FOLDED SURFACE
EMTECH BOOTCAMP DOCUMENTATION GROUP 8
CHAITANYA CHAVAN | ANTONIA MOSCOSO CARLOS OCHANDO | ALICAN SUNGUR
ABSTRACT Our aim was to achieve a doubly curved surface by introducing a series of folds into a flat material increasing it’s stiffness. Each fold pattern allows an specific type of deformation when compression, torsion or tension are applied. Therefore, our hypothesis was that by controlling the parameters responsible for this deformation, as well as combining different studied geometries, we would be able to generate a controlled overall geometry. As an starting point for our exploration, in a bottom up approach, we studied the Miura-Ori origami pattern and defined it as our base folding component. We then evaluated the material’s performance in a series of physical models, where variations of it’s parameters were introduced in both local and regional scale.This understanding of the geometrical pattern and how the local actions have a material response, was applied to the generation of a surface supported in three points.
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Simultaneously we defined a light material for this exploration. We chose a starched fabric that would have both the stiffness to accept the folds, and the malleability to let us play with the combination of patterns. Besides, the fabric will permit to also study the interaction between the light and the folds.
[CONTENTS] 1 LOCAL SCALE +THE COMPONENT the miura-ori pattern [p 01]
++ PERFORMANCE material’s behaviour [p 03] +++ VARIATION parameters [p 04] ++++ PERFORMANCE material’s behaviour [p 06]
2 REGIONAL SCALE + COMBINING PATTERNS [p 07]
3 GLOBAL GEOMETRY + THE MATERIAL fabric, light [p 13] ++ PSEUDO CODE pattern, logic [p 17] +++ ANALYSIS scale, weight [p 19] ++++ DIGITAL EXPLORATION [p 21] 4 CONCLUSION [p 23]
5 BIBLIOGRAPHY [p 24]
BOOTCAMP DOCUMENTATION | 2014
OCAL SCALE 1LTHE COMPONENT The experimentation began with the study of the Miura Ori Pattern, and the material’s performance resulting from this folded geometry. The pattern is composed by a tessellation of parallelograms, which rely on the following parameters:
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+ the dimension of the sides (a, b) ++ the acute angle � +++ the angle Ø Є (0 ; �/2) adjacent to the 2 folds, that determines the height of the fold. Shown in Fig. 2
01
This pattern is composed by alternating mountains and valleys in a regular frequency, and can be folded to become a flat surface. Shown in Fig 1.
Fold Legend Mountain Valley
ɣ
b
Ɵ
Mountain Valley
Regular Fold Miura Patern Mountain Fold CODE : M V M V .. ..
Fig. 1
a
a Ω
b
Fig. 2
BOOTCAMP DOCUMENTATION | 2014
stiffness test 1
in plane deformation
out of plane deformation
out of plane deformation
L O C AL S C AL E PERFORMANCE
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For in plane deformation the Miura Ori pattern has a negative Poisson’s ratio, since there is a transverse expansion when tension is applied into the fabric. Whereas for out of plane bending deformation, when lateral compression is applied, this pattern has a positive Poisson’s ratio acquiring a saddle shape and anticlastic curvature.
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VARIATIONS
Searching for a better understanding of the relation between the component’s geometry and the material’s behaviour, we tested changing the parallelogram’s parameters. Physical models showed that changing the angle � in all of the parallelograms or changing the size of the sides (a,b) do not have an impact on the overall performance of the material. Therefore, our next exploration was to tessellate 2 different parallelograms, which implies in a loss of the symmetry of the folds.
BOOTCAMP DOCUMENTATION | 2014
Fold Legend ɣ Mountain Valley Mountain Valley
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Angular Fold Miura Patern Fold CODE : V M V M V Mountain ɣ=120 deg
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stiffness test 1
in plane deformation
out of plane deformation
out of plane deformation
L O C AL S C AL E PERFORMANCE
By changing the angle ďż˝ to 60 ĚŠand creating a tessellation composed by two different parallelograms where the sides are no longer equal, and removing the symmetry axis between the folds, the overall stiffness of the material increases. The transverse expansion when stretching the fabric decreases, and so does the curvature.
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2R E G I O NAL
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S C ALE COMBINING PATTERNS
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After studying or component at a local scale, we started exploring combining the patterns by introducing variations of: + dimensions ++ frequency +++ direction of the folds in a regional scale. This sequence of patterns allowed us to understand the relation between the geometry and the resulting curvature. Moreover we created a code for each combination so we could replicate this curvature in our final surface.
Fold Legend
ɣ Mountain
2Valley Mountain Irregular-Angular Fold Miura Patern Fold CODE : V M 2V 2M 2V M V M V Valley ɣ=120 deg
BOOTCAMP DOCUMENTATION | 2014
Fold Legend
ɣ1
Mountain change directionValley Mountain
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Valley
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Grid Rotation Miura Patern Fold CODE : V 5M cd V M V M V ɣ1=30 deg
Fold Legend ɣ - Skip
2 Mountain l Mirror Mountain
Changing Direction Miura Patern Fold CODE : V M V M l 2M - V M V ɣ=90 deg
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Fold Legend ɣ
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4Mountain Irregular Fold Miura Patern Fold CODE : V 4M V 4M Valley ɣ=90 deg
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Fold Legend ɣ Mountain
Irregular Fold Miura Patern Fold CODE : V M 3V M 3V Mountain ɣ=90 deg 3Valley
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3G L OB AL
S C A LE THE MATERIAL
Searching for a material stiffer than paper but more malleable than mdf or cardboard, we decided to explore fabric for it’s light weight. We chose starched linen because of it’s high tensile strength, stronger than cotton, which is further stiffened by the starch. Furthermore, linen has a low elastic recovery, which means that after deformation by compression or expansion it doesn’t come back to it’s original form. Therefore a plastic behaviour once folded. The linen however presents little resistance to compression and this also has to be taking into account.
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INTERACTION WITH THE LIGHT
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One of the benefits of working with a permeable fabric such as linen is that this it’s orthogonal grid of fibers enable the passing of light. Consequently, the field of research exceeds the manipulation of the flat sheet by folding by introducing the game of light and shadow produced by the pattern. Therefore, we tested different lighting angles over our physical models in the dark room, and it showed that the smaller the pattern the more the interaction between the fabric and the light becomes interesting, the more the valleys and the mountains can be read in the shadow.
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3G L OB A L
S C A LE THE PSEUDO CODE
ɣ
ɣ
ɣ
INPUTS
ɣ
ɣ
ɣ
LOCAL PATTERN
RESULTANT FORM
DESIRABLE ? YES
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FOLDING
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FLAT SHEET MATERIAL
BEHAVIOUR ANALYSIS
BEHAVIOUR ANALYSIS COMPUTATIONAL INPUTS
MATERIAL ANALYSIS
PERMUTATION OF PATTERNS
GLOBAL PATTERN
NO
ɣ
THE PATTERN BOOTCAMP DOCUMENTATION | 2014
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ANAYLISIS
On the one hand, our physical model allowed us to perceive the relation between the scale of the patterns facets, their weight and the material’s resistance. In order to improve the fabric’s performance we layered pieces of fabric increasing it’s cross section.This proved to be an effective strategy for the supports. On the other it showed that our pattern had a few weak points were the folds were either buckling under compression
or flattening. Besides, the overall pattern had the longest components on the higher part of the curvature 15cm, while the supports were composed by tighter pattern, 5cm. This contributed to creating a flat area on the upper part of our surface. In order to achieve an effective overall pattern, computer modelling was necessary taking into account the materials properties.
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// anchor points: 1 / angle: [valley:pi/2], [mountain:-pi/2]
// anchor points: 3 / angle: [valley:pi/2], [mountain:-pi/2]
// anchor points: 3 / angle: [valley:pi/4], [mountain:-pi/4]
// anchor points: 3 / angle: [valley:pi/2], [mountain:-pi/2]
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// anchor points: 2 / angle: [valley:pi/4], [mountain:-pi/4]
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// anchor points: 1 / angle: [valley:pi/2], [mountain:-pi/2]
var
1
var
2
var
3
var
4
var
5
var
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DIGITAL EXPLORATION
To enable a top down approach, we developed a digital model based on our final pattern. We were aiming that EXPERIMENTATIONS this DIGITAL model would show us were the Final pattern is a combination of previously pattern was failing to contribute to analyzed patterns at the experimentation stage.overall Third dimension of the We final pattern a the geometry. wereisable prediction with respect to previous form. At tothisstudy the variations of the angle of stage, form of final pattern is analyzed fold saw how changing anchorage and and 6 variations produced according to certain inputs and their combinations. points does a few variations on the overall geometry. First variation is folding angles of "Mountain" and "Valley" edges between "pi" clockwise However the model had no information and "pi" counter-clockwise. Secondly, for about the fabric’s properties (strength, each variation, different anchorage points are set to perform differentiation on elasticity) and applied the whole same s u r f a c e . fold angle in all of the patterns, so it These twoless parameters and their supplied information thatcombinawhat we tions created 6 variations that perform in originally intended. same logic but in different shape.
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5C ON C LU S I O N Our study of the geometry of the folded patterns and the resulting materials’ behaviour proved to be only the starting point for the generation of a surface based on a hierarchical organisation of a simple controlled component. By manipulating the sequence of folds in scale, angle and frequency, we achieved a self supported surface supported in 3 points. However, our bottom up approach of how the local and regional actions inform the global geometry presented new weakness when we scaled up the patterns. On the one hand, the material’s stiffness was challenged by the weight of larger facets. We tried to overcome this difficulty by introducing new layers of fabric as reinforcement. Nevertheless for an efficient use of this strategy, a less empirical application is required, along with a better understanding of the global form. On the other hand, the combination of patterns as a systematic growth also presented issues, since the pattern requires different structural performance according to their location on the overall surface. Therefore it was clear that a top down approach was missing in our process, and we would require further development of the computational model to allow an efficient back and forward local-global communication. One criteria that should be included in this interaction from the structural performance, is the fabric’s interaction with light and that the shadows produced by the pattern. Taking into consideration that the more the folds are tight, and smaller the more this interaction becomes interesting.
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We experienced difficulties too create a digital model with different fold angles as well as the fabric’s properties into account; but we are positive that further develop on the digital model would enable a more accurate definition of the folds.
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6BI BL IO GR A P H Y Jackson, P. 2011. Folding Techniques for designers: from sheet to form. 2nd Edition. London: Laurence King Publishing Schenk, M and Guest, S. 2013. Geometry of Miura-folded metamaterials. PNAS: Proceedings of the National Academy of Sciences of the United States of America. 110 (9). pp 3276–3281 http://www-g.eng.cam.ac.uk/advancedstructures/files/pdf/2013GuestD.pdf[Accessed25 October 2014] Schenk, M and Guest, S. 2010. Origami Folding: A Structural Engineering Approach. Origami proceedings of 5OSME, 5th international conference on Origami in Science, Mathematics and Education. Singapore. pp. 293-305. http://www2.eng.cam.ac.uk/~sdg/preprint/5OSME. pdf [Accessed 23 October 2014] Schmidt, P and Stattmann, N. 2009. Unfolded : paper in design, art, architecture and industry. Basel : Birkhauser, Vyzoviti, S.2006. Supersurfaces: folding as a method of generating forms for architecture, products and fashion. Amsterdam : BIS Publishers
BOOTCAMP DOCUMENTATION | 2014