Emergent Technologies & Design Boot Camp Architectural Association - October 2014 Directors: Michael Weinstock, George Jeronimidis Studio Master : Evan Greenberg Master Tutors : Manja VandeWorp, Mehran Gharleghi Design Team : Arnold tejasurya, Spyros Efthymiou, Yutao Song, Arpita Parmar
Abstract The project involves the introduction of material properties and performance as a key driver for design. It constitutes an exploration of the process of creating complex spatial configurations through simple manipulation of materials. Material behaviours are introduced into system specific assembly logics through physical and digital experimentations. Conclusions coming from physical investigations on corroborative prototypes are digitalized by the use of digital and computational tools in order to enhance the overall design process. The outcome of the project is derived through the handling of a flat sheet material all the way up to the creation of a double-curved self supporting articulated surface.
INDEX_ 1.0 Introduction 6 1.1 Design Process 1.2 Material 1.3 System Variables 1.4 Behaviour 7
2.0 Experiments 9 2.1
Bending behaviour | Rubber Band
11
2.2 Bending behaviour | Length differentiation
15
2.3 Twisting behaviour | Curve differentiation
19
3.0 Surface Articulation 23 3.1
System specific - Assembly Logic
24
3.2 Surface manipulation 26
4.0 Digital Modelling Pseudocode
30
4.1
31
Physics Simulations - Rubber band
4.2 Physics Simulations - Varying Length
32
4.3 Physics Simulations - Angle Difference
33
5.0 Fabrication Process 34
6.0 Resulting Surface 36 6.1
Conclusions and further development
39
1.1 Design Process Our team questioned the possibility of creating complex form configurations through articulating relatively simple geometrical components, under the context of an evolutionary design process. The coherent combination of varying components gave as the chance to explore the manipulation of articulated surfaces based on their material properties. In order to explore these properties, and later introduce them in the design process, we worked both with physical and digital investigations. Initially we tested various materials according to their bending, twisting and stiffness properties. Results were documented and the material was decided. Later we set up a number of experiments to better understand the material behaviours. Different parameters were introduced for each experiment. After documenting the results and conclusions, prototypes were produced for each case in order to test the material limits and the geometrical possibilities for the resulting surface. Later, experiment conclusions were digitalized and introduced into digital design tools to enhance the design project. Further digital experimentations were done using physic simulation plug-ins and the results were also documented. Continuously ,and after a design direction was decided, a system specific assembly logic was defined. By that point, the final computational model was implemented and a family of design solutions were possible. Finally, a specific morphology was selected and later on fabricated.
1.2 Material In order to match our research goal , study bending and twisting behaviours, we chose a list of potential material for testing. Card board, MDF, polypropylene, aluminium sheet, plywood e.t.c. After comparing various experimentation results, we decided to deeper explore material behaviours and capabilities of plywood . This material was selected due to its flexibility and stiffness properties, that could be combined for the creation of a single component, able to participate in the creation of a self supportive surface. It has several critical features that fit our design approach the most. Along the grain direction, it has high stiffness while perpetual with grain has high elasticity. Proper implementations were able to provide stable structures and large range of durability. The high impact resistance provided benefits during the construction (short-term overloads do not destroy the structure). Furthermore ,the high strength to weight ratio makes the self-load affects less important to the global structure performance. Finally the high panel shear performance allow us to explore the twisting performance and form up our final model.
1.3 System Variables SYSTEM VARIABLES: Three parameters were differentiated during the physical experimentations in order to understand plywood behaviours and performance capabilities. Those are :
01 DIFFERENT LENGTH OF PLYWOOD STRIPS:
02 DIFFERENT WIDTH OF PLYWOOD STRIPS:
03 CURVATURE DIFFERENTIATION BETWEEN PLYWOOD STRIPS:
| 6
Bootcamp Documentation
1.4 Behaviour Our team was interested in exploring two particular material behaviours of plywood. Those would be Bending & Twisting. Through experimenting both with analytical and empirical approach, reliable data in understanding were later introduced in the design process.
Bending Behaviour Bending behaviour was tested using two methods. By combining two strips of plywood using screws and by applying constant force to a single strip of plywood. On the first case, one strip was always of the same length while the other one was gradually longer. On the second case, constant force was applied to plywood strips of the same length but with varying widths. Deformations were documented for each case and later translated into curvature graphs and bending equations.
Twisting Behaviour
The twisting behaviour was studied through combining straight plywood strips with curved ones Our effort was to map the consequences of the curvature differentiations between the plywood strips.
Bending
Twisting Introduction
7 |
| 8
Bootcamp Documentation
2.0
Experiments
The objective for these experiments is to understand and to explore the behaviours and capabilities of the material (in this case we used 1.5mm & 0.8 mm plywood) in terms of deformation caused by constant forces. a. Bending The material bends following curvature graphs when it receives forces. By manipulating the width and also the length of the plywood stripe (perpendicular wood grain direction), it formed unique bending behaviour which we can used to create an articulated surface. b. Twisting On the other hand the material will implement twisting behaviour when it forces to follow curvature shape. This behaviour also can be measured, documented and can be manipulated to create surface c. Maximum Fracture In these experiments, the material tested to the maximum deformation it can take, then as the result it will be some limitations and certain points which the material could or couldn’t afford
Experiments
9 |
| 10 Bootcamp Documentation
2.1 Bending Rubber Band (Width Parameter) Method
Using rubber bands as constant force, subsequently changing the width of the plywood strips. The plywood various deformations were documented, measured and afterwards predicted. This bending behaviour was used to create components which can be articulated for the creation of spatial configurations. Step Differentiating the width of the plywood stripes (1.5cm/2cm/2.5cm/3cm/3.5cm/4cm). Same amount of rubber bands were applied (same force) for each element. Relevant deformations and bending relation graphs were documented Output Curvature graphs and equations were extracted. Width differentiation could manipulate the behaviour of the material to achieve the desired effect.
Experiments
11 |
Bending Behaviour Diagrams 2.1 The diagrams show bending alterations due to the plywood strip width differentiation (same amount of rubber bands were used - constant force). 1.
1.5cm plywood stripes 2 rubber bands 1.5cm
deformation 11cm
2.
2cm plywood stripes 2 rubber bands 2cm
deformation 9.5cm
3.
2.5cm plywood stripes 2 rubber bands 2.5cm
deformation 6.5cm
4.
3cm plywood stripes 2 rubber bands 3cm
deformation 3.4cm
5.
3.5cm plywood stripes 2 rubber bands 3.5cm
deformation 2.1cm
6.
4cm plywood stripes 2 rubber bands 4cm
| 12 Bootcamp Documentation
deformation 1.3cm
Deformations Table 2.1 Contains data from experiments, deformation and height differentiation results.
Deformations Chart 2.1 Relation between width of the plywood strips and relevant bending deformations (height - length).
Experiment Results 2.1 The elasticity from the rubber band made the global performance of this surface becomes quite hard to control, because elastic material does not have the ability to get back to it’s origin form. This surface also need extra step in the case of connecting each component and some problems in fabrication process are quite complicated. Our experiment showed that by doubling the width of the plywood strips, the deformation decreases by a factor of 50%
Experiments
13 |
| 14
Bootcamp Documentation
2.2 Bending Length Differentiation (Length Parameter) Method Differentiating the plywood length between two joined plywood strips. One element was always of the same length. Strips were joined using screws in specific points. Results were documented. Step Use 2 strips of plywood with different length to form one element (0,5cm step difference). The magnitude of the bending can be controlled by this method, thereafter these elements can be articulated together to form a surface. Output By changing the length of one element, the bending behaviour of this material could be manipulated
Experiments
15 |
Bending Behaviour Diagrams 2.2
The diagrams show bending alterations due to the plywood strip length differentiation.
1.
plywood A 17cm plywood B 19cm height deformation 3.7cm 2.
plywood A 17.5cm plywood B 19.5cm height deformation 3.3cm 3.
plywood A 18cm plywood B 20cm height deformation 2.95cm 4.
plywood A 18.5cm plywood B 20.5cm height deformation 2.7cm 5.
plywood A 19cm plywood B 21cm height deformation 2cm 6.
plywood A 19.5cm plywood B 21.5cm height deformation 1.4cm
| 16 Bootcamp Documentation
Deformations Table 2.2 Contains data from experiments, deformation, length and height differentiation results.
Deformations Chart 2.2 Relation between length of the plywood strips and relevant bending deformations (height - length).
height (cm) 5
H-1 H-2
0
19
19.5
20
20.5
21
21.5
22
17
17.5
18
18.5
19
19.5
20
length (cm)
Experiment Result 2.2 Length parameter can be manipulated to reflect on the resulting surface. This method results on two dimensional growth process of the surface (X- Direction). However it does not allow three dimensional manipulations on the global surface. By decreasing the length of the plywood stripes, bending deformations increase. Results and conclusions from this experiment are used for the next step of design development process.
Experiments
17 |
| 18 Bootcamp Documentation
02.3 Twisting Different Curvature (Angle Parameter) Method The twisting behaviour is observed by attaching straight plywood strips with curved ones. The behaviour is tested by the curvature differentiation of the middle element ( tangent lines at joint points) By using this material property, double curved surface could be possible. Step Set 6 different angle degrees to create 6 curvatures, for the middle strip element where the 2 straight strips of plywood will be attached. As a result, twisting behaviour, is controllable by adjusting the angle degree of the curvature. Output By changing the curvature degree, the twisting behaviour of plywood could be manipulated, controlled and introduced in the overall design process.
Experiments
19 |
Twisting Behaviour Diagrams 2.3
The diagrams show twisting alterations due to the middle plywood strip curvature differentiation.
0o
1.
curvature angle 0O angle of twisting 0O 2.
4o
curvature angle 4O angle of twisting 5.74O 3. 8o
curvature angle 8O angle of twisting 9.21O 4. 12o
curvature angle 12O angle of twisting 16.26O 5 16o
curvature angle 16O angle of twisting 19.88O | 20 Bootcamp Documentation
Deformations Table 2.3 Contains data from experiments, deformation and height differentiation results.
Deformations Chart 2.3 Relation between curvature of the middle plywood strips and relevant bending deformations (height - length). Distance (cm)
19.9 16.3 9.2 5.7 degree 0
4
8
12
16
Trigonometry Relation ( Height & Angle) a = arcsin((D2 - D1)/5)
2.5
cm b-2
.5cm
D2
D1
2
b
Experiment Result 2.3 By combining twisting and bending behaviours, a double curved surface could be designed and fabricated. The bending is controlled by varying the elements length. Furthermore, curvature differentiation, is controlling the twisting behaviour. By that, those behaviours could be controlled and implemented for the creation of a global surface By increasing the curvature degree of the middle plywood strip, the twisting degree changes by a known equation.
Experiments
21 |
| 22 Bootcamp Documentation
3.0
Surface Articulation
By this time and after implementing the results and conclusions we had from our experiments, we started defining a way of articulating our surface. The process by which our surface is being formed could be summarized in four steps that are described below.
Surface Articulation
23 |
3.1 System specific - Assembly Logic 01 Construct A - Module
A - Module
A - Module its constructed by combining three plywood strips. Two strips are straight while the middle one is fabricated within a range of different curvatures.
02 Combine n - number of A - Modules on X - Direction == A - Component
A - Component
Each A - module (middle part) has its own curvature.The relative curvature differnece (tangent lines at joint points) between each module results in different twisting behavior in each A - Component. X - Direction
03 Combine n - number of A - Components on X - Direction == B - Component
B - Component
The relative curvature differnece (tangent lines at the joints) between each A - Component results in different twisting behavior in each B - Component. X - Direction
By combining a B - Components on the Y - Direction a family of articulated surfaces could be possible. The outcome is a combination of Geometrical actions that result in global bending and twisting behaviours.
| 24 Bootcamp Documentation
C - Surface
Y - Direction
04 Combine n - number of B - Components on Y - Direction == C - Surface
01 A - Module As mentioned, each A - Module is constructed by combining three plywood strips ( Two straight ( S01 & S02 ) and a curved one (Mst01) ). The strips are joined using screws in fixed positions. The straight strips are longer than the middle curved one. By changing this length difference and based on experiment results we can achieve the desired bending behaviour. As concerning the twisting behaviour, is controlled through the curvature differentiation of the middle strip.
A - Module
Length (l0)
Width (w0)
St (01)
St (02)
Mst (01)
St (01)
Mst (01)
St (02)
A - Module
Mst (01)
(h1)
Joint
(h2)
Joint
(h1) (h2)
Height (h0)
St (01)
St (02)
Length (l0)
Surface Articulation
25 |
02 A - Component A - Components are composed by combining n - number of A - Modules..Their twisting behaviour (in this case that n =2) is defined by the curvature differentiation at the point where the two modules are joined. The angle (a°) , which is formed by the tangent lines at the joints, reflects on the final form of A - Components.
(A1) - Module
A - Component
(A2) - Module
St (01) Mst (01) St (02)
a˚
03 B - Component B - Components are composed by combining n - number of A - Components..Their twisting behaviour is defined by the curvature differentiation at the point where the A - Components are joined. The final form comes from the combination of angles (a°),(b°),(c°) , which are formed by the tangent lines at the joints. The twisting behaviours of of B - Components are relevant to the adjucent angles. Thus (a°+b°)/2 etc.
B - Component
St (01) Mst (01) St (02)
a˚
| 26 Bootcamp Documentation
b˚
c˚
04 C - Surface The resulting surface is the outcome of combining n - number of B - Components together. Each module in those components twists according to the adjacent angles described earlier. The surface is formed as a combination of two factors, the twisting & bending behaviours forced by the curvature given by the middle parts and the overall geometry of those parts .
C - Surface
B - Component (01)
B - Component (02)
B - Component (03)
C - Surface
B - Component (01)
B - Component (02)
B - Component (03)
Surface Articulation
27 |
03.2 Surface Manipulation Based on the system - assembly logic we could summarize the way that the articulated surface could be manipulated to result in a family of possible solutions. The surface could grow in two possible ways reflecting on two directions, The first one ( Diagram 1 ) is a result of geometrical intentions as the middle parts are designed with specific curvatures. The second one ( Diagram 2 ) is an effect of the first move as the twisting behaviour comes from the curvature differentiation of the middle parts.
1. Diagram 1 - Geometrical Differentiation - X Direction
2. Diagram 2 - Twisting Behaviour - Y Direction
| 28 Bootcamp Documentation
1. Geometrical Differentiation
2. Twisting Behaviour
Surface Manipulation
29 |
4.0
Digital Modelling | Pseudocode
The logic of final digital model is develop from the experiment data. In order to construct the digital model, curve fitting method was used to obtain the equation between two parameters. We use the equation to convert parameter between each other. We set up a group of ribs with gradually changing curvature and use the algorithm we set up to predict the construction result for the final surface. Finally, the level of tolerance between prediction and construction turn out to be acceptable.
| 30 Bootcamp Documentation
04.1 Physics Simulation - Rubber bands / Varying width strips With Kangaroo simulator, three plywood bending test with rubber band has been create to compare and verify the physical experiments. In this digital model, it has one variable: width. The simulation will shows how the model perform with different width. In order to achieve this, we subdivide the strip into meshes along the span direction. The corners are defined as the supports that are constrained to move along specific direction. We assign the digital model with Bend resistance strength and high stiffness edges, after that, we add a spring system connect corners on both end to simulate the rubber band and the force.
Digital Modelling
31 |
04. Physics Simulation Fixed upper part length / Varying Lower Strip length In this model, the only variable is the lower strip’s length. The changing of the length will cause the upper strip deform, the tangent on both end cause the lower strip bend at the same time. in order to create this digital model, we assume the upper part is the fix length arc and the lower part is a various line.. We use trigonometry method to construct this fix length arc base on the line with various length. The simulator will relax the geometry to the natural form with properly setup of the joints.
| 32 Bootcamp Documentation
04.1 Physics Simulation : Curvature of middle Ribs / twisting angles The plywood bending & twisting test is developed from the second simulation. The only variable in this model is angle which provide two different edge length on both sides, that force the strip twisting when it apply to the ribs . after run the relaxation with physic simulator, the twisting of strip will be much closer to the shape of our physical model.
Digital Modelling
33 |
5.0
Fabrication Process
For the final prototype we used 1,6 mm plywood. The plywood pieces were cut with laser cutter. The total fabrication process lasted 4 hours. We started by having two sets of plywood strips. The first one contained only straight strips with the same length and a series of holes arranging in equal distance, while the other one curved ribs with various curvatures. Initially we started by joining three strips each time to create all the components of the geometry. Each component was then joined to its adjacent components to form the final surface.
| 34 Bootcamp Documentation
1.
2.
3.
4.
5.
6.
1. Two sets of plywood strips. Straight strips ( same length ) and curved 4. Building all the components separately to their final state so that we ones ( same length different curvature ) . have all the elements that will form the surface. 2. Combination of three strips to create each component. The strips were joined together using screws.
5. Combining all the components together on the other direction by joining them in specific points using screws.
3. The Combination gave each component its final form ( twisting + bend- 6. Overall surface configuration perceived through implementing the ing + Curved part ). computational model,
Fabrication
35 |
6.0
Resulting Surface
A double - curved surface that tends to form a saddle shape geometry. Our surface could be analyzed down to three elements that reflect to the final morphology. The bending behaviour that defines the porosity of the system, the twisting behaviour as a growing factor on one direction and the curved middle parts that manipulate the surface on the other direction.
| 36 Bootcamp Documentation
Resulting Surface
37 |
| 38 Bootcamp Documentation
06.1 Conclusions
Based on the three experiments we did, we developed the system assembly logic that could manipulate a saddle shape surface. The linear relation between the curvature of ribs and the twist angle between ribs made the overall morphology predictable. The double curved surface is controlled by the curvature of the middle ribs. In our design process we limited the varying parameters to one, in order to better observe the results. However, some deviations between the digital and physical model were observed The angle between two ribs at each component, made the distance at the free ends larger than the middle. By this ,same length strips are hard to connect. A possible solution is to have specific length of strip correspondence to the distance changing.
Further Implementations / Possibilities
Our current physical model has the same width in every plywood strip. For further development, we found that the change of width will not affect the angle of twisting or the bending behaviour. A possible idea to transform our final surface into a dynamic geometry is to use elastic, changeable middle parts in some modules to change the global performance. Further more we could have different module lengths to enhance the design process. Varying lengths will give different twisting and bending behaviours in each component but will also make the connection between them more complicated. Finally we could introduce another material (membrane) that could give varying porosity to our surface . This could give possibilities for lighting, air circulation and visibility manipulations.
Resulting Surface
39 |
Architectural Association - October 2014 Arnold tejasurya, Spyros Efthymiou, Yutao Song, Arpita Parmar