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Is there any optimal way for a membrane conformal with a given surface

wangyouhua10's picture

Good day, all!

Currently, I'm interested in the conformability of a membrane with a given surface.

Considering an arbitrarily stretchable but not compressible membrane, whose thickness can be neglected and another two dimensions are enough large, and a given non-developable surface that can't be deformable, namely, stiff, is there any optimal method to let the membrane conformal with the given surface so that the max principle strain of the deformed membrane is minimum? What relation between the strain or stress of the membrane and the geometrical properties of the given surface is? Here we can ignore the adhesive energy between the interface. 

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