Origami for Engineers: Folded Shell Structures – Mark Schenk – Graduate Research Forum (GRF) Clare College, Cambridge 9th December 2008

Presentation Outline Introduction Folded Shell Structures textured sheets Folded Shell Structures origami tessellations deformation of folded sheets applications

Shell Structures – Counterexamples Forth Rail Bridge (1964) Forth Road Bridge (1964)

Example Shell Structures - Architecture Eero Saarinen (1962) Milo Ketchum (1910-1999) Norman Foster (1997)

Example Shell Structures - Engineering Verner Panton (1969) http://flickr.com/photos/okenezak/317648353/sizes/l/

Shell Structures shell structures widespread use thickness is small relative to other dimensions carry loads (in-plane and bending) geometry is extremely important widespread use architecture piping, pressure vessels, etc. aircraft fuselages, car bodies, etc.

Textured Shell Structures Adding a local texture to thin-walled sheets in order to change their global mechanical properties. The local texture is of an intermediate scale, between the global structural dimensions and material level.

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

Novel Textured Shell Structures bistable corrugated sheets (Norman et al., 2006) combination of prestress and geometry

Novel Textured Shell Structures dimpled sheets (Seffen, 2007) pre-stressed bistable dimples global shape depends on local up/down pattern

Novel Textured Shell Structures bistable textured sheets (Golabchi et al., 2008) doubly-periodic corrugations prestress through plastic deformation

Folded Shell Structures

Folded Shell Structures Introducing a local texture to thin-walled sheets by means of a fold pattern. In other words: origami folding

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

Origami Tesselations http://www.flickr.com/photos/origomi/290031886/ http://www.flickr.com/photos/brdparker/ http://www.flickr.com/photos/infinite-origami/

Origami Tesselations http://www.flickr.com/photos/9874847@N03/ http://www.flickr.com/photos/polyscene/2200937797/

Analysis of Folded Textured Sheets Miura sheet Eggbox sheet

Deformation of Folded Textured Sheets

Deformation of Folded Textured Sheets mid-surface plane of the sheet can assume a global saddle shape; folds allow local expansion/contraction

Miura sheet – planar deformation It expands in all directions under a uni-axial strain: negative Poisson’s ratio!

Miura Sheet – out-of-plane deformation Saddle-shaped deformation corresponds to materials with a positive Poisson’s ratio.

Eggbox sheet – planar deformation It contracts transversely to a uni-axial strain: positive Poisson’s ratio

Eggbox Sheet – out-of-plane deformation Spherical shaped deformation corresponds to materials with a negative Poisson’s ratio.

Resch ‘waterbomb’ sheet Resch sheet

Resch ‘waterbomb’ sheet Strong bending-extension coupling

Resch ‘waterbomb’ sheet regular iso-area

Properties of Folded Textured Sheets provide extra flexibility have intriguing mechanical properties, e.g. opposite sign for Poisson’s ratio under bending and extension (Miura & eggbox) strongly coupled bending and extension (Resch) These sheets have not previously been studied!

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

Applications of Folded Textured Sheets Architecture inspiration for design adaptable facades

So now what? My PhD research on Folded Textured Sheets understand their mechanical behaviour, find efficient ways to model them, develop manufacturing methods

Questions? Q & A