint(vector03_02) curve03_01=rs.AddInterpCurve([bottompointlist[2],vector03_01,vector03_02,bottompointlist[2]],1) srf03_01=rs.ExtrudeCurvePoint(curve03_01,pyramidtop03) srf03_02=rs.AddSrfPt([bottompointlist[2],vector03_01,vector03_02]) jointsrfpyramid03=rs.JoinSurfaces([srf03_01,srf03_02],delete_input=True) scalepoint03=rs.SurfaceVolumeCentroid(jointsrfpyramid03) jointsrfpyramid03scaled=rs.ScaleObject(jointsrfpyramid03,scalepoint03[0],[1.1,1.1,1.1],copy=True) booleanlist02.append(jointsrfpyramid03scaled) #BOTTOM pyramidbottom03A=rs.VectorAdd(toppointlist[2],pyramidcentroidnormals[2]*-1) #pyramidbottom03=rs.AddPoint(pyramidbottom03) #VECTOR L01-C03-01 vector03A_01=rs.VectorAdd(toppointlist[2],vector02A) #rs.AddPoint(vector03_01) #VECTOR L01-C03-02 vector03A_02=rs.VectorAdd(toppointlist[2],vector03A*-1) #rs.AddPoint(vector03_02) curve03A_01=rs.AddInterpCurve([toppointlist[2],vector03A_01,vector03A_02,toppointlist[2]],1) srf03A_01=rs.ExtrudeCurvePoint(curve03A_01,pyramidbottom03A) srf03A_02=rs.AddSrfPt([toppointlist[2],vector03A_01,vector03A_02]) jointsrfpyramid03A=rs.JoinSurfaces([srf03A_01,srf03A_02],delete_input=True) scalepoint03A=rs.SurfaceVolumeCentroid(jointsrfpyramid03A) jointsrfpyramid03Ascaled=rs.ScaleObject(jointsrfpyramid03A,scalepoint03A[0],[1.1,1.1,1.1],copy=True) booleanlist02.append(jointsrfpyramid03Ascaled)

#PYRAMID LAYER 01 CORNER 04 #TOP pyramidtop04=rs.VectorAdd(bottompointlist[3],pyramidcentroidnormals[3]) #pyramidtop04=rs.AddPoint(pyramidtop04) #VECTOR L01-C04-01 vector04_01=rs.VectorAdd(bottompointlist[3],vector03) #rs.AddPoint(vector04_01) #VECTOR L01-C04-02 vector04_02=rs.VectorAdd(bottompointlist[3],vector04*-1) #rs.AddPoint(vector04_02) curve04_01=rs.AddInterpCurve([bottompointlist[3],vector04_01,vector04_02,bottompointlist[3]],1) srf04_01=rs.ExtrudeCurvePoint(curve04_01,pyramidtop04) srf04_02=rs.AddSrfPt([bottompointlist[3],vector04_01,vector04_02]) jointsrfpyramid04=rs.JoinSurfaces([srf04_01,srf04_02],delete_input=True) scalepoint04=rs.SurfaceVolumeCentroid(jointsrfpyramid04) jointsrfpyramid04scaled=rs.ScaleObject(jointsrfpyramid04,scalepoint04[0],[1.1,1.1,1.1],copy=True) booleanlist02.append(jointsrfpyramid04scaled) #BOTTOM pyramidbottom04A=rs.VectorAdd(toppointlist[3],pyramidcentroidnormals[3]*-1) #pyramidbottom04=rs.AddPoint(pyramidbottom04) #VECTOR L01-C04-01 CELLULAR COMPLEXITY vector04A_01=rs.VectorAdd(toppointlist[3],vector03A) #rs.AddPoint(vector04_01) #VECTOR L01-C04-02 vector04A_02=rs.VectorAdd(toppointlist[3],vector04A*-1)

203

--------------

#---------------------------------------------------------------------------------------------------------------------------------#---------------------------------------------------------------------------------------------------------------------------------DUAL GEOMETRY WHICH IS #--------------------------------------------------------------------------------------------------------------------------------THEN SUBTRACTED FROM -THE STRUCTURE INTO LEAVE #------------------------------ GRADIENT GRADIENT GRADIENT GRADIENT ----------------------------------------------THE STRUT THICKNESS IN THE -DESIRED SCALE print len(centroids) cells=[] allmaterialthicknessdistances=[] allinsidescaledistances=[] insidescaledistances=[] materialthicknessdistances=[] for g in range (0,len(centroids)): for a in range(0,len(insidescaleattractors)): insidescaledistancehelp=rs.Distance(centroids[g],insidescaleattractors[a]) #insidescaledistances.append(insidescaledistancehelp) #insidescaledistance=sum(insidescaledistances) allinsidescaledistances.append(insidescaledistancehelp) print allinsidescaledistances

for b in range(0,len(materialthicknessattractors)): materialthicknessdistancehelp=rs.Distance(centroids[g],materialthicknessattractors[b]) #materialthicknessdistances.append(materialthicknessdistancehelp) #materialthicknessdistance=sum(materialthicknessdistances) allmaterialthicknessdistances.append(materialthicknessdistancehelp) print allmaterialthicknessdistances mininsidescaledistance=min(allinsidescaledistances) maxinsidescaledistance=max(allinsidescaledistances) minmaterialthicknessdistance=min(allmaterialthicknessdistances) maxmaterialthicknessdistance=max(allmaterialthicknessdistances) mhigh1=maxmaterialthicknessdistance ilow1=mininsidescaledistance mlow2=actualminmaterialthickness ihigh1=maxinsidescaledistance mhigh2=actualmaxmaterialthickness ilow2=actualmininsidescalefactor mvalue=allmaterialthicknessdistances ihigh2=actualmaxinsidescalefactor ivalue=allinsidescaledistances insidescalelist=[] materialthicknesslist=[] mlow1=minmaterialthicknessdistance for s in range (0,len(allinsidescaledistances)): insidescale=ilow2+(allinsidescaledistances[s]-ilow1)*(ihigh2-ilow2)/(ihigh1-ilow1) materialthickness=mlow2+(allmaterialthicknessdistances[s]-mlow1)*(mhigh2-mlow2)/(mhigh1-mlow1) insidescalelist.append(insidescale) materialthicknesslist.append(materialthickness) print materialthicknesslist print insidescalelist

for y in range(0,len(centroids)): listofsurfacecentersmoved=[] listofcentroidvectors=[] listofmovepointlistquad=[] listofmovepointlistquadA=[] for e in range (0,len(surfacepoints)): #create vector between 4 points of each face movevectordirection01=rs.VectorCreate(surfacepointslist[y][e][1],surfacepointslist[y][e][0]) movevectordirection02=rs.VectorCreate(surfacepointslist[y][e][2],surfacepointslist[y][e][1]) movevectordirection03=rs.VectorCreate(surfacepointslist[y][e][3],surfacepointslist[y][e][2]) movevectordirection04=rs.VectorCreate(surfacepointslist[y][e][0],surfacepointslist[y][e][3]) movevectordirection=[movevectordirection01,movevectordirection02,movevectordirection03,movevectordirection04] movevectorscale=[] for d in range (0,len(movevectordirection)): movevectoruni=rs.VectorUnitize(movevectordirection[d]) movevectorscales=rs.VectorScale(movevectoruni,materialthicknesslist[y]) movevectorscale.append(movevectorscales) #vectors for points of dual on surface edges movevector01=rs.VectorAdd(surfacepointslist[y][e][0],movevectorscale[0]) movepoint01=rs.AddPoint(movevector01) movevector02=rs.VectorAdd(surfacepointslist[y][e][1],movevectorscale[1]) movepoint02=rs.AddPoint(movevector02) movevector03=rs.VectorAdd(surfacepointslist[y][e][2],movevectorscale[2]) movepoint03=rs.AddPoint(movevector03) movevector04=rs.VectorAdd(surfacepointslist[y][e][3],movevectorscale[3]) movepoint04=rs.AddPoint(movevector04) movevector01A=rs.VectorAdd(surfacepointslist[y][e][1],movevectorscale[0]*-1) movepoint01A=rs.AddPoint(movevector01A) movevector02A=rs.VectorAdd(surfacepointslist[y][e][2],movevectorscale[1]*-1) movepoint02A=rs.AddPoint(movevector02A) movevector03A=rs.VectorAdd(surfacepointslist[y][e][3],movevectorscale[2]*-1) movepoint03A=rs.AddPoint(movevector03A) movevector04A=rs.VectorAdd(surfacepointslist[y][e][0],movevectorscale[3]*-1) movepoint04A=rs.AddPoint(movevector04A) movepointlistquad=[movepoint01,movepoint02,movepoint03,movepoint04] movepointlistquadA=[movepoint01A,movepoint02A,movepoint03A,movepoint04A]

#edgemidpoints edgemidpointline01=rs.AddLine(surfacepointslist[y][e][1],surfacepointslist[y][e][0]) edgemidpointline02=rs.AddLine(surfacepointslist[y][e][2],surfacepointslist[y][e][1]) edgemidpointline03=rs.AddLine(surfacepointslist[y][e][3],surfacepointslist[y][e][2]) edgemidpointline04=rs.AddLine(surfacepointslist[y][e][0],surfacepointslist[y][e][3]) edgemidpointlinelist=[edgemidpointline01,edgemidpointline02,edgemidpointline03,edgemidpointline04]

surfacecentervectors=[] centroidvectors=[] surfacecentersmoved=[] 204

APPENDIX for f in range (0, len(edgemidpointlinelist)): #create edgemidpoints of 4 edges of each quadsurface edgemidpointlist=rs.DivideCurve(edgemidpointlinelist[f],2)

#edgemidpoints edgemidpointline01=rs.AddLine(surfacepointslist[y][e][1],surfacepointslist[y][e][0]) edgemidpointline02=rs.AddLine(surfacepointslist[y][e][2],surfacepointslist[y][e][1]) edgemidpointline03=rs.AddLine(surfacepointslist[y][e][3],surfacepointslist[y][e][2]) edgemidpointline04=rs.AddLine(surfacepointslist[y][e][0],surfacepointslist[y][e][3]) edgemidpointlinelist=[edgemidpointline01,edgemidpointline02,edgemidpointline03,edgemidpointline04]

surfacecentervectors=[] centroidvectors=[] surfacecentersmoved=[]

DUAL GEOMETRY WHICH IS THEN SUBTRACTED FROM THE STRUCTURE INTO LEAVE THE STRUT THICKNESS IN THE DESIRED SCALE

for f in range (0, len(edgemidpointlinelist)): #create edgemidpoints of 4 edges of each quadsurface edgemidpointlist=rs.DivideCurve(edgemidpointlinelist[f],2) edgemidpoint=edgemidpointlist[1] centroidvectordirection=rs.VectorCreate(edgemidpoint,centroids[y]) centroidvectoruni=rs.VectorUnitize(centroidvectordirection) centroidvectorscale=rs.VectorScale(centroidvectoruni,materialthicknesslist[y]) centroidvector=rs.VectorAdd(centroids[y],centroidvectorscale) centroidvectorpoint=rs.AddPoint(centroidvector) centroidvectors.append(centroidvectorpoint) #surfacecentervector surfacecentervectordirection=rs.VectorCreate(edgemidpoint,listofsurfacecenterlists[y][e]) surfacecentervectoruni=rs.VectorUnitize(surfacecentervectordirection) surfacecentervectorscale=rs.VectorScale(surfacecentervectoruni,materialthicknesslist[y]) surfacecentervector=rs.VectorAdd(listofsurfacecenterlists[y][e],surfacecentervectorscale) surfacecentersmoved.append(rs.AddPoint(surfacecentervector)) listofsurfacecentersmoved.append(surfacecentersmoved) listofcentroidvectors.append(centroidvectors) listofmovepointlistquad.append(movepointlistquad) listofmovepointlistquadA.append(movepointlistquadA) booleanlist=[]

A_00=rs.AddSrfPt([listofmovepointlistquad[0][0],listofmovepointlistquadA[0][0],listofsurfacecentersmoved[0][0]]) A_01=rs.AddSrfPt([listofmovepointlistquad[0][0],listofmovepointlistquadA[0][0],listofsurfacecentersmoved[4][0]]) A_02=rs.AddSrfPt([listofmovepointlistquad[0][0],listofsurfacecentersmoved[4][0],listofcentroidvectors[0][0]]) A_03=rs.AddSrfPt([listofmovepointlistquadA[0][0],listofsurfacecentersmoved[4][0],listofcentroidvectors[0][0]]) A_04=rs.AddSrfPt([listofsurfacecentersmoved[0][0],listofcentroidvectors[0][0],listofmovepointlistquad[0][0]]) A_05=rs.AddSrfPt([listofsurfacecentersmoved[0][0],listofcentroidvectors[0][0],listofmovepointlistquadA[0][0]]) porosA=rs.JoinSurfaces([A_00,A_01,A_02,A_03,A_04,A_05],delete_input=True) A1_00=rs.AddSrfPt([listofmovepointlistquad[0][2],listofmovepointlistquadA[0][2],listofsurfacecentersmoved[0][2]]) A1_01=rs.AddSrfPt([listofmovepointlistquad[0][2],listofmovepointlistquadA[0][2],listofsurfacecentersmoved[5][2]]) A1_02=rs.AddSrfPt([listofmovepointlistquad[0][2],listofsurfacecentersmoved[5][2],listofcentroidvectors[0][2]]) A1_03=rs.AddSrfPt([listofmovepointlistquadA[0][2],listofsurfacecentersmoved[5][2],listofcentroidvectors[0][2]]) A1_04=rs.AddSrfPt([listofsurfacecentersmoved[0][2],listofcentroidvectors[0][2],listofmovepointlistquad[0][2]]) A1_05=rs.AddSrfPt([listofsurfacecentersmoved[0][2],listofcentroidvectors[0][2],listofmovepointlistquadA[0][2]]) porosA1=rs.JoinSurfaces([A1_00,A1_01,A1_02,A1_03,A1_04,A1_05],delete_input=True) B_00=rs.AddSrfPt([listofmovepointlistquad[1][0],listofmovepointlistquadA[1][0],listofsurfacecentersmoved[1][0]]) B_01=rs.AddSrfPt([listofmovepointlistquad[1][0],listofmovepointlistquadA[1][0],listofsurfacecentersmoved[4][1]]) B_02=rs.AddSrfPt([listofmovepointlistquad[1][0],listofsurfacecentersmoved[4][1],listofcentroidvectors[1][0]]) B_03=rs.AddSrfPt([listofmovepointlistquadA[1][0],listofsurfacecentersmoved[4][1],listofcentroidvectors[1][0]]) B_04=rs.AddSrfPt([listofsurfacecentersmoved[1][0],listofcentroidvectors[1][0],listofmovepointlistquad[1][0]]) B_05=rs.AddSrfPt([listofsurfacecentersmoved[1][0],listofcentroidvectors[1][0],listofmovepointlistquadA[1][0]]) porosB=rs.JoinSurfaces([B_00,B_01,B_02,B_03,B_04,B_05],delete_input=True) B1_00=rs.AddSrfPt([listofmovepointlistquad[1][2],listofmovepointlistquadA[1][2],listofsurfacecentersmoved[1][2]]) B1_01=rs.AddSrfPt([listofmovepointlistquad[1][2],listofmovepointlistquadA[1][2],listofsurfacecentersmoved[5][3]]) B1_02=rs.AddSrfPt([listofmovepointlistquad[1][2],listofsurfacecentersmoved[5][3],listofcentroidvectors[1][2]]) B1_03=rs.AddSrfPt([listofmovepointlistquadA[1][2],listofsurfacecentersmoved[5][3],listofcentroidvectors[1][2]]) B1_04=rs.AddSrfPt([listofsurfacecentersmoved[1][2],listofcentroidvectors[1][2],listofmovepointlistquad[1][2]]) B1_05=rs.AddSrfPt([listofsurfacecentersmoved[1][2],listofcentroidvectors[1][2],listofmovepointlistquadA[1][2]]) porosB1=rs.JoinSurfaces([B1_00,B1_01,B1_02,B1_03,B1_04,B1_05],delete_input=True) C_00=rs.AddSrfPt([listofmovepointlistquad[2][0],listofmovepointlistquadA[2][0],listofsurfacecentersmoved[2][0]]) C_01=rs.AddSrfPt([listofmovepointlistquad[2][0],listofmovepointlistquadA[2][0],listofsurfacecentersmoved[4][2]]) C_02=rs.AddSrfPt([listofmovepointlistquad[2][0],listofsurfacecentersmoved[4][2],listofcentroidvectors[2][0]]) C_03=rs.AddSrfPt([listofmovepointlistquadA[2][0],listofsurfacecentersmoved[4][2],listofcentroidvectors[2][0]]) C_04=rs.AddSrfPt([listofsurfacecentersmoved[2][0],listofcentroidvectors[2][0],listofmovepointlistquad[2][0]]) C_05=rs.AddSrfPt([listofsurfacecentersmoved[2][0],listofcentroidvectors[2][0],listofmovepointlistquadA[2][0]]) porosC=rs.JoinSurfaces([C_00,C_01,C_02,C_03,C_04,C_05],delete_input=True) C1_00=rs.AddSrfPt([listofmovepointlistquad[2][2],listofmovepointlistquadA[2][2],listofsurfacecentersmoved[2][2]]) C1_01=rs.AddSrfPt([listofmovepointlistquad[2][2],listofmovepointlistquadA[2][2],listofsurfacecentersmoved[5][0]]) C1_02=rs.AddSrfPt([listofmovepointlistquad[2][2],listofsurfacecentersmoved[5][0],listofcentroidvectors[2][2]]) C1_03=rs.AddSrfPt([listofmovepointlistquadA[2][2],listofsurfacecentersmoved[5][0],listofcentroidvectors[2][2]]) C1_04=rs.AddSrfPt([listofsurfacecentersmoved[2][2],listofcentroidvectors[2][2],listofmovepointlistquad[2][2]]) C1_05=rs.AddSrfPt([listofsurfacecentersmoved[2][2],listofcentroidvectors[2][2],listofmovepointlistquadA[2][2]]) porosC1=rs.JoinSurfaces([C1_00,C1_01,C1_02,C1_03,C1_04,C1_05],delete_input=True) D_00=rs.AddSrfPt([listofmovepointlistquad[3][0],listofmovepointlistquadA[3][0],listofsurfacecentersmoved[3][0]]) SCALE CELL BOUNDING BOX D_01=rs.AddSrfPt([listofmovepointlistquad[3][0],listofmovepointlistquadA[3][0],listofsurfacecentersmoved[4][3]]) originalobject=rs.ScaleObject(jointsurfacelist[y],centroids[y],[0.8,0.8,0.8]) WHICH IS THEN SUBTRACTED D_02=rs.AddSrfPt([listofmovepointlistquad[3][0],listofsurfacecentersmoved[4][3],listofcentroidvectors[3][0]]) originalobjectcopy=rs.CopyObject(originalobject) TO ACHIEVE THE DESIRED SIZE D_03=rs.AddSrfPt([listofmovepointlistquadA[3][0],listofsurfacecentersmoved[4][3],listofcentroidvectors[3][0]]) OF THE OPENING D_04=rs.AddSrfPt([listofsurfacecentersmoved[3][0],listofcentroidvectors[3][0],listofmovepointlistquad[3][0]]) D_05=rs.AddSrfPt([listofsurfacecentersmoved[3][0],listofcentroidvectors[3][0],listofmovepointlistquadA[3][0]]) porosD=rs.JoinSurfaces([D_00,D_01,D_02,D_03,D_04,D_05],delete_input=True)

originalobject2=rs.ScaleObject(originalobjectcopy,centroids[y],[insidescalelist[y]/10,insidescalelist[y]/10,insidescalelist[y]/10] ) D1_00=rs.AddSrfPt([listofmovepointlistquad[3][2],listofmovepointlistquadA[3][2],listofsurfacecentersmoved[3][2]]) D1_01=rs.AddSrfPt([listofmovepointlistquad[3][2],listofmovepointlistquadA[3][2],listofsurfacecentersmoved[5][1]]) D1_02=rs.AddSrfPt([listofmovepointlistquad[3][2],listofsurfacecentersmoved[5][1],listofcentroidvectors[3][2]]) D1_03=rs.AddSrfPt([listofmovepointlistquadA[3][2],listofsurfacecentersmoved[5][1],listofcentroidvectors[3][2]]) booleanlist.append(originalobject2) D1_04=rs.AddSrfPt([listofsurfacecentersmoved[3][2],listofcentroidvectors[3][2],listofmovepointlistquad[3][2]]) bool=rs.BooleanDifference(originalobject,booleanlist) D1_05=rs.AddSrfPt([listofsurfacecentersmoved[3][2],listofcentroidvectors[3][2],listofmovepointlistquadA[3][2]]) bool2=rs.ScaleObject(bool,centroids[y],[1.26,1.26,1.26]) porosD1=rs.JoinSurfaces([D1_00,D1_01,D1_02,D1_03,D1_04,D1_05],delete_input=True) cells.append(bool2) E_00=rs.AddSrfPt([listofmovepointlistquad[0][3],listofmovepointlistquadA[0][3],listofsurfacecentersmoved[0][3]]) E_01=rs.AddSrfPt([listofmovepointlistquad[0][3],listofmovepointlistquadA[0][3],listofsurfacecentersmoved[3][1]]) E_02=rs.AddSrfPt([listofmovepointlistquad[0][3],listofsurfacecentersmoved[3][1],listofcentroidvectors[0][3]]) rs.BooleanUnion(cells) E_03=rs.AddSrfPt([listofmovepointlistquadA[0][3],listofsurfacecentersmoved[3][1],listofcentroidvectors[0][3]]) E_04=rs.AddSrfPt([listofmovepointlistquad[0][3],listofsurfacecentersmoved[0][3],listofcentroidvectors[0][3]]) E_05=rs.AddSrfPt([listofmovepointlistquadA[0][3],listofsurfacecentersmoved[0][3],listofcentroidvectors[0][3]]) porosE=rs.JoinSurfaces([E_00,E_01,E_02,E_03,E_04,E_05],delete_input=True) F_00=rs.AddSrfPt([listofmovepointlistquad[0][1],listofmovepointlistquadA[0][1],listofsurfacecentersmoved[0][1]]) F_01=rs.AddSrfPt([listofmovepointlistquad[0][1],listofmovepointlistquadA[0][1],listofsurfacecentersmoved[1][3]]) CELLULAR COMPLEXITY F_02=rs.AddSrfPt([listofmovepointlistquad[0][1],listofsurfacecentersmoved[1][3],listofcentroidvectors[0][1]]) F_03=rs.AddSrfPt([listofmovepointlistquadA[0][1],listofsurfacecentersmoved[1][3],listofcentroidvectors[0][1]]) F_04=rs.AddSrfPt([listofmovepointlistquad[0][1],listofsurfacecentersmoved[0][1],listofcentroidvectors[0][1]])

205

RHINO PYTHON SCRIPT - GENERATED SYSTEM import rhinoscriptsyntax as rs rs.EnableRedraw(False)

HEX1cp = HEX1cp0[0] HEX1n = rs.SurfaceNormal(HEX1,HEX1cp)

def draw_primitive(basepoint,porosity,scale,grid,amount_x,amount_y,amount_z):

if porosity == 0: HEX_1 = HEX1 else: opl_1 = rs.OffsetCurve(HEX1pl,HEX1cp,porosity*dcp) #HEX_1 = rs.AddLoftSrf([HEX1pl,opl_1]) #rs.DeleteObject(HEX1)

vector = rs.VectorCreate(basepoint,[0,0,0]) ###INDEX### #A1 - BOTTOM SQUARE #A2 - TOP SQUARE #A3 - BOTTOM LEFT SQUARE #A4 - TOP RIGHT SQUARE #A5 - BOTTOM RIGHT SQUARE #A6 - TOP LEFT SQUARE

HEX2 = rs.JoinSurfaces([HEX2a,HEX2b],True) HEX2pl=rs.DuplicateSurfaceBorder(HEX2) rs.DeleteObject(HEX2) HEX2 = rs.AddPlanarSrf(HEX2pl) HEX2cp0= rs.SurfaceAreaCentroid(HEX2) HEX2cp = HEX2cp0[0] HEX2n = rs.SurfaceNormal(HEX2,HEX2cp)

b = 1/6*scale dcp = 0.33*scale ###SQUARE BOTTOM#1# a1_LL = rs.AddPoint([2*b,2*b,0]) a1_LR = rs.AddPoint([4*b,2*b,0]) a1_UL = rs.AddPoint([2*b,4*b,0]) a1_UR = rs.AddPoint([4*b,4*b,0]) a1 = rs.AddSrfPt([a1_LL,a1_UL,a1_UR,a1_LR])

if porosity == 0: HEX_2 = HEX2 else: opl_2 = rs.OffsetCurve(HEX2pl,HEX2cp,porosity*dcp) #HEX_2 = rs.AddLoftSrf([HEX2pl,opl_2]) #rs.DeleteObject(HEX2)

###SQUARE TOP#2# a2_LL = rs.AddPoint([2*b,2*b,5.65*b]) a2_LR = rs.AddPoint([4*b,2*b,5.65*b]) a2_UL = rs.AddPoint([2*b,4*b,5.65*b]) a2_UR = rs.AddPoint([4*b,4*b,5.65*b]) a2 = rs.AddSrfPt([a2_LL,a2_UL,a2_UR,a2_LR])

HEX3 = rs.JoinSurfaces([HEX3a,HEX3b],True) HEX3pl=rs.DuplicateSurfaceBorder(HEX3) rs.DeleteObject(HEX3) HEX3 = rs.AddPlanarSrf(HEX3pl) HEX3cp0= rs.SurfaceAreaCentroid(HEX3) HEX3cp = HEX3cp0[0] HEX3n = rs.SurfaceNormal(HEX3,HEX3cp)

###SQUARE BOTTOM LEFT#3# a3_L = rs.AddPoint([1*b,1*b,1.42*b]) a3_U = rs.AddPoint([1*b,1*b,4.24*b]) a3_MR= rs.AddPoint([2*b,0*b,2.82*b]) a3_ML= rs.AddPoint([0*b,2*b,2.82*b]) a3 = rs.AddSrfPt([a3_L,a3_MR,a3_U,a3_ML])

if porosity == 0: HEX_3 = HEX3 else: opl_3 = rs.OffsetCurve(HEX3pl,HEX3cp,porosity*dcp) #HEX_3 = rs.AddLoftSrf([HEX3pl,opl_3]) #rs.DeleteObject(HEX3)

###SQUARE TOP RIGHT#4# a4_L = rs.AddPoint([5*b,5*b,1.42*b]) a4_U = rs.AddPoint([5*b,5*b,4.24*b]) a4_MR= rs.AddPoint([4*b,6*b,2.82*b]) a4_ML= rs.AddPoint([6*b,4*b,2.82*b]) a4 = rs.AddSrfPt([a4_L,a4_MR,a4_U,a4_ML])

HEX4 = rs.JoinSurfaces([HEX4a,HEX4b],True) HEX4pl=rs.DuplicateSurfaceBorder(HEX4) rs.DeleteObject(HEX4) HEX4 = rs.AddPlanarSrf(HEX4pl) HEX4cp0= rs.SurfaceAreaCentroid(HEX4) HEX4cp = HEX4cp0[0] HEX4n = rs.SurfaceNormal(HEX4,HEX4cp)

###SQUARE BOTTOM RIGHT#5# a5_L = rs.AddPoint([5*b,1*b,1.42*b]) a5_U = rs.AddPoint([5*b,1*b,4.24*b]) a5_MR= rs.AddPoint([6*b,2*b,2.82*b]) a5_ML= rs.AddPoint([4*b,0*b,2.82*b]) a5 = rs.AddSrfPt([a5_L,a5_MR,a5_U,a5_ML])

if porosity == 0: HEX_4 = HEX4 else: opl_4 = rs.OffsetCurve(HEX4pl,HEX4cp,porosity*dcp) #HEX_4 = rs.AddLoftSrf([HEX4pl,opl_4]) #rs.DeleteObject(HEX4)

###SQUARE TOP LEFT#6# a6_L= rs.AddPoint([1*b,5*b,1.42*b]) a6_U= rs.AddPoint([1*b,5*b,4.24*b]) a6_MR=rs.AddPoint([0*b,4*b,2.82*b]) a6_ML=rs.AddPoint([2*b,6*b,2.82*b]) a6 = rs.AddSrfPt([a6_L,a6_MR,a6_U,a6_ML])

HEX5 = rs.JoinSurfaces([HEX5a,HEX5b],True) HEX5pl=rs.DuplicateSurfaceBorder(HEX5) rs.DeleteObject(HEX5) HEX5 = rs.AddPlanarSrf(HEX5pl) HEX5cp0= rs.SurfaceAreaCentroid(HEX5) HEX5cp = HEX5cp0[0] HEX5n = rs.SurfaceNormal(HEX5,HEX5cp)

########################################### HEX1a= rs.AddSrfPt([a1_LL,a1_LR,a5_L,a3_L]) HEX1b= rs.AddSrfPt([a5_L,a3_L,a3_MR,a5_ML]) HEX2a= rs.AddSrfPt([a1_LL,a1_UL,a6_L,a3_L]) HEX2b= rs.AddSrfPt([a6_L,a3_L,a3_ML,a6_MR]) HEX3a= rs.AddSrfPt([a1_UL,a1_UR,a4_L,a6_L]) HEX3b= rs.AddSrfPt([a4_L,a6_L,a6_ML,a4_MR]) HEX4a= rs.AddSrfPt([a1_UR,a1_LR,a5_L,a4_L]) HEX4b= rs.AddSrfPt([a5_L,a4_L,a4_ML,a5_MR]) HEX5a= rs.AddSrfPt([a2_LL,a2_LR,a5_U,a3_U]) HEX5b= rs.AddSrfPt([a5_U,a3_U,a3_MR,a5_ML]) HEX6a= rs.AddSrfPt([a2_LL,a2_UL,a6_U,a3_U]) HEX6b= rs.AddSrfPt([a6_U,a3_U,a3_ML,a6_MR]) HEX7a= rs.AddSrfPt([a2_UL,a2_UR,a4_U,a6_U]) HEX7b= rs.AddSrfPt([a4_U,a6_U,a6_ML,a4_MR]) HEX8a= rs.AddSrfPt([a2_UR,a2_LR,a5_U,a4_U]) HEX8b= rs.AddSrfPt([a5_U,a4_U,a4_ML,a5_MR])

if porosity == 0: HEX_5 = HEX5 else: opl_5 = rs.OffsetCurve(HEX5pl,HEX5cp,porosity*dcp) #HEX_5 = rs.AddLoftSrf([HEX5pl,opl_5]) #rs.DeleteObject(HEX5) HEX6 = rs.JoinSurfaces([HEX6a,HEX6b],True) HEX6pl=rs.DuplicateSurfaceBorder(HEX6) rs.DeleteObject(HEX6) HEX6 = rs.AddPlanarSrf(HEX6pl) HEX6cp0= rs.SurfaceAreaCentroid(HEX6) HEX6cp = HEX6cp0[0] HEX6n = rs.SurfaceNormal(HEX6,HEX6cp)

########################################## ## HEXAGONS ############################## ## HEXn = surface ######################## ## HEXncp = centerpoint ################## ## HEXnpl = outline/polyline ############# ## HEXn = surface normal ################# ########################################## ## HEX1 ## LOW FRONT ##################### ## HEX2 ## LOW LEFT ###################### ## HEX3 ## LOW BACK ###################### ## HEX4 ## LOW RIGHT ##################### ## HEX5 ## HIGH FRONT #################### ## HEX6 ## HIGH LEFT ##################### ## HEX7 ## HIGH BACK ##################### ## HEX8 ## HIGH RIGHT #################### ##########################################

if porosity == 0: HEX_6 = HEX6 else: opl_6 = rs.OffsetCurve(HEX6pl,HEX6cp,porosity*dcp) #HEX_6 = rs.AddLoftSrf([HEX6pl,opl_6]) #rs.DeleteObject(HEX6) HEX7 = rs.JoinSurfaces([HEX7a,HEX7b],True) HEX7pl=rs.DuplicateSurfaceBorder(HEX7) rs.DeleteObject(HEX7) HEX7 = rs.AddPlanarSrf(HEX7pl) HEX7cp0= rs.SurfaceAreaCentroid(HEX7) HEX7cp = HEX7cp0[0] HEX7n = rs.SurfaceNormal(HEX7,HEX7cp) if porosity == 0: HEX_7 = HEX7 else: opl_7 = rs.OffsetCurve(HEX7pl,HEX7cp,porosity*dcp) #HEX_7 = rs.AddLoftSrf([HEX7pl,opl_7]) #rs.DeleteObject(HEX7)

HEX1 = rs.JoinSurfaces([HEX1a,HEX1b],True) HEX1pl=rs.DuplicateSurfaceBorder(HEX1) rs.DeleteObject(HEX1) HEX1 = rs.AddPlanarSrf(HEX1pl) HEX1cp0= rs.SurfaceAreaCentroid(HEX1)

206

APPENDIX

HEX8 = rs.JoinSurfaces([HEX8a,HEX8b],True) HEX8pl=rs.DuplicateSurfaceBorder(HEX8) rs.DeleteObject(HEX8) HEX8 = rs.AddPlanarSrf(HEX8pl) HEX8cp0= rs.SurfaceAreaCentroid(HEX8) HEX8cp = HEX8cp0[0] HEX8n = rs.SurfaceNormal(HEX8,HEX8cp) if porosity == 0: HEX_8 = HEX8 else: opl_8 = rs.OffsetCurve(HEX8pl,HEX8cp,porosity*dcp) #HEX_8 = rs.AddLoftSrf([HEX8pl,opl_8]) #rs.DeleteObject(HEX8) HEXS = rs.JoinSurfaces([HEX1,HEX2,HEX3,HEX4,HEX5, HEX6,HEX7,HEX8,a1,a2,a3,a4,a5,a6]) #### INNER TUBES #### ##TUBE1 1&7 #rs.ReverseCurve(opl_1) #rs.CurveSeam(opl_7,(rs.CurveClosestPoint(opl_7,(rs.CurveStartPoint(opl_1))))) #TUBE1 = rs.AddLoftSrf([opl_7,opl_1]) #TUBE_1=rs.CapPlanarHoles(TUBE1) #T1 = rs.AddPlanarSrf(opl_1) #T7 = rs.AddPlanarSrf(opl_7) ##TUBE2 2&8 #rs.CurveSeam(opl_8,(rs.CurveClosestPoint(opl_8,(rs.CurveStartPoint(opl_2))))) #TUBE2 = rs.AddLoftSrf([opl_2,opl_8]) #TUBE_2= rs.CapPlanarHoles(TUBE2) #T2 = rs.AddPlanarSrf(opl_2) #T8 = rs.AddPlanarSrf(opl_8) #TUBE3 3&5 rs.ReverseCurve(opl_3) rs.CurveSeam(opl_5,(rs.CurveClosestPoint(opl_5,(rs.CurveStartPoint(opl_3))))) TUBE3 = rs.AddLoftSrf([opl_3,opl_5]) rs.CapPlanarHoles(TUBE3) #T3 = rs.AddPlanarSrf(opl_3) #T5 = rs.AddPlanarSrf(opl_5) TUBE3cnt= rs.SurfaceVolumeCentroid(TUBE3) TUBE4=rs.RotateObject(TUBE3,TUBE3cnt[0],90,[0,0,1],True) TUBE1=rs.RotateObject(TUBE3,TUBE3cnt[0],180,[0,0,1],True) TUBE2=rs.RotateObject(TUBE3,TUBE3cnt[0],270,[0,0,1],True) #T1_2 = rs.BooleanUnion([TUBE1,TUBE2]) #T3_4 = rs.BooleanUnion([TUBE3,TUBE4]) #HEXS1 = rs.BooleanDifference(HEXS,T1_2) #HEXS2 = rs.BooleanDifference(HEXS,T3_4) ##TUBE4 4&6 #rs.CurveSeam(opl_6,(rs.CurveClosestPoint(opl_6,(rs.CurveStartPoint(opl_4))))) #TUBE4 = rs.AddLoftSrf([opl_4,opl_6]) #TUBE_4= rs.CapPlanarHoles(TUBE4) #T4 = rs.AddPlanarSrf(opl_4) #T6 = rs.AddPlanarSrf(opl_6)

#PRIMITIVE1 = rs.JoinSurfaces([HEX1,HEX2,HEX3,HEX4,HEX5,HEX6,HEX7,HEX8,a1,a2,a3,a4,a5,a6],True) ############################################################################ ########################## PRIMITIVE ####################################### ############################################################################ PRIMITIVE1 = rs.JoinSurfaces([HEX1,HEX2,HEX3,HEX4,HEX5,HEX6,HEX7,HEX8,a1,a2,a3,a4,a5,a6],True) ###SPACE PACKING VECTORS### x_space_vector = rs.VectorCreate(a5_MR,a1_LL) #x_space_vector1b = rs.VectorCreate(a5_MR,a2_LL) y_space_vector = rs.VectorCreate(a6_ML,a1_LL) ###DISTANCE### dist = (rs.Distance(a3_ML,a5_MR)+rs.Distance(a3_MR,a5_ML)) PRIMITIVE0 = rs.ScaleObject(PRIMITIVE1,[0,0,0],[scale,scale,scale]) rs.DeleteObjects([a1_LL,a1_UL,a1_UR,a1_LR,a2_LL,a2_UL,a2_UR,a2_LR,a3_L,a3_MR,a3_U,a3_ML,a4_L, a4_MR,a4_U,a4_ML,a5_L,a5_MR,a5_U,a5_ML,a6_L,a6_MR,a6_U,a6_ML]) CELLULAR COMPLEXITY

PRIMITIVE = rs.MoveObject(PRIMITIVE0, vector)

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x_primitives = [] for i in range(0,amount_x): vect_x = [dist*(i+1),0,0] x_primitives.append(rs.CopyObjects(blocks4, vect_x)) x_primitives.append(blocks4) listx = len(x_primitives) s_block_y1 = rs.CopyObjects(x_primitives[0],y_space_vector) s_block_y2 = rs.CopyObjects(x_primitives[1],y_space_vector) s_block_y1.append(rs.CopyObject(s_block_x,y_space_vector)) s_block_y1.append(rs.CopyObject(PRIMITIVE,y_space_vector)) y_primitives = [] for j in range(0,amount_y): for k in range(0,listx): vect_y = [0,dist*(j+1),0] y_primitives.append(rs.CopyObjects(x_primitives[k],vect_y)) listy = len(y_primitives) z_primtives = [] for a in range(0,amount_z): vect_z = [0,0,0.94*(a+1)] for b in range(0,listx): z_primtives.append(rs.CopyObjects(x_primitives[b],vect_z)) for c in range(0,listy): z_primtives.append(rs.CopyObjects(y_primitives[c],vect_z)) # primitives_x = [] # for i in range(0,amount_x): # vect = rs.VectorScale(x_space_vector,i+1) # rs.CopyObject(PRIMITIVE,vect) ##draw_primitive(base point, porosity offset,scale(bounding box),grid(0or1), amount x, amount y, amount z) ## draw_primitive([0,0,0],0.25,1,0,3,3,3)

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APPENDIX

CELLULAR COMPLEXITY

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