Texperiments Part 1: The fabric is stretched and fixed on a wooden plate, the s�ff elements are placed and glued in posi�on. The same stencils are used for computer simula�on. Last, the tension of the fabric is released. Part 2: Since there are no anchors in a real model, the first difficulty, also for the shape, is to constrain the model to not collapse in itself indefinitely. A�er that, development comes down to the rela�on between the stresses in the fabric and the amount of added forces to create a mo�on in a specific manner.
Organic ruling
Descrip�on of the workflow
How would a ruled surface made from fabric look like, using prestressed material? How does a computer simula�on of the stresses within the fabric compare to the ones in real life? The samples on display are types of ‘planar’ models that answer the first ques�on, one of them answers the second as well. The main topic was to discover and understand the connec�on of real samples and computergenerated ones through a series of experiments. The first part is making the real samples using laser cut MDF, cardboard and swimsuit tex�les. Prestressing the fabric and releasing its tension later can give desired shapes. With just a bit of hand pulling force and by one’s imagina�on, ruled surfaces may be obtained from the samples. The second part of the project is done in Flexhopper (Grasshopper component) and shows the computed visualiza�on, that can be compared with the real-world example. The certain shape is achieved just by slightly pulling and rota�ng the end-middle s�ff cons�tuent as seen in the video.
Anna Wetzel – Bachelor in Fashion Design (Germany) Marina Mudri – Bachelor in Architecture (Serbia)
∞44 The BAMBOO Model This star-shaped bamboo sculpture is the second representa�on of a hypercube, with a similar geometrical frame. The sculpture is made from plenty bamboo s�cks and a bag full of rubber bands. There are 3 sizes of bamboo s�cks, 12 pieces of big and medium each and over 200 pieces of smaller ones.
The outer shape is an 8-star, stellated octahedron, named Stella octangula by Johannes Kepler in the early 17th century, whose 8 ver�ces make a cube with invisible edges. It was made so, because a square is not a stable figure while a triangle is. The cube is thus constructed as a convex hull of a regular compound of two tetrahedrons, self-dual Platonic solids with 4 ver�ces.
Lines 4 Arts
Geometrically, these two tetrahedrons are congruent and their intersec�on is an octahedron. Their combined Boolean difference consists of 8 smaller congruent tetrahedrons. In each of the small tetrahedrons two hyperbolic paraboloids are placed to contain among them all the edges of the tetrahedron. Small bamboo s�cks present one system of rulings of each hyperbolic paraboloid and they are all
Dr. Iva Kodrnja – mathema�cian Dr. Helena Koncul – mathema�cian
LSP Line Space Portal
Straight__ ____ to the future
During the form-finding process our top priority was on iden�fying the geometry that enables us to produce our design in large scale. For this, we used the “line geometry” plug-in for Grasshopper. Our main constraints were the size of the Styrofoam blocks and the limita�ons of the 4-axis CNC hot-wire cu�er. Shape, size and number of the elements were op�mized to both fit into the available Styrofoam blocks and inside the machine’s workspace. Each block had to be cut at least twice: once for top, bo�om, front and back surface, and another �me for side surfaces. This made the cu�ng process �me consuming and the posi�oning of the Styrofoam blocks inside the machine workspace extremely challenging. For the connec�ons we used a combina�on of glue with small wooden s�cks.
“Line Geometry and Lightweight Structures”includes ruled surfaces as the one of the main tools for the design. They are extensively used because of their interes�ng proper�es: descrip�on of the shape through a series of straight lines, nega�ve doubly curved shape, ease of produc�on and large design space. The idea for this project was to implement ruled surfaces in more contemporary design cases and carry out a futuris�c design for intergalac�c spaceships. Ini�al solu�on was a variety of designed spaceships that could be used for explora�on of the universe. We demonstrated the power of ruled surface geometry in design, but due to produc�on limita�ons we decided to make a Line Space Portal to take you into the future where you can see and explore a wide range of all possibili�es. Intriguing, right? For the produc�on we developed algorithms in Grasshopper to segment the geometry into elements that are possible to produce with the 4-axis hot-wire cu�er. The process of the produc�on was complex and at the end the result is a growing project of a space portal that con�nues as we are passing through it…
Zlata Tošić – University of Niš – Department of Architecture Nikolaos Xenos – University of Stu�gart – ITECH Milan Varga – University of Belgrade – Deparment of Architecture Katrin Pohl – University of Applied Sciences – Leipzig
SHELLCRETE light
Es werde Licht!
Nach Entwurf und Zeichnung der Form mi�els branchensüblicher CADProgrammme erfolgte zunächst der Zuschni� der Hyparschalenform aus extrudiertem Hartschaum mit Hilfe eines Heißdrahtschneidegerätes. Im Anschluss an die Montage der aüßeren Schalungselemente, wurde das eigentliche Bauteil mi�els schichtenweisem Laminieren von Betonmatrix und tex�ler Glasfaserbewehrung realisiert. Im finalen Arbeitsgang wurden die erforderlichen Öffnungen zur Aufnahme von Leuchtmi�el und Befes�gung hergestellt.
Das ausgestellte Lichtelement, ist im Rahmen des Teilprojekts SHELLCRETE light, der LGLS (line geometry for lightweight structures) Summer School entstanden. Der Zusatz light spiegelt sich dabei sowohl in der Leich�gkeitkeit der Struktur selbst, als auch in der Funk�on des Objektes wieder. Das Fundament der Idee bildete die intelligente Kombina�on von Tragstruktur, Hochleistungswerkstoff und Funk�on. Der hyperbolische Paraboloid wurde bewusst als Form gewählt und erinnert an die Werke eines der bedeutensten, deutschen Ingenieure des 20. Jahrhunderts - Ulrich Müther. Durch die Verwendung von quatroaxialen Glasfasergelegen und einer fließfähigen sowie hochfesten Betonmatrix konnte eine funk�onierende, nur weniger Millimeter starke Tragstruktur hergestellt warden. Die Integra�on des Leuchtmi�els verleiht der Hyparschale zusätzliche Funk�onalität und hebt das Kunstobjekt nicht nur op�sch auf eine höhere Ebene.
Dipl.-Ing. Paul M. Busse ist wissenscha�licher Mitarbeiter am Ins�tut für Baustoffe der TU Dresden und beschä�igt sich dort unter anderem mit der Entwicklung von tex�l- und faserverstärkten Betonen
∞ 44 The String MODEL This string model is a homage to the first material mathema�cal models used to study ruled surfaces in the 19th century. The outer frame and the inner octahedron are made from HDF panels cut by a laser cu�er. The cube is made from 24 pieces and the octahedron from 5, glued and colored. The strings are recycled wool. The spirals are made of one piece of steel wire.
Strings represent the rulings, lines en�rely contained in the ruled surfaces. The geometrical structure of the model is a homage to number 4. It represents, as a spa�al object, a 4dimensional cube, called a hypercube or a tesseract, a polytope with 4 edges going out of each vertex. The outer frame is a 3D cube, Platonic solid with 8 ver�ces and the inner object is an octahedron, a Platonic solid dual to the cube, with 8 edges.
Lines 4 Arts
They are connected with 4 hyperbolic paraboloids, each one containing 1 edge of the cube and 1 edge of the octahedron, 4 ver�ces of the hypercube. Hyperbolic paraboloids are 2nd degree ruled surfaces with 2 system of rulings. The strings belong to one system and the 2 edges of the hypercube belong to the other one. Octahedron is decorated with 2 spirals which pass through 3 ver�ces of the hypercube.
Dr. Iva Kodrnja – mathema�cian Dr. Helena Koncul – mathema�cian
CUBE RULES
Carbon Concrete Composite
I order to develop the CUBE model, it was decided to use a combina�on of different possible produc�on techniques. Thus, 3D prin�ng produc�on using plas�c material applied to develop complicated loadbearing shell with mul�ple ribs. Laser cu�ng technology perfectly fits for produc�on of the flat elements, such as columns and walls. And finally, hot wire cu�er was used to prepare a special Styrofoam formwork for the correct shaping of the glass fibre grid element.
CUBE as a part of C3 Project (Carbon Concrete Composite), assumed to be a building, constructed en�rely of carbon concrete un�l 2020. The planning started at the end of 2017. The main aim of the CUBE building is a demonstra�on of the benefits of carbon concrete and its poten�al for development of lightweight, delicate and sustainable construc�ons. Addi�onally, CUBE building designed to exhibit recent achievements in development of products made of carbon concrete, as well as provide loca�on for mul�ple research projects. The main task for the LGLS Summer School was development the CUBE building model with scale 1:50, in order to demonstrate the current state of the building design process, verify different workflows for the produc�on of complicated formworks for concrete cas�ng and in general obtain experience in development of the ruled surfaces with determina�on of possible cri�cal geometrical aspects and features regarding modelling of load bearing parts with required precision.
Dr.-Ing. Maria Patricia Garibaldi – research associate TUD IMB M.Sc. Iurii Vakaliuk – research associate TUD IMB Dr.-Ing. Sebas�an Wilhelm – research associate TUD IMB
Construc�on
CINÉTIQUE A�er collec�ng our ideas and references, we started building some small models to study the probable behavior of a larger structure. We used Grasshopper to design some digital models who also showed the reac�on of the structure to gravity and an addi�onal pulling force. With this tool, we tested various parameter to choose the most sui�ng design for the construc�on.
Kine�c Mobile in Line Geometry
We developed lightweight and easy to produce joints, which allow the s�cks to have a certain degree of freedom to make the aimed flapping movement possible.
To design and build a kine�c hanging object which uses the principle of line geometry and consists of the given bamboo s�cks as a lightweight structure was the star�ng point of the project. The form of the mobile should show an elegant movement and also move through wind or other impact. During the process, the picture of a bird flapping his wings became the theme of the design. Another aspect was the inclusion of the observer, who is able to interfere with the artwork by pulling a string. This par�cipa�on resolves in the bird, composed out of two mirrored moving ruled surfaces, star�ng to flap his wings and to show the whole beauty of the line geometry and his principles.
Marie Bartz – M. Sc. Architecture Julien Antoine Schmidtke – Architect, Designer and Carpenter GH-Script, Moun�ng – Mar�n Friedrich Eichenauer – Dipl.-Ing.
CHooL BAR This heterogeneous team had a precise task – to build a BAR, but (luckily) was not given a clear explana�on what the bar is…
Riding through the space
This project was a perfect polygon for tes�ng the workflow between synchronizing a physical and digital model during the process. The structure had to be constantly tested for stability and posi�on in the exhibi�on place, and at the same �me it had to be well-defined in its dimensions because of the fabrica�on and styrocu�ng. It went through several phases – from a paper model, parametric digital model, through small scale wooden s�ck model, middle size bamboo s�ck model to the full-scale model.
This project represents the constant ba�le between the ar�s�c approach of libera�ng space and architectural approach of controlling space at the same �me. The main idea was to build a structure that does not emulate the bar, that floats through the space and emphasizes it, and at some point it “catches it” and tames it. The line structure consisting of several HP geometries provided us the perfect tool for this, poin�ng the “saddle” at the end of this con�nuity as a horizontal plate that would serve the purpose of the bar. This form, with its geometry, is adaptable and it can adjust to every space. It is a spa�al con�nuum with certain “points of rest”.
Maja Ilić – architect – Bosnia and Herzegovina Birgit Schuh – ar�st – Germany Biljana Jović – landscape architect – Serbia Shinnosuke Tsubaki – architect – Japan
Cloud LINE The line geometry tool provided by Prof. Daniel Lordick was used to generate ruled surfaces from a series of lines. The neural computa�on was performed with a newly developed version of Crow – a machine learning plugin for the CAD so�ware Rhino.
Self-Organising Ruled Surface Networks
The hologram was made using simple acrylic glass, cardboard and a reused PC screen.
The project Cloud Line aimed at playfully exploring the poten�als of combining self-organising neural networks and line geometry. Ruled surfaces, which are only curved in one direc�on, can be generated by lo�ing through a series of straight lines. Such a series can be either be defined manually or managed in a predefined network topology similar to a rectangular grid or a polygon mesh. In this way each node of a rectangular grid is replaced by a straight line. The connec�ons between these nodes define the order in which lines are connected through a lo� surface. Thus intricate ruled surfaces can be generated by lo�ing along the topological seems of a userdefined mesh. This pre-defined mesh can be distorted and adapted to fit through control lines using a selforganisa�on algorithm. This neural computa�on approach enables the user to drag, pull and shape pull a network of ruled surfaces to his or her will. A few examples of this exercise are shown as a hologram to highlight its spa�al quality.
Benjamin Felbrich PhD Candidate at the Ins�tute for Computa�onal Design and Construc�on – University of Stu�gart
torrojometry To produce formworks for our shells we used a hot wire foam cu�ng robot. Because of that, the size of the foam pieces set up another boundary condi�on for our geometrical op�miza�on. Using carbon reinforcement and fine-grained concrete we produced the shells with a minimum thickness of 5mm.
The roof of Hippodromo Zarzuela, a horse race track in Spain, designed by master shell builder Eduardo Torroja was our first shell to work on. The second shell was “System Silberkuhl”, a roof element invented by Prof. Silberkuhl in the 1950th. The shape of both shells originates from the hyperboloid of one sheet. While Hippodromo Zarzuelas elements are strings cut out in tangen�al direc�on of the hyperboloid, System Silberkuhls elements are cut out in radial direc�on. The geometrical op�miza�on was performed using evolu�onary algorithms to evaluate the structural behavior. To obtain an efficient shell structure, its curvature has to be maximized within the boundary condi�ons.
Geometry
Op�mizing Shell
The torroja-roof is supported by one row of compression columns and one row of tension members. To connect everything to the concrete shell we used industrial glue.
Shell structures are known to be amongst the most efficient structural systems ever build. Nevertheless, our idea was to parameterize two famous examples of built shells and try to op�mize them geometrically.
Juan Pablo Letelier – civil engineer – TU Berlin Jack Lehrecke – civil engineer – TU Berlin Max Dombrowski – civil engineer – TU Berlin Jan Philip Schulze-Ardey – civil engineer – RWTH Aachen