Lace Wall Report Booklet

CITA: Centre for I T and Architecture

23 December 2016

9

LACE WALL CABLE NET PROJECT FORM-ACTIVE HYBRID STRUCTURES

2

CONTENT

5

13

7 INTRODUCTION

CONTEXT

DEVELOPMENT

103 REFERENCES

METHODS

95

81

51

3

PROPOSAL

OUTLOOK

4

INTRODUCTION INVESTIGATING THE INTERACTION OF FORCES IN HYBRID STRUCTURES We are finding ourselves in a time of rethinking our material practices. In architecture, the ability to use materials in smarter and less intense manners is fundamental building blocks for the conception of lighter building culture.

Lace Wall explores hybrid structures that combine elements in tension and compression in a pre-calculated balance. Here two elements of low stiffness - a fibreglass beam and a textile cable network – are combined in interdependent relationships to create one whole of high stiffness.

Lace Wall examines the design methods necessitated to design and develop such structures. By learning from prior research into hybrid structures our aim is to formalise and extend an otherwise mainly empirical methodology of hands-on testing, instead developing digital design methods that incorporate the simulation of interacting material systems, enable structural variation and local optimisation and bridge to fabrication.

Left page: Lace Wall final demostrator, Complex Modelling exhibition, 2016.

5

CONTEXT

8

STATE

OF

ART

FORM ACTIVE HYBRID STRUCTURES Lace Wall is part of a larger investigation into the design and fabrication of form-active hybrid structures. It builds on prior work in the Complex Modelling project Tower expanding the vocabulary of these structures by investigating a distributed cell-based structural system and replacing the full textile membrane with a strategic network of tensile cables.

At present the design of form-active hybrid structures is impeded by the lack of design tools that enable their investigation. Recent interest has resulted in new methods for shaping and form-finding form-active hybrid structures including finite element modelling (1), spring-based modelling (2) and force-density methods (3). However, these methods focus on validation of structures and omit the initial processes of defining assemblies of elements and supports (4).

Top: ICD ITKE Textil Hybrid, 2012 Middle: Bat Wing Sail, R Off, 2007 Bottom: Membrane Restrained Column, UDK 2012

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10

This design concept can be described as a “deep form active hybrid skin�. That is, a generic and modular space frame-like FAHS system, which can be extended in a spatial array to construct large enclosures such as walls, roofs, domes and more complex macro shapes. The design challenge is thus to develop a modular system with an increased focus on local and global topology of the structural system in comparison to Hybrid Tower. To focus the research on exploratory assembly topology

DISTRIBUTED SYSTEMS SPATIAL HYBRID SURFACES: FROM TEXTILE TO NETS Lace Wall is a 12 meter long and 5 meter high wall constructed from 80 cable net units. Lace Wall follows a textile logic of cells and arrays.

Just as in knit or lace, individual cells are manipulated locally to allow for global shaping as well as compensate for the different structural impact of self-load across the structure.

Lace Wall includes methods for simulating the assemblies and analyse the structural interaction between cells and their aggregate behaviour. This allows us to understand and control how different cell topologies with different tiling dimensions can be manipulated to form the overall macro shape. The Lace Wall Project investigates the transition of membrane restrained active bending systems to a new class of net restrained systems.

Top: Pringle topology prototype restrained by textile membrane Bottom: Pringle prototype restrained by the net system Left page: Deep surface prototype with discontinuous bending elements

11

METHODS

2016-02-02T10:52:31

PHYSICAL PROTOTYPING

CRUCIAL VARIABLES FOR THE PRIMITIVE

EXPLORING THE DIVERCITIES In the early design stage of the project focussed on building an understanding of topological diversity. By working through physical prototyping the fundamental material behaviour of the units were understood and an intuition for their variation was built. Prototypes were built in scaled models using 1.5mm glass fibre rod and waxed thread. The complexity of units was varying depending on the length of the active bending rod that was used as well as amount of tension cable present in each element.

will perform my bigger bending resistance

The prototype investigation was documented in a catalogue of “primitives”, that later was used to understand the further topology exploration of the primitive, the array and field.

1. very important the proportion between the circumference of the loop in the relation to the line to line self overlap 2. the cable attached in all examples in the same pattern location: middle of loop to the end of line-line self overlap 3. self overlap in all examples is till the middle of tail

Top: Single ‘tail’ prototype primitives in which hte tail allows connection to furtherunits.

Middle: Difference between the loop based primitives Left: Catalog of primitives

15

NonPeriodic Connection is achived using developing CVs Self, Point, End-end, Periodic

Self, Point, End-end, NonPeriodic

Self, Point, Inside-Inside

Self, Overlap, End-Inside

Self, Point, End-Inside

Overlapping Edges

Self, Overlap, End-end, Periodic

16

Non-Periodic connection achieved using acute angle Self, Point, End-end, NonPeriodic

Overlapping Edges

Overlapping Edges

Self, Overlap, End-End, NonPeriodic

Self, Overlap, End-Inside

Self, Point Inside-Inside & Self Point, End-End, Periodic

Self, Overlap, End-Inside

Overlapping Edges Self, Overlap, Inside-Inside

DIGITAL PROTOTYPING NUMERICAL SKETCHING In parallel to the physical prototyping we developed a digital modelling environment that is able to simulate the reciprocal relations between the active bent rod and the cable net.

Form active hybrid structures are constructed by transforming stress-free linear and planar elements into an assembly of curved elements through elastic bending of beams and tensioning of membranes/cables. This process is similar whether using physical or computational modelling. As a modelling problem, this is characterised by a high degree of interdependent behaviour, which adds complexity of the modelling tool.

The digital modelling environment allows us to engage in an investigations of base topologies and their inherent performance. By modelling in digital and physical in parallel performances could be compared and corrected.

Top: Digital primitives exploration Left: Digital explorations on subject of cable net diversity Left page: Catalog of beam self connections

17

18

AGGREGATION OF

PRIMITIVES

EARLY ATTEMPTS ON GEOMETRICAL ORGANISATION LOGICS The interest in the primitive is the ability for them to aggregate into larger systems. To understand the inherent ability for the primitive to aggregate, a series of parallel digital and physical prototypes were designed exploring connectivity and variation.

Left: Digital explorations on primitive arrays

19

Simulation of one unit from gh (60% scaled the same image as on the previous page)

Simulation of one unit from gh (60% scaled the same image as on the previous page)

Simulation of one unit from gh (60% scaled the same image as on the previous page) Simulation of one unit from gh (60% scaled the same image as on the previous page)

Field image top (simulation)

Simulation of one unit from gh (60% scaled the same image as on the previous page)

Field image top (simulation) Simulation of one unit from gh (60% scaled the same image as on the previous page)

Simulation of one unit from gh (60% scaled the same image as on the previous page)

Field image top (simulation)

Simulation of one unit from gh (60% scaled the same image as on the previous page)

Field image top (simulation)

Field image perspective (simulation)

Simulation of one unit from gh (60% scaled the same image as on the previous page)

Simulation of one unit from gh (60% scaled the same image as on the previous page)

20

Simulation of one unit from gh (60% scaled the same image as on the previous page)

Field image perspective (simulation)

Simulation of one unit from gh (60% scaled the same image as on the previous page)

Simulation of one unit from gh (60% scaled the same image as on the previous page)

Field image perspective (simulation)

Field image perspective (simulation)

Field im

Simulation of one unit from gh (60% scaled the same image as on the previous page)

Simulation of one unit from gh (60% scaled the same image as on the previous page)

Simulation of one unit from gh (60% scaled the same image as on the previous page)

Field image perspective (simulation)

Field image perspective (simulation)

Field image perspective (simulation)

Simulation of one unit from gh (60% scaled the same image as on the previous page)

Simulation of one unit from gh (60% scaled the same image as on the previous page) Simulation of one unit from gh (60% scaled the same image as on the previous page)

Field image perspective

Field image perspective (simulation)

Field image perspective (simulation)

Field image perspective (simulatio

formation of half-unit

formation of unit by attaching two half units

cable net structure>

pull down the free beams end with cables

cable net modification 1

01.

a

TRANSFORMING OPERATIONS. RULES FOR AGGREGATION

b

By building an understand of the inherent 21 asymmetries of the primitives we became (3mm in- model01) terested in how macro behaviour emerges from the base design of the unit structures. By looking at arraying, pairing and mirroring primitives we were interested in how these behaviours can become controllable design dimensions.

01.

01. 01.

a

a

02. no cables!!!!!

a b

b

a

b

b

!

Depending on the angle of rotation and the translation vector it was possible to achieve a variety of geometrical macro behaviours.

02.

02. 02.

03. a

a

a

b

a

b

b

The final unit design is made from a mirrored pair of bent rods with varying cable network optimised for its particular position in the assembly.

03.

03. 03.

04.

a

a

a

a

B

Left page: Digital explorations on pringle primitive arrays Top: Sequantial diagram for attaching two primitive elements Left: Translation transformation to form a linear array 04.

04. 04.

Initial parameters: -translation vector -rotation angle

translation vector causes the shift of the base unit translation angle to create an array

mirrored internal cable net

internal cable net

translation vector causes the shift of the base unit to create an array

translation angle 40

anchor points

anchor points

22

step 01

step 02

half circular arrangement without constraining cables, hinge freedom

half circular arrangement cables are only withon the unit, hinge freedom remains

mirrored internal cable net

internal cable net

external cable net translation vector causes the shift of the base unit to create an array translation angle 40

mirrored internal cable net

internal cable net

extended external cable net

23

step 03

step 04

half circular arrangement, cables are within the units as well as in between units

half circular arrangement, with expanded network of cables

Line/line overlap connections could be Line/Line overlap connections could be reduced to leave more freedom to the system reduced to leave more freedome to the system Applies mostly for non planar targer geometries (curved wall, etc) Applies only for non-planar target geometries (curved wall, etc)

“Open“ part of the component: opportunity "Open" part of the component, to varydimension the dimension toopportunity vary the of cable and affect the geometry of cables and affect the target geometry.

Local plane deforLocal planes deformations by cable tension mations by cable tensioning

a initial element, loop with tail

“Open“ part of the component: opportunity to vary the dimension "Open" part of the component, ofopportunity cables and affect the to vary the dimension target geometry. of cable and affect the geometry

Setamount up with Minimal of cablesminimal for self support amount of cables

a+ mirrored bottom causes the change of the neck angle

-a mirrored in two planes

24 If the cluster has elements that are mirrored in 4 planes, theoretically it means that it will stabilize itself and not perform and directional performance (e.g. twisting in one direction, etc.)

This one will be suitable for: PLANAR SOLUTIONS WITH LOCAL DEFORMATIONS (texture) TARGET GEOMETRIES WITH THE ENCLOSED EDGE (cylinder)

-a+ initial a mirrored in 4 planes

INTERDEPENDENT UNIT AGGREGATION TEXTILE LOGIC IN LACE WALL The concept of the distributed form active hybrid structure arises from a deep interest in textile logics and the ability for textiles systems to be transferred into architectural scale structures (4, 5). In textile systems such as knit and lace, base stiches make up the units of the structure. However, these structures have self-binding as the fibres are continuous through the material system.

Lace Wall binds the units together through connection details. While making them tractable, this results in inherently different performances than traditional textile systems.

Left page: Effectiveness of the different cable net on the same beam structure Right page: Physical prototypes of interdependent systems

25

NSIBLE CABLES ENT ASSEMBLY

2016-02-03T15:49:51

LOGIC RESPONSIBLE LOGIC RESPONSIBLE CABLES CABLES INTERDEPENDENT INTERDEPENDENT ASSEMBLYASSEMBLY

2016-02 2016-02-09T14:51:12

LOGIC RESPONSIBLE CABLES bbINTERDEPENDENT ASSEMBLY

b-

a

ab -+

b+

b+

a-

a+

a

ab +

b-

b2016-02-09T14:50:48 ab +

ab -+

b-

b-

ab++

ab++

LOGICa +RESPONSIBLE CABLES INTERDEPENDENT ASSEMBLY

a-

a+

ab-

2016-02-09T14:5

a-

a-

components "b+" andin"b-" work in a pair components "b+" and "b-" work together a pair a together + to fill outgrid theof gaps between grid of "a" components to fill out theagaps between "a" a components

a+

a

a-

a-

a+

a-

a+

a a-

a a-

a+

a-

a+

a

a-

a+

a-

a+

a

a-

a+

***next step ans is tosee build a claster ans see how it ***next step is to build a claster how it works and see if there is any material redundancy see if there is any material redundancy

a-

a+

a+

explosion diagram for the tiling principle

a

puzzling logic

26

a+

a a-

b

a-

a+

a+ a assembly tiling

a

a

a

a

a

aa

a+

a-

a

a a

a

a

a

a

a a

a

to "close the edge"

a

a

a

a

a

a

a + and a are corner condition compo

three of them are needed to "close the edge" three of them are needed

a-

a+

a

a

a

a

a a

b+

a

a

a

a a

aa

b+

a

a

a

a

a

a

b

b

a

a

a + and a are corner growth in the Xcondition direction components

a

a

a

a

a

a

b+ a

a

b b

a-

aa+

a-

a+

a

a

a

a+ a

a a - bb++ b

a- b+

a

growth in both X and Y direction

growth of the field in

a

a-

a+

agrowth of the field in U

a+

a

component a (two tails) can be used for the structure to grow in U and V direction

component a (two tails) can be used for the structure to grow in U and V direction

In the process of working with the highly interdependent systems it was observed the nessesity to have several unit types in order toachieve tilable connection.

LOGIC RESPONSIBLE CABLES INTERDEPENDENT ASSEMBLY

2016-02-03T12:04:54

3

without a third component and cable netwithout third component and work the pair is not stable the cable network is not stableby itself.

2

additional element additional (3) element brings (3) a gives stability to elestability to the 2. behaviour: whole structure ment 2.element material material behavior: leaning to the side, is leaning to the side, need an opposite counneed an opposite counter tension ter tension

link between pairs

pair type is mirrored,

by mirroring the pair type, the both pairs areis counter counter tension achieved so both are balancing eachpair other holding each other in balance

toto reduce redundancy the row, second row, reduce redundancy in the in secong twocomponents components areare replaces with one two replaced withthat one that is having two simmetrical offsprings is having two simmetrical offsprings

Left page: Growth direction in the interdependent unit system Right page: Sequense in interdependen unit systems

27

top view top view top view top top view view

top view top view

top view

top view

2016-02-16T11:16:2 2016-02-16T11:

perspective

2016-02-16T11:16:21 2016-02-16T11:16:21 2016-02-16T1 perspective view perspective view 2016-02-16T11:16

2016-02-16T11 perspective perspective view view perspective view

2016-02-16T11:16:2

perspective view

perspective view perspective view

single interdependent unit, without being fixed to surface is having a trouble to keep in shape

a row of interdependent units, performing a better stability than a single element 28

a row of interdependent units, performing a curling of the surface based on the modification of cable net configuration

2d array of interdependent units, which gain stability from being “intewoven� one to another

2016-02-17T16:04:39 2016-02-17T16:04:39

a a

a

a+

a+a+

a

a a

2016-02-17T16:04:08

a+a+

pair configuration A and A+ with cable net configuration 01

a+

C: CLenF: C: CLenF: 0.83, 0.83, CStr: CStr: 300300 B: SpStr: B: SpStr: 5000, 5000, BStr:190.49, BStr:190.49, BAng: BAng: 1.0 1.0

excercise 01 2016-02-17T16:04:39

pair configuration A and A+ with cable net configuration 02 a

a+

a

a+

2016-02-17T16:05:53 2016-02-17T16:05:53

*PHYSICAL PROTOTYPE AS A REFERENCE

a

a+

-a

-a+

a

aa +

a+

-a

--aa +

-a+

2016-02-17T16:05:53

C: C: CLenF: CLenF: 0.84, 0.84, CStr: CStr: 266 266 B: B: SpStr: SpStr: 5000, 5000, BStr:190.49, BStr:190.49, BAng: BAng: 1.01.0

group configuration A and A+ (double pair)

excercise 02

2016-02-17T16:06:12 2016-02-17T16:06:12

*PHYSICAL *PHYSICAL PROTOTYPE C: CLenF: 0.83, CStr: 300 PROTOTYPE AS A REFERENCE AS A REFERENCE B: SpStr: 5000, BStr:190.49, BAng: 1.0

array build up from above pair configurations

excercise 03

2016-02-17T16:06:12

C: CLenF: 0.84, CStr: 266 B: SpStr: 5000, BStr:190.49, BAng: 1.0

excercise 04

29

defining assembly topology

1

2

defining assembly dimensions

30

3

4 shaped geometry

K2 forces visualisation

0C 245 0 > 180

1C 180 0 > 180

0 > 284

0 > 181

0 > 3159

0 > 1084

11C 235

284 > 181

0 > 3159

0 > 4676

13B 5528

12C 369

180 > 235

9C 284

10C 181

0 > 3888

0 > 4799

0 > 4676

0 > 235

0 > 284

7C 235

284 > 181

180 > 369

4C 180

180 > 235

6C 181

245 > 369

0 > 180

8C 369

0 > 235

5C 284

2C 180

180 > 369

3C 180

0 > 181

245 > 180

0 > 369

2910-3159 > 5528-5278 0-239 > 2755-2515

0 > 1084

0 > 3888

0 > 4799

4613-4862 > 4862-4613 1703-1943 > 811-1051 811-1051 > 1703-1943

14B 5528

5

2910-3159 > 5528-5278 0-239 > 2755-2515

160824_0953_GenGenome8_WedgeAngle5p01_ID10

assembly graph

6

cable net fabrication labeling

process

process

process

1

process

process

2

data

5

6 7

data

process

process data

3

process data

4

data

MODELLING PIPELINE CALLIBRATED MODELLING The modelling of the unit topology is enabled by the discretisation of the primitive geometry through projective based dynamic relaxation.

Here, goals are assigned to the discretised geometry, which allows us to accurately represent real world mechanical behaviour.

This form finding process solves the interaction between the elements in the single unit and allows us to analyse structural performance.

Here, sub models test if the cable network is active and well defined, if the angles of cables are perpendicular to the beams and if the unit as a whole can tile well with adjacent units.

This information is then fed back to the start of the design model enabling a circular and iterative design chain by which to optimise the cable network topologies.

7

fabrication diagram for cables

Top: Modelling pipeline diagram Bottom and left page: Pipeline steps representation through a single unit modelling

31

axial

bending

reactions

shear

32

CUSTOM

GOALS

AND

K2

ENGINEERING TOWARDS MECHANICALLY ACCURATE BEHAVIOUR The Grasshopper plugin Kangaroo has become an established tool for the architectural design community helping to realise many real and conceptual projects. Its functionality has, until recently, largely been associated with simulations independent of, or using arbitrary, material stiffness. However, the implementation of a projection based dynamic relaxation technique and an improved damping scheme in the latest release of Kangaroo facilitate simulation of mechanically accurate structural behaviour with remarkable stability and speed. This version encourages the development of custom goals through an API which was utilised to create a structurally calibrated extension called K2Engineering. The main purpose of this plugin is to offer a direct output of meaningful structural values that can be used to evaluate the performance. The plugin currently contains a bar, cable, rod and support goal from which the axial forces, reactions, shear and bending moments can be extracted.

Left: Gregory Quinn SG2016 workshop Calibrated Modelling of Form-Active Structures, Gothenburg, Sweden Left page: Visualisation of forces in K2 Engineering

33

1C 300

0 > 567

1 > 156

0 > 4067 0 > 248

300 > 567

0

0 > 300

3C

11C248 156

14C 567

0 > 329

0 > 174

arrow: connection data between elements.

0>240 means that element 6C is connecting to element 8C at 0 > 5231 th 0 point of 6C and at 241 point of 8C

1C 300

248 > 329

0C 293

0 > 174

0 > 300

C 74

0 > 159

34

5C 174

0 > 241

300 > 567

0 > 290

0>

300 > 567

13C 329

6C 174 0 > 241

0 > 329

12C 290 0 > 4067

0 > 1569

0 > 174

8C 241

20C 567

0 > 241 248 > 329

8C 14C241 567

174 > 290

17C 18C 156 290

19C 329

174 > 290

18C 290

0 > 159

0 > 156 0 > 5231

159 > 185

0 > 290 300 > 567

0 > 329

0 > 290

0 > 156

0 > 4067

11C 6442156

4C 248

0 > 174

174 > 290

0 > 156

293 > 567

0 > 248

14C 567

0 > 329

241 > 156

0 > 185

0>0

248 > 329

0 > 6442

7C 241

9C 159

241 > 156

0>0

0 > 159

15C 159

0 > 185

0 > 6442

159 > 185

0 > 5231

0 > 1213

0 > 1569

0 > 2415

0 > 5231

0 > 2169

17C 156

0 > 6442

0 > 6442

0 > 967

0>0

0 > 290 0 > 6442

0 > 6442

21B 7366

13C 329 17C

0 > 967

0-258 > 3545-3286 3964-4192 > 7366-7138

2169-2708 > 967-1506 6202-6681 > 6681-6202 967-1506 > 2169-2708

156

16C 185

241 > 156

0 > 1213

21B 7366 0 > 6442

16C 185

0-258 > 3545-3286 3964-4192 > 7366-7138

CableNetwork_FormFound_ID21

0 > 6442

0 > 6442

174 > 290

12C 290

21B 7366

0 > 1569

0-258 > 3545-3286 3964-4192 > 7366-7138

159 > 185

0 > 1213

black node: beam.

21 - the item number in the list, B - beam.2169-2708 > 9 7366 - the length of the element in mm.6202-6681 > 66

0 > 967

0-258 > 3545-3286 3964-4192 > 7366-7138

0 > 967

0 > 2415

0 > 2169

22B 7366

0 > 185

0 > 4067

15C 159

248 > 329 10C 185

4

56

3C 248

12C 290

> 156

C 6

0 > 248

0 > 174

2C

6C300 174

0 > 567

0 > 1569

3 - the item number in the list, C - cable.

0 3C > 248 248 - the length of the element in mm. 248 174 > 290

293 > 300

1C 300

13C 329 white node: cable.

0 > 290

4C 248

0 > 2415

0 > 6442

967-1506 > 21

0 > 2169

2169-2708 > 967-1506 6202-6681 > 6681-6202 967-1506 > 2169-2708

CableNetwork_FormFou 22B 7366

0 > 4067

0-258 > 3545-3286 3964-4192 > 7366-7138

0 > 156

VISUALISATION FABRICATION INFORMATION GRAPHIC REPRESENTATIONS The final process in the pipeline prepares for fabrication. Because of the inherent complexity of the cells, we use graph representation as a means of mapping the relationships between the individual beams and the cables. The graph is a symbolic representation of interconnections that describe the topological interdependencies and also a data structure that captures and annotates all lengths and dimensions.

These are used to generate the fabrication data and, importantly, the assembly order of the structure. All the nodes of the graph are symbolising the elements: black - beam, white - cables. The arrows between nodes are containing information about the location of the connection and arrow direction helps to understand the order of reading the information.

Top: Dot file, GraphViz visualisation for a complex assembly.

Left: Evolution of graph complexity Left page: Graph of one of the final unit

35

initial digital shaping model

input polyline geometry

baked geo from pipelin, zombi solver

pointcloud from the scan

Galapagos solver

36 initial poly with default genepool parameters

initial poly shaped into cables mathing state with target genepool parameters

shaped 3D cables vs. 3D scanned points

average position between shaped end cable points and 3D scanned ones

new cable net is drawn inbetween fitnessed points and a new set of parameteres is generated

resulting genenom can be plugged back in a feedback loop to the shaping in order to shape again through the pipeline the model which is now closer to the real physical model

physical model

points from 3D scan

points from 3D scan with assigned tags

overlayed digital model input with physical scan output

input polyline geo + scanned points

3D

SCANNING

COMPARISON OF A DIGITAL AND BUILD UNIT

tag of the point where cables and beams meet

cable network traced from the scan

3D scan of the unit with overlayed tags

To evaluate and calibrate the precision of the digital simulations, we 3D scan the built units and compare them with the digital models.

Despite being very precise in following the topological set up of the units, there are definite differences between the material behaviour and the simulations.

The 3D scanning aimed to figure out how big are those differences could be. The 3D scanned point cloud is overlaid onto the 3D model of the simulated unit. In order to align both models (3D scan and the digital model) the same location points should be distinguished. The most recognisable places are the points where the cables are meeting the beams.

Those points were labelled in the both models with a corresponding order. Afterwards, the set up was plugged into Galapagos Search Engine in order to extract the difference distances between the points.

The ascertained deviation was used to calibrate the inherent tolerance of the system.

Top and Left Page: 3D scanning exercise Left: Explosion diagram of a 3D scanned model

37

38

SINGLE

UNIT

ASSEMBLY SQUENTIAL BUILDING In order to build a unit there is a sequence for the assembly process: 1. Retract fabrication data from modelling pipeline 2. Distinguish the length of beam and cable members 3. Cut GFRP rods into the particular length 4. Produce cable net with embedded plastic details 5. Label beam in corresponding locations 6. Form the fibre glass loop in two mirrored half-units 7. Attach the two mirrored half-units.

8. Place the cable net to constrain the beams into the shape.

Top and Left: Plan and perspective view of the unit Left page: Stopmotion of building a single unit

39

40

DETAILS PHYSICAL CONNECTIONS Details play an important role in the system.

The detailing is developed in CNC milled HDPE (Hight Density PolyEthilene) which allows us to use the materials inherent flexibility and strength.

All details follow a snap-fit logic in which material bending allow the locking of connections on to the fibreglass beams and allow tightening of the cable net.

Details were explored through a series of iteration in which the connection logic, snap fitting and its local tensioning were optimised.

Left Page: Close up image of the detail of the large instalation Lace Wall

41

Rope wire cutter tool

Ultra Sonic Welder

42

Woven polyester belts

FABRICATION IN HOUSE The details are categorised as three different types: - Beam to beam connection - Cable to beam connection - Cable to cable connection The development of the details were undertaking through an iterative fabrication of designed details and load testing.

Left Page: Fabrication tools that were used for making cable nets Left and Top:: Produced HDPE details for the installation

43

S-shape clamp with a single pin lock

S-shape clamp with a double pin lock

Two part Puzzle solution 44

8-Shape single piece clamp

S-Shape clamp with smoother design

Horse-shoe clamp with the screw solution

BEAM TO BEAM CONNECTIONS The beam to beam connections close the mirrored part-unit and attach the two part units to each other. Both case imply an overlap connection in which beams pass by each other in a double connection so as to avoid hinge rotation in the system.

Challenges occur when trying to prevent beam from twisting and introducing torsion into the sytem. To achieve this, a further layer of rubber was added between the plastic detail and the rod to create additional friction.

Top and left page: Development of the beam to beam connection Left: Photos of the beam to beam connection prototypes

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CABLE TO BEAM AND CABLE TO CABLE CONNECTIONS Cable to beam connections employ a snap-fit hook solution. This solution was chosen in order to facilitate easy on-site assembly and support the challenge of sequencing assembly in a rational way.

To organise the connection between cables a closed nylon ring was used for its stability and strength in the highly tensioned cable networks.

Top: Ring variations Left Page: Development of the cable beam connection (hooks) Left: Plexiglass details for early cable nets

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S-shape clamp for beam to beam connection with the screw connection

Hook for cable to beam connections

Hook for cable to beam connections

Two-component puzzle clamp for beam to beam connection

Horse-shoe clamp for beam to beam connection

8-shape clamp for beam to beam self connection (to form a loop)

3D AXIS MILLING OF DETAILS All the details were prototyped and fabricated in house at the CITA Fabrication Lab on two 3 axis milling machines. The milling strategy was developed in accordance to the large amount of details and the complexity and detail of the designs.

Horse-shoe clamp for beam to base connection (attach to the base metal rim)

S shape clamp for beam to beam connection

Left page top: Nesting of the details for milling, milling path in RhinoCAM Top: Photo of the milling process Bottom: Milling paths of the prototyped details

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DEVELOPMENT

M1 nit based system

SYSTEM 1 Single unit based system

Cable net 3d

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3 1

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0.100662

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10 8

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0.098315 0.13354

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attach the open cable from the previous unit in

Attach the open cable from previous unit in the middle over here

5 0.083

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cable net unrolled flat with the target beams location tags and length

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Cable net unrolled flat with the target beam locations and length

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Cable net unrolled flat with the target beam locations and length

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641

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WORKSHOP INVOLVING STUDENTS INTO THE RESEARCH Throughout the project period, CITA invited students from CITA Studio to participate in one of the development phases. Students were involved in analysing the fabrication data drawings and building units according to the generated graph instructions.

During the workshop two types of units were tested: - the hugging unit - the open tail loop unit The workshop resulted in that the hugging unit was considered the most diverse and promising solution and was selected for further development.

It was a very successful exchange. The project team got some useful input on fabrication data optimisation as well as on the cable net design.

In turn, students got experience in designing for and with active bending and understanding fabricating.

Top: Built prototype Left Page: Fabricational drawings for unis assembly Left: Students participating in the workshop

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anchored last row Anchors for the last row to supp A due to Duethe to inderdependency of uniD interdependency condition

beams, Beam B GFRP 4mm by GFRP rod 4mm Represented R

cables, Cable C Represented by nylon polyesteR 12mm nylon t textile bandpolyes12 mm ter band

SYSTEM 1 Single unit based system Polyline input geometry Array 5*4

Single unit based system Array 5*4 Polyline input Top view

SYSTEM 1 Single unit based system Polyline input geometry Array 5*4

Single unit based system Single Array unit based system Single unit based system 5*4 Form found geometry Form found geometry Shaped output Array 5*4 Array 5*4 Top view

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Single unit based system Array 5*4 Polyline input

port its

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Pair system B

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ASSEMBLY ENCODING /NO SUB TITLE SO FAR/ Assembly encoding refers to the process of algorithmically defining FAHS assemblies such that they may be generated from a list of numerical values (known as a genome) determining assembly topology and geometry. This enables the integration of generic meta-heuristic solvers (such as Genetic Algorithms and Simulated Annealing) for the search and optimization of good fit FAHS assemblies. This is structured as a three-stage process: 1) Generate a beam unit using a parameterisation that define beam overlaps and ring diameters. 2) Generate a cable network using a parameterisation that samples points along the beam unit to serve as the outer nodes of the cable network (as the input for the closest pair minimal network algorithm). 3) Slide the outer nodes of the cable network along the beams using a parameterisation that defines the total beam unit distance as one 0.00-1.00 parameter space.

Left Page: Assembly encoding visualisation with involved data outcome Left: Genome defined topology and fitness box for better tiling

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tile

box

Distribution of elements in 3D

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Puzzling of the volumetric rombo units

unit

Empty rectangles between units A+ A+ A+ A+

Empty rectangles between piar rows A+ A+ A+ A+

ARRAYING HIERARCHICAL ARRAYS

Empty rectangles between double pairs A+ A- A+ A-

For the investigation into arraying the units into a two dimensional array, the three dimensional beam unit was simplified to the box-like geometry in order to understand the arraying possibilities more clearly. The arraying turned out to be complex in that it needs to ensure the fundamental connectivity of the system without introducing curving.

The terminology of the approach could be councluded in the following definitions:

Empty rectangles between pairs and rows A+ A- A+ A-

Shift of the vertical rows A+ A+ A+ A+

- A tile: the tile is the highest of the hierarchical relations and is understood as a two dimensional rhomboid shape that easily packs into a packing system - A box: the box is a volumetric representation of the unit that fits around the rhomboid while giving it spatial depth - A unit: the units is the actual polyline beam configuration Left Page: Tiling principles on the levels of tile, box and unit Left: Tiling topology exercises

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initial point cloud

pairwise connectivity

relaxed network

topological centrality

CABLE

NET

DEVELOPMENT METHODS FOR GENERATION VARYING CABLE NET S The generation of cable networks is informed by the typologies produced during interactive and physical modelling. Here a general tendency towards minimal trivalent networks was observed. That is, networks which have few members (i.e. cables), yet are efficient at restraining a beam unit and typically only have three cables meeting in one internal node.

These properties are similar to the class of graph networks known as Steiner trees. There are no known fast algorithm for generating these. Instead, we developed a pseudo Steiner tree algorithm that will generate a minimal valence 3 network algorithm fast and in linear time. This is based on a logic in which we iteratively find the closest node pair from a set of points, connect these nodes with an edge (i.e. a line/cable), remove the nodes from the set and add the midpoint of the edge to the node set.

The resulting network is subsequently relaxed once it is fully connected.

Top: General methods for collapcing edges Left: Implementation of K2 Engineering Left page: Branching method for cable networks

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Genome: 0.519 0.140 0.258 0.634 0.865 0.157

Entries: 5 Iterations: 106 Genome Size: 6 Max Fitness: 0.7 Max Similarity: 1.0

DESIGN

SPACE

SEARCH NOVELTY EXPLORATION The design space search was primarily focused on generating diversity of cable networks using one well-known beam unit. That is, to generate a large set of well performing cable networks looking for diversity both in terms of network size and topology. In regards to evaluating performance, several methods of analysis were implemented to define fitness to use with the meta-heuristic search and optimization processes. These can described as being either binary or continuous. To be considered a candidate, an assembly has to pass both geometric analysis (do all cables connect to beams at acceptable angles? Does any cable connect at too many overlapping beams?), dynamic analysis (is the solution stable? Which can evaluated by whether or not it reached an equilibrium within N iterations), structural analysis (are all cables taut? are all cables evenly taut?). Once it passes these tests, it is evaluated against how well it will tile with its neighbours, which provides the primary fitness score.

Left Page and Left: Novelty Search for Cable networks Top: Close up view on the genom generation for the novelty search engine

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0.6856

ALGORYTHIMIC APPROACH IN CABLE NET DESIGN Due to the topological nature of generating the cable networks, the phase space of the search problem is not continuous. The implementation of generic optimization solvers is therefore not guaranteed to find global minima. We there therefore use these more as a method of generating a pool of many good solutions from which we pick candidates. This is managed by recording all good fit candidates over several rounds of search; at each run the genome size is increased to generate larger networks. Each round lasts two hours and yields about 50-100 candidates. To ensure that we do not simply record the same or very similar candidates during a run, candidates are only recorded if they are sufficiently different (measured by comparing genomes) from the already recorded candidates in the pool. If a new candidate is fitter than a similar candidate in the recorded pool, it replaces the old one.

Top: Fitness criteria for the tiling, value 0,6856.

0 - perfect match.

Left: Cable net iterations with the fitness criteria with the max low fitness criteria

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Pipeline provides information about the orientation of planes as well as all the angles between the elements which helps to visualise the model with the materil thicknesses

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Colour demonstrates the hierarchy in the cable network - more red - the most centric cable it is, more blue - the most outer cable it is

RULES FOR CABLE NET GENERATION The cable net algorithm generates a large diversity of cable networks based on the input of a polyline beam geometry and the direction of the future cable net growth (“spine“), as well as the amount of cables and outer nodes.

In order to narrow down the cable net outcomes the search range was also minimised by defining the angle between cables in the node and the angle by which the cable meets the beam. These angles were predefined through empirical testing of the system.

The cable networks with uneven distribution of angles in the nodes were deselected as were the those with steep angles between beam and cable.

Left: Growth direction for the cable nets Left page: Units with the detailed cable nets (details and rings)

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Top and Left: Overlay of the cable net search engine solutions Left page: Resulted solutions of cable net engine

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STRESSES AND TENSION IN THE CABLE NETWORKS slack cables: 0 evently taut: 28.95

slack cables: 0 evently taut: 31.15

The shaping and form finding process implements the mechanically accurate K2Engineering elements of bar, rod and cable for representing the beams and cables. This means that we can evaluate the structural performance of a FAHS unit in terms of stresses and forces at any point during solving. Specifically we evaluate: 1) The axial stresses in the discretised bar/ cable elements along the beams and cable to determine how much tension (blue) or compression (red) they are under. 2) The rod elements along the beams to determine local bending stresses (red-yellow-green-blue gradient). 3) The reaction forces at anchored nodes and point loads. The axial stresses in the cable element are used downstream to evaluate for slack and unevenly taut cables in the network.

Top: Tension forces in cable nets Left: Slack cable analisys Left page: Forces visualisation from K2 component

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Left page: Tension forces distributed on the wall design Top: Tension forces visualised only on the level of cables

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MACHINE LEARNING FOR

CABLE

NET

GENERATION SUPERVISED LEARNING The exploration of the design space of the wall requires us to develop an intuition about the relationship between the single unit and the macro behaviour of the structure. So far, to find a suitable cable net we’ve been using an evolutionary solver which was searching the solution space for the design meeting all of the buildability/performance criteria. While we can optimize a small sample of the wall in that way, applying the same method for the overall assembly is futile - the amount of solutions to evaluate grows exponentially with each parameter introduced into the system.

Left page, top-left: Computation of stresses Left page, top-right: Discretized stress distributions Left page, bottom: Unit classification based on stresses Right page, from the top: Output values for each of the units during the learning process.

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Initialization

Initial Design

Structural Analysis Data

Naive Pick Initialization

Classification Loop Optimization (Evolutionary Solver)

Database Solutions

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Data Classification (Neural Network)

Comparison

Altered Design

Was Improved ?

Yes No

Final Design

Smallest Output Value Case

To overcome this limitation we use a simple heuristic - we look for a single unit which performs the worst, optimize it and reintroduce it into the wall with changed cable layout - repeating this process multiple times greatly improves the overall performance of the wall. The challenge in the execution of this method is the lack of a proper metric which could indicate the worst performing unit. Rather than inventing this metric directly, we employ a supervised machine learning method - backpropagation neural network. This kind of neural network is used commonly for pattern recognition, and it is known for its flexibility and robustness in classification.

We train the network with load distribution data of the units for which we know the optimal cable net solution. We ask the network about each of the units in the wall, and it indicates the one which it is least familiar with - this is what we interpret as the worst performing unit, which is then optimized and the whole process repeats.

Top and Left: Optimisation Diagram Left page: Visualisation of the Network’s learning process

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PROPOSAL

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BEST PERFORMING UNITS EVALUATION OF THE SELECTION The process of generating cable networks yielded ten datasets with roughly 130-190 good fit candidates in each dataset. These networks ranged in size from six to sixteen cables (these are always a multiple of two). From these data sets, eleven candidates were picked through first sorting and filtering out the top twenty best performing candidates in each set.

Then communally going through these candidates over three rounds of discussion and voting, evaluating them based on our built up intuitive knowledge of how well they might perform structurally and by their aesthetic value. The eleven chosen units were fully prototyped and evaluated through load testing and analysis of symmetry, cable angles and cable distribution. From this, the final four candidates that would go into the wall were chosen. These were distributed strategically across the wall, with smaller networks at the top and larger networks at the bottom.

Top and Left: Fabrication data of preselected units Left page: User preselected units

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Offset 0.000

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Offset 0.015

Offset 0.025

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Right page: Offset approach for achieving the global curvature Left page: Overlay of the diamond grid of the global shape with different offset values

Shaping of the wall

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Tension and compression analysys of the wall

External forces analysys of the wall

LACE

WALL

DESIGN ITERATIONS MACRO SIMULATIONS To evaluate structural performance on the macro scale of the entire wall, the chosen cable networks were generated using the described distribution across a parametric encoding of a full wall. This was managed using a generative model that describes the overall wall curvature from the slight offset of a single tile, generating an array of identical tiles upon which the beam unit can be deployed and the cable networks generated. Just as with single units, this geometry can be plugged into the form finding and structural analysis model for a mechanically accurate simulation of the entire wall. To reach an effectively zero moment state of equilibrium took roughly 250000 iterations with a similar amount of goals to solve. This equates to about 10 hours of solving an a standard PC.

Left: K2 Engineering visualisation on the wall design iterations Left page:Different layers for visualisation

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Right page: Side view diagram of the final design iteration Left page: Top view of the final design iteration

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Final Design Decision

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OUTLOOK

COMPLEX MODELLING FINAL EXHIBITION PROOF OF CONCEPT

Centre for Information and Technology and Architecture

The Complex Modelling research exhibition explores new design strategies for architectural construction.

Digital design and fabrication and the integration of simulation into our design tools are enabling new ways of using materials and building. The research exhibition presents results from CITA’s latest research into hybrid structures combining tension and compression based elements and into the strategic corrugation of steel plates using robotic fabrication. The exhibition presents the final three digital-material experiments that make up this research.

The Royal Danish Academy of Fine Arts Schools of Architecture, Design and Conservation School of Architecture

Complex Modelling is a Sapere Aude Advanced Research project granted by The Danish Council for Independent Research and undertaken by CITA: the Centre for IT and Architecture at KADK. It investigates the infrastructures of our design models. By questioning the tools for integrating information across the expanded digital design chain, the project asks how to support feedback between different scales of design engagement moving from material design, across design, simulation and analysis to specification and fabrication.

PARTICIPANTS

RESEARCH EXHIBITION

2. SEPT - 11. DEC 2016 ROYAL DANISH ACADEMY OF FINE ARTS, SCHOOLS OF ARCHITECTURE, DESIGN AND CONSERVATION

MELDAHLS SMEDIE DANNESKIOLD-SAMSØES ALLÉ 51-53 1436 KØBENHAVN K

cita.kadk.dk www.complexmodelling.dk

Lace Wall was exhibited in the Complex Modelling exhibition in Copenhagen, which showcased the last three of a total of six demonstrator projects, which were built within the research project.

Lace Wall contributes in two main areas to the profession: 1) Lace Wall proposes how future architecture can work with materials in a highly optimized manner, creating super light structures.

As our social and environmental contexts are changing, it is paramount that we develop new building practices for a less intensive material culture. Where Lace Wall is speculative and removed from the requirements of everyday architecture it demonstrates a new structural system, that is based on a minimal inventory of bend rods and constraining tension wires. In order to design and fabricate the structure new computational techniques were developed, which integrate design and simulation of bending active hybrid systems. These techniques are fast and robust, can handle unprecedented Left page:Lace Wall final demostrator Right page: Complex Modelling exhibition poster.

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amounts of interacting elements and can be adapted and programmed to fit to a broad range of design cases in- and outside of the field of lightweight structures.

2) Lace Wall presents new computational workflows and tools to tackle highly interdependent design problems and exceeds current design optimization strategies, which are centered around the idea of linear and hierarchical approaches. Lace Wall develops novel computational approaches, that couple design iterations in physical and digital models, define clear feedback loops for the development of structural system and detail and introduce finally methods from Machine Learning into the canon of tools of designers.

Left page: Lace Wall, close up view on the elements

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References: 1.

2.

3.

4.

5.

Lienhard, J. & Knippers, J., 2015. Bending-Active Textile Hybrids. Journal of the International Association for Shell and Spatial Structures, 56(October), pp.37–48.

Ahlquist, S. & Menges, A., 2013. Frameworks for Computational Design of Textile Micro-Architectures and Material Behavior in Forming Complex Force-Active Structures. In ACADIA. pp. 281–292.

Mele, T. Van et al., 2013. Shaping Tension Structures with Actively Bent Linear Elements. International Journal of Space Structures, 28(3), pp.127–135.

Thomsen, M.R., Bech K., 2011. Textile Logic for a soft space. Royal Danish Academy of Fine Arts, Schools of Architecture.

Thomsen, M.R; Bech, K; Sigurdardottir, K., 2012. Textile Logics in a Digital Architecture.

Proceedings of the 30th eCAADe Conference - Volume 2 / ISBN 978-9-4912070-37, Czech Technical University in Prague, Faculty of Architecture (Czech Republic) 12-14 September 2012, pp. 621-628

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CITA | Centre for Information Technology and Architecture The Royal Danish Academy of Fine Arts, Schools of Architecture, Design and Conservation Philip de Langes AllĂŠ 10 1435 Copenhagen K Denmark http://cita.karch.dk