AdvancedStructures Group

Origami in Engineering and Architecture An art spanning Mathematics, Engineering and Architecture

Dr Mark Schenk (ms652)October 25th 2012

Origami

Objective:

introduction to Origami in mathematics, engineering and architecture. Examples from academic research and real life applications.

Today

- lecture (~1 hr)

- workshop + presentations (~2 hrs)

Origami

origami– from Japanese for ‘oru’ (fold) and ‘kami’ (paper)

– earliest book to describe origami dates to 1682, with the classic crane dating to a 1797 book “The Secret of One Thousand Cranes Origami”

– resurgence of interest in 20th century– rapid development over the last 2 decades.

Origami Art

Pho

to courtesy of A

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http://w

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From simple…

Origami Art

Designed and folded by Robert J. Lang

… to advanced

Origami Art

http://www.flickr.com/photos/origamijoel/3226036918/

Joel Cooper (2008)

Origami Art : tessellations

‘Star Tessellation’ by Eric Gjerde

http://ww

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/photos/874778

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Origami Art : tessellationshttp://w

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http://www.flickr.com/photos/9874847@N03/

Origami Art : tessellations

http://ww

w.flickr.com

/photos/polyscene/220093

7797/

http://www.flickr.com/photos/cambridgeuniversity-engineering/4706414628/

http://www.nytimes.com/2004/06/22/science/22orig.html

http://www.theiff.org/oexhibits/paper04.html

http://www.graficaobscura.com/huffman/index.html

David Huffman (1925-1999)

Origami Art : curved folding

Origami Art : developments

increased model complexity– crease patterns vs. linear folding instructions– computer aided design of models– a more fundamental understanding of the

underlying mathematics of origami

Designed and folded by Robert J. Lang

Origami : Mathematics

Origami Mathematics

origami & mathematics are deeply intertwined

• origami foldability

i.e. can a crease pattern actually be folded?

• surface geometry

i.e. what shapes can you attain?

Origami Mathematics : foldability

Example : Miura-ori sheet

flat and rigid foldable

Origami Mathematics : flat foldability

• flat foldability

after folding all creases by ±180°, the final pattern lies in a plane

Kawasaki-Justin theorem: θ1 − θ2 + θ3 − θ4 = 0

Origami Mathematics : flat foldability

• flat foldability – counter example

engineering : compact stowage

Origami Mathematics : rigid foldability

• rigid foldability

if the pattern were made of rigid panels connected by hinges, it can be folded.

Dureisseix (2011)

engineering : deployable (or rigid) plate structures

Origami Mathematics : rigid foldability

• rigid foldability – counter example

paper shopping bag only ‘exists’ in either the collapsed or upright position.

Balkcom (2004)

Origami Mathematics : rigid foldability

a rigid-foldable shopping bag:

Wu and You (2011)

Further research: Huffman (1976), Wu and You (2010), Stachel (2009,2010), Tachi (2009)

Origami Mathematics : foldability

the ‘unfoldable’ hyperbolic paraboloid

Demaine et al. (2009)

Origami Mathematics : foldability

modelling the 'unfoldable'

Dias, Dudte, Mahadevan, Santangelo (2012)

Origami Mathematics : surface geometry

Sphere: positive Gaussian curvature

Atlas: zero Gaussian curvature

surface geometry (aka, differential Geometry)

What kind of folded shapes can we attain?

- assume no stretching deformations (i.e. developable)

?

Origami Mathematics : surface geometry

Sphere: positive Gaussian curvature

Atlas: zero Gaussian curvature

Origami Mathematics : surface geometry

developable surface (i.e. a sheet of paper)

Gaussian curvature is invariant under bending

Origami Mathematics : surface geometryK

ilian et al. (2008)

engineering : curved surfaces from flat sheets

Image courtesy of Carol M. Highsmith

Frank Gehry (1999) Walt Disney Concert Hall (Los Angeles, USA)

Origami Mathematics : surface geometry

Summary

Origami Mathematics

be aware of certain concepts:

- flat foldability

- rigid foldability

- surface geometry (Gaussian curvature)

It is an active field of mathematics!

Origami : Engineering

Engineering Origami

Engineering Origami :

application of origami to solve technical problems.

Examples from my current research (i.e. shameless self-promotion):

i) Deployable Space Structures

ii) Folded Meta-Materials

Engineering Origami : deployable

i) Deployable Space Structures

• inflatable satellite de-orbiting device• large sail structure (2x2m)• 3U CubeSat

3U CubeSat

Inflatable booms2μm mylar membrane

Engineering Origami : deployable

Inflatable Booms• Inflatable Antenna Experiment (IAE, 1996)

L'Garde & NASA JPL (1996)

Engineering Origami : deployable

So, how do you fold an inflatable boom?

Engineering Origami : deployable

So, how do you fold an inflatable boom?

• rolling/coiling• folding

- z-fold

- origami patterns

• conical stowageILC Dover (ITSAT)

Wang and Johnson (2003); NASA LaRC

Engineering Origami : deployable

origami booms (1/3)

Guest and Pellegrino (1994)

Barker and Guest (2004) Hoberman (1993)

Engineering Origami : deployable

origami booms (2/3)

EADS Astrium

Senda et al (2006)

Engineering Origami : deployable

origami booms (3/3)

- stowed volume (flat-foldable)

- material deformation (rigid-foldable)

- straightness of deployment

Schenk, Viquerat, Seffen and Guest (2012)

Engineering Origami : deployable

conical telescopic booms (1/2)

- concentric folds

- telescopic deployment

Palisoc (2004)

L'Garde, ISPSS (2005)

Engineering Origami : deployable

conical telescopic booms (2/2)

experiments

analysis

Engineering Origami : Meta-Materials

ii) Folded Meta-Materials

“Meta-Material - A synthetic composite material engineered to display properties not usually found in natural materials.”

• fold patterns introduce kinematic properties

Schenk and Guest (2012)

Engineering Origami : Meta-Materials

Basic component: Miura-ori sheet

a) Folded Shell Structure

b) Folded Cellular Meta-Material

Engineering Origami : Meta-Materials

a) meta-material : Folded Shell Structures

Engineering Origami : Meta-Materials

novel property :

• doubly-curved surface

Engineering Origami : Meta-Materials

novel property :

• negative in-plane Poisson’s ratio

Engineering Origami : Meta-Materials

novel property :

• positive out-of-plane Poisson’s ratio

Engineering Origami : Meta-Materials

application : morphing structures

- change shape

- maintain continuous surface

Example: morphing wings

Engineering Origami : Meta-Materials

b) Folded Cellular Meta-Material

- stacking of folded layers

- maintains folding motion

Engineering Origami : Meta-Materials

novel properties:

- omni-directional negative Poisson's ratio

- highly anisotropic material properties

Engineering Origami : Meta-Materials

Folded Sandwich Panel Core

- blast impact mitigation

blastimpact

Schenk, Guest, McShane (2012)

Engineering Origami : Meta-Materials

folded sandwich panel core

- numerical simulations

- core manufacture

Engineering Origami : applications

Engineering Origami : application of origami to solve technical problems.

i) deployability

ii) increased stiffness

iii) impact absorption

iv) meta-materials

v) energy-efficiency

Miura-ori sheet

Engineering Origami : deployable

i) deployable structures– space telescope – solar panels

Miura and Natori (1989)

Lang (2003)

Engineering Origami : deployable

i) deployable structures– solar sails

Leipold et al. (2002) JAXA IKAROS (2010)

Guest (1992)

Engineering Origami : deployable

i) deployable structures– emergency shelters– medical stent– bio-mechanics

de Temmerman (2007)

Kuribayashi et al. (2006)

Kobayashi (1999)

Engineering Origami : deployable

most common fold pattern: Miura-ori

– flat-foldable– rigid-foldable

Engineering Origami : deployable

generalized Miura-ori: rigid-foldable and flat-foldable

Tachi (2009–2011)http://www.tsg.ne.jp/TT/software/

Engineering Origami : deployable

rigid-foldable hyperbola

Tac

hi (

2010

)

Engineering Origami : deployable

i) deployable structures– programmable matter

Hawkes et al. (2010)

Engineering Origami : stiffness

ii) increased stiffness– architecture : folded plates

Engineering Origami : stiffness

ii) increased stiffness– folded plates

Engel (1968)

Origami Engineering : stiffness

ii) increased stiffness– sandwich panel cores

Miura (1972)

Rapp (1960)

Heimbs (2007)

Engineering Origami : impact resistance

iii) impact resistance– sandwich panel cores

Elsayed and Basily (2004)

Tessellated Group (2010)

Engineering Origami : impact resistance

iii) impact resistance– car crash boxes

Wu (2010)

Miura (1969)

Tarnai (1994)

Engineering Origami : meta-materials

iv) meta-materials– deployable cellular solids

Miura and Tachi (2010), Tachi (2011)

Engineering Origami : meta-materials

iv) meta-materials– curved corrugated

shell structures

Seffen (2012)

Norman (2009)

Engineering Origami : energy efficiency

v) energy-efficient manufacturing

- sheet metal bending

- curved folding

Tachi and Epps (2011)

Engineering Origami : curved folding

• curved folding : RoboFold

www.robofold.com

Rhino3D with Grasshopper and Kangaroo

Summary

Origami Engineering

used for a wide range of technical applications:

i) deployable structures

ii) increased stiffness

iii) impact resistance

iv) meta-materials

v) sheet metal folding

And more applications are being developed!

Origami : Architecture

Origami Architecture : Bauhaus

Josef Albers (1927)

Origami Architecture : applications

1) folded plate roofs / façades– mechanical advantage

– visual appeal

– materiality : timber, glass, etc.

– approximation to curved surfaces

2) deployable architectural structures

3) transformable / kinematic architecture

Origami Architecture : folded plates

Milo Ketchum (1910-1999)

Origami Architecture : folded platesEngel (1968)

Origami Architecture : folded plates

Engel (1968)

Origami Architecture : folded plates

Skidmore, Owings and Merill (1956)US Air Force Academy Cadet Chapel, Colorado Springs

Origami Architecture : folded plates

Tonon (1993)

Coppa (1970)

Miura (1969)

Origami Architecture : folded plates

Renzo Piano (1966)

Mobile Sulphur Extraction Factory, Pomezia, Rome

Origami Architecture : foldable dome

Ron Resch (1939-2009)

Origami Architecture : Ron Resch

Origami Architecture : Ron Resch

http://ww

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resch.co

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"Made with Paper Show" Nov. 1967

(1960-1963)

Origami Architecture : foldable dome

http://flickr.co

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http://w

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Origami Architecture : folded plates

Foreign Office Architects (2002)Yokohama International Cruise Terminal

http://www.richardsweeney.co.uk

Origami Architecture : folded plates

St. Bridget Church

Gdańsk, Poland

From “Heavenly vaults: from Romanesque to Gothic in European architecture”

Origami Architecture : folded plate

Revival of interest in folded plate structures?

Recent developments

• timber / glass structures

• computer design tools

• free-form geometry (i.e. BLOB architecture)

Origami Architecture : timber panels

Buri et al. (2009)

Origami Architecture : timber panels

computer design tools

case study:temporary chapel of St. Loup

Buri et al. (2009)

Origami Architecture : timber panels

case study:temporary chapel of St. Loup

Origami Architecture : glass panels

Trometer et al. (2006)

Origami Architecture : glass panels

Olafur Eliasson (2007)

One-way Colour Tunnel

http://www.designboom.com/weblog/cat/10/view/1647/take-your-time-olafur-eliasson.html

http://flux.net/take-your-time-olafur-eliasson-new-york

Origami Architecture : free-form

Trautz et al. (2009)

Origami Architecture : free-form

Heinzelmann (2009)

Origami Architecture : deployable

De Temmerman (2007)

Origami Architecture : deployable

http://www.inhabitat.com/2008/10/22/origami-inspired-folding-bamboo-house-by-ming-trang/

Origami Architecture : deployable

http://www.inhabitat.com/2008/09/03/matthew-malone-recovery-shelter/

accordeon reCover shelter

Boler and Tandon (1967)

Origami Architecture : deployable

Tachi (2009)

Origami Architecture : deployable

Emilio Pérez Piñero (1935-1972)

http://ww

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/photos/wan

nesdeprez/4663

71180/

http://www.u.arizona.edu/~shunter/pinero.jpg

Origami Architecture : deployable

Daniel MacGibbon (2008)

http://designstudio5.blogspot.com/

http://www.archnet.org/library/sites/one-site.jsp?site_id=851

Origami Architecture : transformable

L’institut du Monde Arabe, ParisJean Nouvel (1987)

Origami Architecture : transformable

Chuck Hoberman

Hoberman Arch (2002)Salt Lake City, USA

Iris Dome, 2000Worlds Fair, Hannover, Germany

Adaptable Sunshade, 2006Building Center Trust, London, UK

Origami Architecture : transformable

http://ww

w.hob

erm

an.com

http://www.adaptivebuildings.com

Chuck Hoberman

Origami Architecture : transformable

Kiefer Technic Bad GleichenbergGiselbrecht + Partner ZT GmbH (2007)

http://hyposurface.org/

Hyposurface (concept)Hyposurface Corp (2000)

Origami Architecture : transformable

Robotic Membrane (concept); OrangeVoid

http://www.orangevoid.org.uk

Origami Architecture : transformable

Origami Architecture : transformable

“Responsive Kinematics”, John Hobart-Culleton

Origami : Summary

Summary

Origami Artrecent developments due to computational tools and improved understanding of its mathematics

Origami Mathematics– active field of mathematics– be aware of some of the concepts

• foldability (flat & rigid)

• surface geometry (Gaussian curvature)

Summary

Origami Engineeringused for a variety of applications, mainly for the design of deployable structures

Origami Architecture– folded plate structures

• visual appeal / strength / deployability / materiality

– kinematic architecture• very much under-explored; plenty of challenges

Origami : Workshop

Workshop

Origami Engineering– 3 different assignments (limited copies of each)– groups of ~5 people

– explore aspects of• inflatable foldable cylinders• curved folding• …