compliant shells

In differential geometry, rigidity theory investigates whether a surface can deform by pure bending without stretching. The central problem is to find or disprove the existence of isometric deformations.

Classical examples in the "discrete" category include:

• The finite rigidity of convex polyhedra by Cauchy
• The infinitesimal rigidity of convex polyhedra by Dehn
• The existence of flexible (non-convex) polyhedra by Connelly

In the "smooth" category, we have: