Infinitesimal Rigidity of Strain Tensors for Shells with Mixed Type and its Applications

TL;DR

This paper establishes an infinitesimal rigidity lemma for strain tensors on surfaces with changing curvature signs and applies it to determine the optimal Korn inequality constant for mixed-type shells.

Contribution

It introduces a new rigidity lemma for shells with mixed curvature and derives the optimal Korn inequality scaling law for such structures.

Findings

Rigidity lemma for surfaces with sign-changing curvature

Optimal Korn inequality constant scales as h^{4/3} for mixed-type shells

Application to shell stability analysis

Abstract

We derive an infinitesimal rigidity lemma for the strain tensor of surfaces with their curvatures changing sign. As an application, we obtain the optimal constant in the first Korn inequality scales like $h^{4/3}$ for such shells of mixed type.