New asymptotically sharp Korn and Korn-like inequalities in thin domains

TL;DR

This paper establishes new asymptotically sharp Korn and Korn-like inequalities in thin curved domains with variable thickness, aiding the analysis of buckling in compressed shells and critical load calculations.

Contribution

It introduces novel Korn inequalities tailored for thin, curved domains with non-uniform thickness, advancing elasticity theory and buckling analysis.

Findings

Derived asymptotically sharp Korn inequalities for thin curved domains.

Applicable to buckling analysis of shells with variable thickness.

Provides tools for more accurate critical load estimations.

Abstract

It is well known that Korn inequality plays a central role in the theory of linear elasticity. In the present work we prove new asymptotically sharp Korn and Korn-like inequalities in thin curved domains with a non-constant thickness. This new results will be useful when studying the buckling of compressed shells, in particular when calculating the critical buckling load.