Linear Strain Tensors on Hyperbolic Surfaces and Asymptotic Theories for Thin Shells

TL;DR

This paper analyzes the solvability of linear strain equations on hyperbolic surfaces, showing that infinitesimal isometries can be extended to high order, with implications for the elasticity of thin shells.

Contribution

It establishes the high-order matching of infinitesimal isometries on hyperbolic surfaces, advancing the understanding of their elasticity behavior.

Findings

Any first order infinitesimal isometry can be extended to arbitrarily high order.

Results apply to smooth noncharacteristic regions on hyperbolic surfaces.

Implications for the elasticity theory of thin hyperbolic shells.

Abstract

We perform a detailed analysis of the solvability of linear strain equations on hyperbolic surfaces. We prove that if the surface is a smooth noncharacteristic region, any first order infinitesimal isometry can be matched to an infinitesimal isometry of an arbitrarily high order. The implications of this result for the elasticity of thin hyperbolic shells are discussed.