ArchEng2012 Lecture Web

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

w.flickr.com

/photos/874778

35@N

00/503

86421

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Origami Art : tessellationshttp://w

ww

.flickr.com/p

hotos/o

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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


• rigid foldability – counter example

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

Balkcom (2004)


a rigid-foldable shopping bag:

Wu and You (2011)

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


the ‘unfoldable’ hyperbolic paraboloid

Demaine et al. (2009)


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)

?


Sphere: positive Gaussian curvature

Atlas: zero Gaussian curvature


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)


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


Inflatable Booms• Inflatable Antenna Experiment (IAE, 1996)

L'Garde & NASA JPL (1996)


So, how do you fold an inflatable boom?


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


origami booms (1/3)

Guest and Pellegrino (1994)

Barker and Guest (2004) Hoberman (1993)


origami booms (2/3)

EADS Astrium

Senda et al (2006)


origami booms (3/3)

- stowed volume (flat-foldable)

- material deformation (rigid-foldable)

- straightness of deployment

Schenk, Viquerat, Seffen and Guest (2012)


conical telescopic booms (1/2)

- concentric folds

- telescopic deployment

Palisoc (2004)

L'Garde, ISPSS (2005)


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)


Basic component: Miura-ori sheet

a) Folded Shell Structure

b) Folded Cellular Meta-Material


a) meta-material : Folded Shell Structures


novel property :

• doubly-curved surface


novel property :

• negative in-plane Poisson’s ratio


novel property :

• positive out-of-plane Poisson’s ratio


application : morphing structures

- change shape

- maintain continuous surface

Example: morphing wings


b) Folded Cellular Meta-Material

- stacking of folded layers

- maintains folding motion


novel properties:

- omni-directional negative Poisson's ratio

- highly anisotropic material properties


Folded Sandwich Panel Core

- blast impact mitigation

blastimpact

Schenk, Guest, McShane (2012)


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


i) deployable structures– space telescope – solar panels

Miura and Natori (1989)

Lang (2003)


i) deployable structures– solar sails

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

Guest (1992)


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

de Temmerman (2007)

Kuribayashi et al. (2006)

Kobayashi (1999)


most common fold pattern: Miura-ori

– flat-foldable– rigid-foldable


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

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


rigid-foldable hyperbola

Tac

hi (

2010

)


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)


Engel (1968)


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


Tonon (1993)

Coppa (1970)

Miura (1969)


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

m/photos/7256

7727@N

00

/pa

ge2/

http://w

ww

.flickr.com/photos/elelvis/


Foreign Office Architects (2002)Yokohama International Cruise Terminal

http://www.richardsweeney.co.uk


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)


computer design tools

case study:temporary chapel of St. Loup

Buri et al. (2009)


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)


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


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

accordeon reCover shelter

Boler and Tandon (1967)


Tachi (2009)


Emilio Pérez Piñero (1935-1972)

http://ww

w.flickr.com

/photos/wan

nesdeprez/4663

71180/

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


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)


Chuck Hoberman

Hoberman Arch (2002)Salt Lake City, USA

Iris Dome, 2000Worlds Fair, Hannover, Germany

Adaptable Sunshade, 2006Building Center Trust, London, UK


http://ww

w.hob

erm

an.com

http://www.adaptivebuildings.com

Chuck Hoberman


Kiefer Technic Bad GleichenbergGiselbrecht + Partner ZT GmbH (2007)

http://hyposurface.org/

Hyposurface (concept)Hyposurface Corp (2000)


Robotic Membrane (concept); OrangeVoid

http://www.orangevoid.org.uk



“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• …

ArchEng2012 Lecture Web

Documents

Transcript of ArchEng2012 Lecture Web