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

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

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

4. Example Shell Structures - Architecture
Eero Saarinen (1962)
Milo Ketchum ( )
Norman Foster (1997)

5. Example Shell Structures - Engineering
Verner Panton (1969)

6. 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.

7. 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.

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

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

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

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

12. Folded Shell Structures

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

14. Origami (as you may know it)
Photo courtesy of Andreas Bauer
Designed and folded by Robert J. Lang

15. Origami Tesselations http://www.flickr.com/photos/origomi/290031886/

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

17. Analysis of Folded Textured Sheets
Miura sheet
Eggbox sheet

18. Deformation of Folded Textured Sheets

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

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

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

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

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

24. Resch ‘waterbomb’ sheet
Resch sheet

25. Resch ‘waterbomb’ sheet
Strong bending-extension coupling

26. Resch ‘waterbomb’ sheet
regular
iso-area

27. 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!

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

29. Applications of Folded Textured Sheets
Architecture
inspiration for design
adaptable facades

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

31. Questions?
Q & A