Origami : Art, Architecture

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Origami Art, Architecture Engineering

• Mark Schenk (ms652)
• 12th November 2009
• Cambridge University Engineering Department

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Outline

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

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Origami Art
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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
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Origami (as youve never seen it)
http//www.flickr.com/photos/origamijoel/322603691
8/
Joel Cooper (2008)
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Origami Tessellations
http//www.flickr.com/photos/origomi/290031886/
http//www.flickr.com/photos/brdparker/
http//www.flickr.com/photos/infinite-origami/
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Origami Tessellations
http//www.flickr.com/photos/9874847_at_N03/
http//www.flickr.com/photos/polyscene/2200937797/
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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
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Origami Engineering Applications
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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

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Deployable Solar Panels

• Miura-ori
• maps
• solar panels
• folding leaves

Miura (1981)
Miura and Natori (1989)
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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
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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
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Deployable Cylinders
Hoberman (1993)
Tachi (2009)
Guest (1994)
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Deployable Plate Mechanisms
Tachi (2009)
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Sandwich Panel Cores
Heimbs (2007)
Miura (1972)
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Sandwich Panel Cores
Nojima (2007)
Tesselated Group (2009)
Elsayed and Basily (2004)
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Inextensional Post-Buckling Modes
Miura (1969)
Tarnai (1994)
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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.

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Textured Shell Structures - Examples

• corrugated sheets
• improved stiffness to weight ratio
• countless examples in daily life

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Novel Textured Shell Structures

• bistable corrugated sheets
• combination of prestress and geometry

Norman et al. (2006)
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Novel Textured Shell Structures

• bistable textured sheets
• doubly-periodic corrugations
• prestress through plastic deformation

Golabchi et al. (2008)
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Example Folded Textured Sheets
Miura sheet
Eggbox sheet
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Deformation of Folded Textured Sheets
Miura sheet
Eggbox sheet
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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
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In-plane Deformation - Miura sheet
The Miura sheet expands in all directions under a
uni-axial strain negative Poissons ratio
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In-plane Deformation - Eggbox sheet
The Eggbox sheet contracts transversely to a
uni-axial strain positive Poissons ratio
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Out-of-plane Deformation Miura Sheet
Saddle-shaped (anticlastic) deformation
corresponds to a positive Poissons ratio.
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Out-of-plane Deformation - Eggbox sheet
Spherical (synclastic) deformation corresponds
to a negative Poissons ratio.
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Summary of Deformation Kinematics
Poissons ratio of the sheets
Both sheets have oppositely signed Poissons
ratio for bending and stretching.
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Resch waterbomb sheet
Resch sheet
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Resch waterbomb sheet
Strong bending-extension coupling
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Resch waterbomb sheet
regular
iso-area
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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.

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Applications of Folded Textured Sheets

• Morphing Structures
• change shape
• maintain continuous surface
• Example morphing wings

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Origami Architectural Applications
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Origami in Architecture Bauhaus
Albers (1927)
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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

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Folded Plate Structures

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

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Folded Plate Structures
http//www.ketchum.org/shellpix.html
Milo Ketchum (1910-1999)
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Folded Plate Structures
Engel (1968)
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Folded Plate Structures
Engel (1968)
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Folded Plate Structures
Miura (1969)
Coppa (1970)
Tonon (1993)
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Folded Plate Structures Examples

• Mobile Sulphur Extraction Factory, Pomezia, Rome
  Renzo Piano (1966)

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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
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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/
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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)

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Folded Plates Timber Panels
Buri et al. (2009)
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Folded Plates Timber Panels
Case Study Temporary Chapel of St. Loup
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Folded Plates Glass Sheets
Trometer et al. (2006)
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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
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Folded Plates Solar Panels

• Folded Plate Solar Panels?

http//www.freepatentsonline.com/4296736.html
Soot (1981)
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Folded Plates Free-Form Geometry
Trautz et al. (2009)
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Folded Plates Free-Form Geometry
Heinzelmann (2009)
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Folded Plates Shading
Heinzelmann (2009)
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Free-Form Geometries
Westfield shopping centre development in
Shepherds Bush, west London
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Developable Domes
http//www.ronresch.com
Ron Resch
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Ron Resch
http//www.ronresch.com
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Ron Resch
http//www.ronresch.com
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Developable Domes
http//www.flickr.com/photos/elelvis/
http//flickr.com/photos/72567727_at_N00/page2/
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Origami Hyperbolic Paraboloids
http//erikdemaine.org/hypar/
Felix Candela (1910-1997)
Milo Ketchum (1910-1999)
Explored by le Corbusier, Frei Otto, etc.
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Deployable Architecture
De Temmerman (2007)
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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/
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Emergency Shelters
accordeon reCover shelter
http//www.inhabitat.com/2008/09/03/matthew-malone
-recovery-shelter/
Boler and Tandon (1967)
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Deployable Architecture
Emilio Pérez Piñero (1935-1972)
http//www.flickr.com/photos/wannesdeprez/46637118
0/
http//www.u.arizona.edu/shunter/pinero.jpg
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Deployable Architecture
Daniel MacGibbon (2008)
http//designstudio5.blogspot.com/
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Transformable Architecture
Institut du Monde Arabe (Paris)? Jean Nouvel
(1987)
http//www.archnet.org/library/sites/one-site.jsp?
site_id851
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Transformable Architecture
Chuck Hoberman
http//www.designboom.com/eng/interview/hoberman.h
tml
http//farm2.static.flickr.com/1031/1284318386_5c3
12ca714.jpg?v0
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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
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Transformable Architecture
Robotic Membrane (concept)? OrangeVoid
http//www.orangevoid.org.uk
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Transformable Architecture
Hyposurface (concept)? Hyposurface Corp (2000)
http//hyposurface.org/
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Transformable Architecture
Adaptable Chevron Façade Panchuk (2006)
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Conclusions
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Conclusions

• Origami
• a versatile source of inspiration for
  architects, and a rich source of challenges for
  engineers!

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Origami Folding and Geometry
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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
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Curved Origami Tessellations
http//www.flickr.com/photos/polyscene/
Polly Verity (2008)
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Computational Curved Folding
http//graphics.stanford.edu/niloy/research/foldi
ng/folding_sig_08.html
Kilian et al. (2008)
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Computational Curved Folding
http//graphics.stanford.edu/niloy/research/foldi
ng/folding_sig_08.html
Kilian et al. (2008)
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Folded Façade?
Image courtesy of Carol M. Highsmith
Frank Gehry (1999) Walt Disney Concert Hall
(Los Angeles, USA)
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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.

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Curvature of a surface
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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(?)
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Gaussian curvature examples
positive
zero
negative
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Gaussian curvature

• Gaussian curvature is
• an intrinsic measure of curvature
• and hence is
• invariant under an inextensional deformation of
  the surface!

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Gaussian curvature Origami

• Gaussian curvature Origami
• Gaussian curvature of a flat sheet of paper
  iszero!
• 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!
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Zero Gaussian Curvature Surface
http//graphics.stanford.edu/niloy/research/foldi
ng/folding_sig_08.html