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

TL;DR

This paper analyzes infinitesimal isometries on developable surfaces and explores their implications for the elasticity of thin shells, establishing high-order matching of infinitesimal isometries under regularity conditions.

Contribution

It proves that first order infinitesimal isometries on developable surfaces can be extended to higher orders if the surface is sufficiently regular.

Findings

First order infinitesimal isometries can be matched to higher order ones.

Results have implications for the elasticity theory of thin developable shells.

Provides a mathematical foundation for understanding deformations of developable surfaces.

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.