Some more testing with wrapping cones.
2009-03-05
Wrapping cones
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This is what the unrolled strip should look like. The yellow lines represent a fixed change of direction.
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Purpose of this page
When you bend a thin strip of an elastic material you get a beautifully shaped curve. What geometry does this curve follow? Please help unravel this mystery by commenting these posts!
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Type of bending
I'm looking at the type of bending that is elastic (not plastic), meaning the material will spring back to its original shape when the force is released. Most materials break or deform permanently before they can reach an 'elastic and beautiful curve', but I think all 'elastic deformation' follow the same principals and therefore the same geometry.
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Hello Marten, A curve that might behave the way you explore with strips of paper, rubber, or metal could be what is sometimes called a plank line (GC.BSplineCurve.PlankLine). The idea of a plank line is that it bends in one direction, twists in the second direction, and is stiff in the third, like a thin but relatively broad board of wood. Julius Natterer did structures like that (http://ibois.epfl.ch/page12022.html; I believe also the Polydome at the Ecole Polytechnique Federale Lausanne) and Judit Leuppi did some research about plank lines published as a paper at the ACADIA 2000 Conference (Plank Lines of Ribbed Timber Shell Structures; available from http://cumincad.scix.net/data/works/att/f197.content.pdf). Another example of such a gridshell seems to be at the Weald and Down Open Air Museum in Singleton, Sussex (images at http://www.flickr.com/search/?w=all&q=downland+gridshell&m=text).
ReplyDeleteRegards,
Volker Mueller