Infinitesimal isometries on developable surfaces and asymptotic theories for thin developable shells

Abstract

We perform a detailed analysis of first order Sobolev-regular infinitesimal isometries on developable surfaces without affine regions. We prove that given enough regularity of the surface, any first order infinitesimal isometry can be matched to an infinitesimal isometry of an arbitrarily high order. We discuss the implications of this result for the elasticity of thin developable shells.

References in corpus (1)

• Persistence of a pinch in a pipe

Cited by in corpus (4)

• Gaussian curvature as an identifier of shell rigidity
• Nambu-Goldstone modes and diffuse deformations in elastic shells
• On Asymptotic Rigidity and Continuity Problems in Nonlinear Elasticity on Manifolds and Hypersurfaces
• The buckling load of cylindrical shells under axial compression depends on the cross-section curvature