Origami Architecture

Transcription

Origami in Engineering and Architecture
An art spanning Mathematics, Engineering and Architecture
Dr Mark Schenk (ms652)
October 25th 2012
Advanced
Structures Group
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
http://www.flickr.com/photos/jasohill/118616905/sizes/m/in/photostream/
Photo courtesy of Andreas Bauer
From simple…
Origami Art
… to advanced
Designed and folded by Robert J. Lang
Origami Art
http://www.flickr.com/photos/origamijoel/3226036918/
Joel Cooper (2008)
Origami Art : tessellations
http://www.flickr.com/photos/87477835@N00/5038642136/
‘Star Tessellation’ by Eric Gjerde
http://www.flickr.com/photos/origomi/290031886/
http://www.flickr.com/photos/9874847@N03/
http://www.flickr.com/photos/polyscene/2200937797/
http://www.flickr.com/photos/cambridgeuniversity-engineering/4706414628/
Origami Art : 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.html
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
surface geometry (aka, differential Geometry)
Atlas: zero Gaussian curvature
What kind of folded shapes can we attain?
- assume no stretching deformations (i.e. developable)
?
Sphere: positive Gaussian curvature
Atlas: zero Gaussian curvature
Sphere: positive Gaussian curvature
developable surface (i.e. a sheet of paper)
Gaussian curvature is invariant under bending
Kilian 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
2μm mylar membrane
Inflatable booms
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 stowage
Wang and Johnson (2003); NASA LaRC
ILC Dover (ITSAT)
Guest and Pellegrino (1994)
origami booms (1/3)
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
bla
im st
pa
ct
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
Lang (2003)
i) deployable structures
– space telescope
– solar panels
Miura and Natori (1989)
– solar sails
Guest (1992)
Leipold et al. (2002)
JAXA IKAROS (2010)
– emergency shelters
– medical stent
– bio-mechanics
Kuribayashi et al. (2006)
de Temmerman (2007)
Kobayashi (1999)
most common fold pattern: Miura-ori
– flat-foldable
– rigid-foldable
generalized Miura-ori: rigid-foldable and flat-foldable
http://www.tsg.ne.jp/TT/software/
Tachi (2009–2011)
rigid-foldable hyperbola
Tachi (2010)
– programmable matter
Hawkes et al. (2010)
Engineering Origami : stiffness
– architecture : folded plates
Engineering Origami : stiffness
– folded plates
Engel (1968)
Origami Engineering : stiffness
– sandwich panel cores
Miura (1972)
Heimbs (2007)
Rapp (1960)
Engineering Origami : impact resistance
iii) impact resistance
– sandwich panel cores
Tessellated Group (2010)
Elsayed and Basily (2004)
Engineering Origami : impact resistance
Miura (1969)
– car crash boxes
Wu (2010)
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
Norman (2009)
Seffen (2012)
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:
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)
Engel (1968)
Engel (1968)
Skidmore, Owings and Merill (1956)
US Air Force Academy Cadet Chapel, Colorado Springs
Miura (1969)
Coppa (1970)
Tonon (1993)
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
(1960-1963)
http://www.ronresch.com
"Made with Paper Show" Nov. 1967
Origami Architecture : foldable dome
http://www.flickr.com/photos/elelvis/
http://flickr.com/photos/72567727@N00/page2/
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://flux.net/take-your-time-olafur-eliasson-new-york
http://www.designboom.com/weblog/cat/10/view/1647/take-your-time-olafur-eliasson.html
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://www.flickr.com/photos/wannesdeprez/466371180/
http://www.u.arizona.edu/~shunter/pinero.jpg
Daniel MacGibbon (2008)
http://designstudio5.blogspot.com/
Origami Architecture : transformable
L’institut du Monde Arabe, Paris
Jean Nouvel (1987)
http://www.archnet.org/library/sites/one-site.jsp?site_id=851
Hoberman Arch (2002)
Salt Lake City, USA
Chuck Hoberman
http://www.adaptivebuildings.com
Chuck Hoberman
Iris Dome, 2000
Worlds Fair, Hannover, Germany
http://www.hoberman.com
Adaptable Sunshade, 2006
Building Center Trust, London, UK
Kiefer Technic Bad Gleichenberg
Giselbrecht + Partner ZT GmbH (2007)
Hyposurface (concept)
Hyposurface Corp (2000)
http://hyposurface.org/
Robotic Membrane (concept); OrangeVoid
http://www.orangevoid.org.uk
“Responsive Kinematics”, John Hobart-Culleton
Origami : Summary
Summary
Origami Art
recent 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 Engineering
used 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
• …

Origami Architecture

Transcription

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