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Title: Origami : Art, Architecture


1
Origami Art, Architecture Engineering
  • Mark Schenk (ms652)
  • 12th November 2009
  • Cambridge University Engineering Department

2
Outline
  • Origami
  • Art, Architecture Engineering
  • Give an idea of the applications of Origami
    (inspired) techniques in architecture and
    engineering.

3
Origami Art
4
Origami (as you may know it)
Photo courtesy of Andreas Bauer
Designed and folded by Robert J. Lang
http//www.serve.com/hecht/origami/galmy.htm
5
Origami (as youve never seen it)
http//www.flickr.com/photos/origamijoel/322603691
8/
Joel Cooper (2008)
6
Origami Tessellations
http//www.flickr.com/photos/origomi/290031886/
http//www.flickr.com/photos/brdparker/
http//www.flickr.com/photos/infinite-origami/
7
Origami Tessellations
http//www.flickr.com/photos/9874847_at_N03/
http//www.flickr.com/photos/polyscene/2200937797/
8
Origami Art Consumer Products
Designed and folded by Robert J. Lang
http//www.flickr.com/photos/10207591_at_N00/96957284
/
http//www.mioculture.com/
http//www.yasutomo.com/project/paperlampshade.htm
http//www.inhabitat.com
9
Origami Engineering Applications
10
Origami Engineering Applications
  • deployable structures
  • e.g. solar panels, stents, cylinders, airbags
  • sandwich panel cores
  • e.g. aircraft skins, doubly-corrugated cardboard
  • post-buckling patterns
  • my work folded textured sheets

11
Deployable Solar Panels
  • Miura-ori
  • maps
  • solar panels
  • folding leaves

Miura (1981)
Miura and Natori (1989)
12
Deployable Reflector
Eyeglass Space Telescope Lens
https//www.llnl.gov/str/March03/Hyde.html
Lawrence Livermore National Laboratory Robert
J. Lang
http//www.langorigami.com/science/eyeglass/eyegla
ss.php4
13
Origami Stent
http//www.theiff.org/publications/cab17-lang.html
Kuribayashi et al., (2006)
http//www-civil.eng.ox.ac.uk/people/zy/research/o
rigamistentgraft.html
14
Deployable Cylinders
Hoberman (1993)
Tachi (2009)
Guest (1994)
15
Deployable Plate Mechanisms
Tachi (2009)
16
Sandwich Panel Cores
Heimbs (2007)
Miura (1972)
17
Sandwich Panel Cores
Nojima (2007)
Tesselated Group (2009)
Elsayed and Basily (2004)
18
Inextensional Post-Buckling Modes
Miura (1969)
Tarnai (1994)
19
Folded Textured Sheets
  • My research Folded Textured Sheets
  • Textured Sheets adding a local texture to
    thin-walled sheets in order to change their
    global mechanical properties.

20
Textured Shell Structures - Examples
  • corrugated sheets
  • improved stiffness to weight ratio
  • countless examples in daily life

21
Novel Textured Shell Structures
  • bistable corrugated sheets
  • combination of prestress and geometry

Norman et al. (2006)
22
Novel Textured Shell Structures
  • bistable textured sheets
  • doubly-periodic corrugations
  • prestress through plastic deformation

Golabchi et al. (2008)
23
Example Folded Textured Sheets
Miura sheet
Eggbox sheet
24
Deformation of Folded Textured Sheets
Miura sheet
Eggbox sheet
25
Deformation of Folded Textured Sheets
  • mid-surface plane of the sheet can be twisted
    into a global saddle shape
  • folds allow local expansion/contraction

Miura sheet
Eggbox sheet
26
In-plane Deformation - Miura sheet
The Miura sheet expands in all directions under a
uni-axial strain negative Poissons ratio
27
In-plane Deformation - Eggbox sheet
The Eggbox sheet contracts transversely to a
uni-axial strain positive Poissons ratio
28
Out-of-plane Deformation Miura Sheet
Saddle-shaped (anticlastic) deformation
corresponds to a positive Poissons ratio.
29
Out-of-plane Deformation - Eggbox sheet
Spherical (synclastic) deformation corresponds
to a negative Poissons ratio.
30
Summary of Deformation Kinematics
Poissons ratio of the sheets
Both sheets have oppositely signed Poissons
ratio for bending and stretching.
31
Resch waterbomb sheet
Resch sheet
32
Resch waterbomb sheet
Strong bending-extension coupling
33
Resch waterbomb sheet
regular
iso-area
34
Properties of Folded Textured Sheets
  • Folded Textured Sheets
  • provide extra flexibility
  • intriguing mechanical properties, e.g.
  • opposite sign for Poissons ratio under bending
    and extension (Miura eggbox)
  • strongly coupled bending and extension (Resch)
  • These sheets have not previously been studied.

35
Applications of Folded Textured Sheets
  • Morphing Structures
  • change shape
  • maintain continuous surface
  • Example morphing wings

36
Origami Architectural Applications
37
Origami in Architecture Bauhaus
Albers (1927)
38
Origami Architecture
  • folded plate roofs / façades
  • mechanical advantage
  • e.g. concrete, timber, glass, etc.
  • approximation to curved surfaces
  • deployable architecture
  • e.g. emergency shelters
  • adaptable/morphing façades

39
Folded Plate Structures
  • Folded Plate Structures
  • improved bending stiffness
  • visual appeal
  • Note
  • developable vs folded plate
  • limited to straight folds

40
Folded Plate Structures
http//www.ketchum.org/shellpix.html
Milo Ketchum (1910-1999)
41
Folded Plate Structures
Engel (1968)
42
Folded Plate Structures
Engel (1968)
43
Folded Plate Structures
Miura (1969)
Coppa (1970)
Tonon (1993)
44
Folded Plate Structures Examples
  • Mobile Sulphur Extraction Factory, Pomezia, Rome
    Renzo Piano (1966)

45
Folded Plate Structures Examples
US Air Force Academy Cadet Chapel, Colorado
Springs Skidmore, Owings and Merill (1956)
http//www.flickr.com/people/paskuhan/
http//jmvigil.blogspot.com/2008/08/us-air-force-a
cademy-cadet-chapel.html
46
Folded Plate Structures Examples
Yokohama International Cruise Terminal Foreign
Office Architects (2002)
http//www.eikongraphia.com/?p324
http//www.richardsweeney.co.uk http//www.flickr.
com/photos/richardsweeney/
47
Folded Plate Structures
  • Revival of interest in folded plate structures?
  • Recent development
  • timber / glass structures
  • computer design tools
  • free-form geometry (i.e. BLOB architecture)

48
Folded Plates Timber Panels
Buri et al. (2009)
49
Folded Plates Timber Panels
Case Study Temporary Chapel of St. Loup
50
Folded Plates Glass Sheets
Trometer et al. (2006)
51
Folded Plates Glass Sheets
  • one-way colour tunnel Olafur Eliasson (2007)

http//flux.net/take-your-time-olafur-eliasson-new
-york
http//www.designboom.com/weblog/cat/10/view/1647/
take-your-time-olafur-eliasson.html
52
Folded Plates Solar Panels
  • Folded Plate Solar Panels?

http//www.freepatentsonline.com/4296736.html
Soot (1981)
53
Folded Plates Free-Form Geometry
Trautz et al. (2009)
54
Folded Plates Free-Form Geometry
Heinzelmann (2009)
55
Folded Plates Shading
Heinzelmann (2009)
56
Free-Form Geometries
Westfield shopping centre development in
Shepherds Bush, west London
57
Developable Domes
http//www.ronresch.com
Ron Resch
58
Ron Resch
http//www.ronresch.com
59
Ron Resch
http//www.ronresch.com
60
Developable Domes
http//www.flickr.com/photos/elelvis/
http//flickr.com/photos/72567727_at_N00/page2/
61
Origami Hyperbolic Paraboloids
http//erikdemaine.org/hypar/
Felix Candela (1910-1997)
Milo Ketchum (1910-1999)
Explored by le Corbusier, Frei Otto, etc.
62
Deployable Architecture
De Temmerman (2007)
63
Deployable Architecture
http//www.inhabitat.com/2008/10/22/origami-inspir
ed-folding-bamboo-house-by-ming-trang/
http//urbanrevision.org/who-we-are/competitions/r
esults-reconstruct/results-construct-notable-entri
es-folded-bamboo/
64
Emergency Shelters
accordeon reCover shelter
http//www.inhabitat.com/2008/09/03/matthew-malone
-recovery-shelter/
Boler and Tandon (1967)
65
Deployable Architecture
Emilio Pérez Piñero (1935-1972)
http//www.flickr.com/photos/wannesdeprez/46637118
0/
http//www.u.arizona.edu/shunter/pinero.jpg
66
Deployable Architecture
Daniel MacGibbon (2008)
http//designstudio5.blogspot.com/
67
Transformable Architecture
Institut du Monde Arabe (Paris)? Jean Nouvel
(1987)
http//www.archnet.org/library/sites/one-site.jsp?
site_id851
68
Transformable Architecture
Chuck Hoberman
http//www.designboom.com/eng/interview/hoberman.h
tml
http//farm2.static.flickr.com/1031/1284318386_5c3
12ca714.jpg?v0
69
Transformable Architecture
http//www.adaptivebuildings.com
Iris Dome, 2000 Worlds Fair, Hanover, Germany
http//www.hoberman.com
Adaptable Sunshade, 2006 Building Center Trust,
London, UK
70
Transformable Architecture
Robotic Membrane (concept)? OrangeVoid
http//www.orangevoid.org.uk
71
Transformable Architecture
Hyposurface (concept)? Hyposurface Corp (2000)
http//hyposurface.org/
72
Transformable Architecture
Adaptable Chevron Façade Panchuk (2006)
73
Conclusions
74
Conclusions
  • Origami
  • a versatile source of inspiration for
    architects, and a rich source of challenges for
    engineers!

75
Origami Folding and Geometry
76
Curved Folding
Curved Folding
David Huffman (1925-1999)
http//www.graficaobscura.com/huffman/index.html
http//www.theiff.org/oexhibits/paper04.html
http//www.nytimes.com/2004/06/22/science/22orig.h
tml
77
Curved Origami Tessellations
http//www.flickr.com/photos/polyscene/
Polly Verity (2008)
78
Computational Curved Folding
http//graphics.stanford.edu/niloy/research/foldi
ng/folding_sig_08.html
Kilian et al. (2008)
79
Computational Curved Folding
http//graphics.stanford.edu/niloy/research/foldi
ng/folding_sig_08.html
Kilian et al. (2008)
80
Folded Façade?
Image courtesy of Carol M. Highsmith
Frank Gehry (1999) Walt Disney Concert Hall
(Los Angeles, USA)
81
Curved Folding What is possible?
  • Seemingly a wide range of shapes possible, but
    in fact it is quite limited…
  • The geometry of curved folds can be described
    using differential geometry.
  • Much simpler and very intuitive explanation of
    the limitations of folding is provided by the
    concept of Gaussian curvature.

82
Curvature of a surface
83
Gaussian curvature of a surface
  • Principal curvatures
  • minimum K1
  • maximum K2
  • extrinsic measure of curvature
  • Gaussian curvature (1828)
  • KGK1.K2
  • intrinsic measure of curvature

P
R(?)
84
Gaussian curvature examples
positive
zero
negative
85
Gaussian curvature
  • Gaussian curvature is…
  • an intrinsic measure of curvature
  • and hence is…
  • invariant under an inextensional deformation of
    the surface!

86
Gaussian curvature Origami
  • Gaussian curvature Origami
  • Gaussian curvature of a flat sheet of paper
    is…zero!
  • Hence the Gaussian curvature of a folded sheet of
    paper is … zero!

Therefore, paper can only be folded into surfaces
with zero Gaussian curvature such as cylinders
and cones!
87
Zero Gaussian Curvature Surface
http//graphics.stanford.edu/niloy/research/foldi
ng/folding_sig_08.html
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