DIGRID SURFACES

BOOTCAMP Alyina Ahmed + Owaze Ansari

Architectural Association 1

M. Arch - Emergent Technologies

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CONTENTS: Abstract - Page 5

Phase 1: Generative Geometries Diagrid Surfaces - Page 8 Pseudo Code - Page 10 Material Experimentation - Page 12 Form Generation - Page 15 Final Form - Page 20

Phase II: Material Intelligence Pseudo Code - Page 24

ABSTRACT: The following research was concentrated on the fabrication of a double curved diagrid surface. Our main intention was to understand the relationship along with its limitations between material behavior and computational design. Further studies also included form generation, production and fabrication.

The project was divided into two material phases; paper and thin plywood, which guided our research. The first phase focused on generating a minimal surface that was populated with geometry to be fabricated using paper. Multiple iterations were generated, and the final production of the paper model was created by using a nip and tuck joint to create a quadrant that was the local component for the global form.

The second phase concentrated on creating the form generated out of phase 1 with thin plywood. In order to understand the material properties of plywood we conducted multiple tests. Through testing we concluded that the best way to manipulate plywood was by soaking it in water to make it malleable and make it easier to fold into our desired shape.

Material Experimentation - Page 26 Form Generation - Page 28 Final Form - Page 32

Stage 2: Conclusions

Throughout the different stages we realized that fabricated geometry differs vastly from the digital models. Although we tested multiple geometries, angles and techniques and recalibrated our digital model to match the knowledge gained from these tests, our final plywood model differed drastically from our digital model and a completely new form emerged.

Conclusions and Analysis - Page 36

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PHASE 1 GENERATIVE GEOMETRIES

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DIAGRID SURFACES: Diagrid Surface and Subdivision:

References and Inspiration:

A diagrid surface is a framework that has diagonally intersecting elements which create a grid structure.

During out initial research, two projects stood out to us and we wanted to use these are base references and develop our own design. By combining complex geometry as shown in the first reference, with a simple diagrid surface we intend to create our final form.

This surface is generated commonly by lofting two or more curves and dividing the geometry generated into further subdivisions. These subdivisions are generated in the U and V directions which intersect to create nodes.

Basic Diagrid Structure

Final Diagrid Surface

Diagrid structures are utilized frequently in faรงades of architectural buildings due to their ability to limit the amount of material, such as steel, used in construction to create a stable frame. The following are some images of buildings that have used the diagrid structure on their facades.

Poly International Plaza - China , S.O.M

30 St. Mary Axe - UK , Foster & Partners

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Hearst Tower - USA , Foster & Partners

Brainchild - Rosemary Dobson

Burning Man - Sam Whitehead

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PSEUDO CODE:

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MATERIAL EXPERIMENTATION: Paper: Due to paper having the ability to be extremely malleable and fold without tearing or breaking, we started to experiment by creating various shapes. Due to its versatility and material properties, it was easy to achieve various geometric forms such as hexagons, pentagons, triangles and rectangles through folding and joining techniques which will be explained further below.

Nip and Tuck Method: The nip and tuck method of fabrication is commonly utilised to achieve double curved surfaces. In our forms we used this method to give a curvature to the upper side of our geometry whilst still having a regular geometry at the lower face. A slit is made on a piece of paper along with a angular line. The slit is then forced to lay exactly on the angled line. These two overlapping edges are joint together using staples or tape to create the curved surface.

We attempted to achieve more a complex surface by trying to populate our diagrid surface with different geometries and tried various bending + folding techniques on different shapes to experiment with. All paper material explorations were done with 300GSM card paper.

Nip & Tuck Diagram

Slotting Method: The slotting method, also known as waffling, is a common joining technique utilized in construction and fabrication. It consists of creating slots in the material that precisely fit into each other to create a stable joint. The slotting method can also be used in conjunction with hardware, such as staples, tape or nails, that would make the connection more stable and prevent the material from sliding out of its slot under pressure. Two slits are made in each piece of material. These are then slotted into each other and fastened with hardware if needed.

Paper Prototypes

Slotting Diagram

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FORM GENERATION: Iteration 1: For our final surface, we wanted to achieve a negative gaussian minimal surface which was populated with a geometry to create our overall form.

Slotting Technique - Quadrant

Slotting Technique - Quadrant Segments

Slotting Technique - Quadrant Combined

Base Curves

Negative Gaussian

Minimal Surface

Form Generation

Nip & Tuck + Slotting Technique Triangle

Nip & Tuck + Slotting Technique - Triangle Underside

Nip & Tuck + Slotting Technique - Triangle Topside

Nip & Tuck Technique - Quadrant

Nip & Tuck Technique - Quadrant Underside

Nip & Tuck Technique - Quadrant Topside

Nip & Tuck Technique - Hexagon

Nip & Tuck Technique - Pentagon Underside

Nip & Tuck Technique - Pentagon Topside

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The minimal surface first had to be planarized in order to create a developable surface which make it easier to unroll and assemble. We fabricated one row of the final form out of carboard with a simple quadrant shape to test whether it would curve. It attained the basic curvature which we intended to achieve so we moved onto testing the quadrant with the nip and tuck joints.

Planar Surface Study Model - Top View

Planar Surface Study Model - Side View

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Iteration 2: For our second experiment we changed our base component from a quadrant into a hexagon. We first assembled a study model with paper without the nip and tuck joints to test if the shape would attain curvature.

Local Scale

Regional Scale

After apply force to the model, it would start to form some curvature but it was only when it was induced by force. Due to the weak connections and random position of the staple pins, a lot of the pieces were coming undone and compromising the over all shape.

Global Scale

During assembly we realized the model was lying flat and was not achieving the intended curvature.

Even with varying sizes of the individual component, when connected together it was not able to attain curvature.

Assembled Model

Overall form due to induced curvature

Regional Scale

The digital model consisting of differently scaled lofted curves was meant to be translated into polymorphism by means of physical experimentation, but on assembly the physical hexagonal local geometry failed to take form of the digital global geometry. The reason for the above is most likely due to not defining the polymorphism in the local geometry in buildable logic. The modifications required to the unroll of our initial unroll of Hexagonal local geometry in a particular location (eg. Local Hexagonal geometry Row 6 Column 5) are by minor angles (for the example illustrates above its 6, 7 and 12.5 degrees), which can be relatively hard to work with through a physical assembly method. As a result of required working distance (1cm in this example) forming at different lengths from the original geometry, scaling the edges unevenly becomes unavoidable to the local geometry in order to reach a polymorphic property demanded by the digital global geometry.

Assembled Model

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Iteration 3: For our final iteration we moved back to the quadrant form to populate our surface using the nip and tuck technique to achieve curvature. Each quadrant was assembled using paper strips and held together with staples. The final form was constructred row by row and then joined together to form the final surface.

Local Scale

Regional Scale

Due to the size of the individual components we faced a lot of difficulty while stapling the nip and tuck joints. If the model was flexed too much, some of the pins were breaking off and changing the geometry of the individual components, as well as the overall aesthetic look of the surface. The staple positions were not thought through, and when completed the connections looked untidy and random.

Global Scale

We experimented with multiple different angles on our individual components to see which would be the most aesthetically pleasing and give the component the most curvature. 30, 45 and 60 degree nip and tuck joint angles were tested. Ultimately we generated our final complete surface with the 60 degree nip and tuck joints.

Nip and Tuck Connections - Top View

Nip and Tuck & Component Connections - Bottom View

Observations: 30 Degrees

45 Degrees

60 Degrees

- Paper was very forgiving and malleable, it would take the form we wanted with a little bit of force and pressure - The nip and tuck joint was easy to fabricate and relatively easy to assemble. It also held its form well.

- The curvature was acheived by the size and dimensions of the component as well as the angle of the nip and tuck joints which was 60 degrees.

- The overall form did not match the intended form.

- The final surface was not very sturdy and could be manipulated by applying small amounts of external forces which was compromising its strength and its form.

Local Scale

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PHASE II MATERIAL INTELLIGENCE

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PSEUDO CODE: TEXT

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MATERIAL EXPERIMENTATION: Plywood: For the second phase of the project, we were assigned thin plywood as our material to experiment further with. Plywood is a material that is made out of multiple layers of thin veneer that are glued together at different alternating 90 degree angles to prevent spitting or cracking. Due to our complex geometry, we wanted the sheet to be as thin as possible to achieve our form. The first was a 0.4mm plywood sheet which consisted of 3 sheets glued together, and the second was a 0.8mm plywood sheet which consisted of 6 sheets glued together. Due to its thickness and its structural properties, it was a material that was quite challenging to work with.

Geometry and Component Explorations

For our initial experiments, we tested 4 different kerfing patters on both thicknesses of plywood. All variables such as height, width were kept the same to allow for uniform testing. Each strip was 2cm high and 21cm long and the only change was the individual kerfing patterns.

During our tests we also wanted to experiment by dampening the individual strips and then testing the flexibility and curvature. After these experiments we discovered that the material is more malleable and foldable when it has been left to soak in water for more than 10 minutes.

Plywood bending tests

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FORM GENERATION: Iteration 1: After experimenting by dampening the plywood pieces in water and multiple kerfing techniques, we attempted to create quadrant components that would match our local geometry from our paper model.

Our intial kerfing trials led to a lot of the pieces ending up cracking, or splitting at the kerfed edges.

This was due to the scoring being done for almost 2 thirds of the height of the old piece. The kerfed lines were also all horizantal which also contrbuted to the splitting and cracking of the components.

Geometry and Component Unrolls

The assembly of the kerfed geometry demonstrated that the location of the flexibility required by the local geometry, when assembled into a regional then global scale, is required on the tension and compression points accumulating within the local geometry.

Quadrant Kerfing Trial 1

Quadrant Kerfing Trial 2

Cracked Geometry

Quadrant Kerfing Trial

The regions of tension can be perceived in upper corners of the geometry and compression accumulates in the lower corners of the local geometry. Taking into account these forces the kerfed regions should be in the upper and lower corners of the local geometry, resulting in a more structural local geometry when subjected to the forces of the overall global geometry. This form would also give us the curvature we intended for the final local component.

Geometry Tension and Compression

Geometry Tension and Compression

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Iteration 2: Our final trial with plywoods were the most successful and led us to experimenting with kerfing patterns on curved strips that eventually formed domed quadrants similar to the local geometry of the paper model. 3 different techniques were tested:

1. No kerfing

2. Cut outs in place of the kerf lines

3. Angled kerfing pattern

All tests were conducted on both 0.4mm and 0.8mm plywood sheets and soaked in water. Different connection tecnhiques were also experimented such as a nut and bolt connection, paper clips, and a combination of both.

Joining Techniques

Geometry Tension and Compression

The final iterations take into account the regions of tension and compression, and for the reason of quicker production of the local unrolled geometry, the regions of tension and compression are completely removed. The global geometry is a result of face to face joints between local geometries, connected together by push pins and paper clips to avoid the wood from spiraling out of position.

Geometry Tension and Compression

Final Plywood Geometry Iterations

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Final Plywood Geometry

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PHASE 1II CONCLUSIONS

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CONCLUSIONS AND OBSERVATIONS: Paper Model: Observations:

Potentials: - The local geometry could be adapted further in terms of scale, angle of the domed component and the size of the overall form.

- Paper was very forgiving and malleable, it would take the form we wanted with a little bit of force and pressure

- Multiple varying local geometries could be populated on the same suface to achieve various curvatures.

- The nip and tuck joint was easy to fabricate and relatively easy to assemble.

- The staples pins were not effecient always and some of the nip and tuck joints were starting to tear and this was affecting the overall structure and aesthetic of the form.

- The curvature was acheived by the size and dimensions of the component as well as the angle of the nip and tuck joints which was 60 degrees.

- The overall physical form did not match the digital model form.

- The final surface was not very sturdy and could be manipulated by applying small amounts of external forces which was compromising its strength and its form.

Plywood Model: Observations: - Plywood was a material that was quite hard to fold and mold into our desired geometries. It required additional steps such as dampening and kerfing to be manipulated.

- The push pins were not efficient at holding the local and regional geometry together and were flexing or popping out altogether if they were under stress.

- The curvature was acheived by the size and dimensions of the component as well as face to face joints and the domed quadrant overall form.

- The overall form did not match the intended form, due to the exaggeration of the values of the components on the digital model.

- The form that emerged could be developed further. The geometry should be explored and manipulated to increase of decrease the spiral form that was emerging.

- This surface could be manipulated and adapted for strength as well as the permeability of light, or wind.

Conclusions: - Material experimentations and digital modelling have to move side by side. Both need to be developed after trials and testing. They cannot work independantly and the final outcome heavily relies on both the digital and physical aspects of the experiment.

- After each physical iteration, the digital model must be calibrated to match the physical outcomes. By forcing a geometry onto a surface of by forcing the form to follow the physical model, your creativity and experiments tend to get limited.

- Further improvements could be applied to this design exercise, in terms of joining techniques and regional geometry.

- More comprehensive testing and modelling material would give us knowledge and information about the actual limits of plywood.

- The implementation of structural analysis, in the early design phase would give us an insight on how the overall surface was behaving and where it could be improved and applied.

- Pre fabrication techniques and methods such as unrolling have to be fully thought out to limit any manual input which increases error and can cause a difference to the overall form.

- The overall form, started spiraling inwards and was significantly different from the digital model and intended form. The final model was extremely sturdy and would spring back to its original form if manipulated by force.

- Although the phsyical and digital form did not match, the physical from that emerged due to the exaggerations of values on the digital file, was extremely interesting and can be explored further in the digital and physicals realms.

- A higher degree of curvature was achieved when the individual unrolled components were more curved. Differences in sizes and scales also contributed to varying curvature patterns.

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