Symmetries in the linear theory of the deformation of thin shells

TL;DR

This paper reveals that symmetries from integrable systems naturally occur in the classical linear theory of thin shell deformations, indicating the existence of numerous shear-free, twist-free deformation modes when the shell's middle surface is integrable.

Contribution

It demonstrates the emergence of integrable system symmetries in shell deformation theory, linking classical shell mechanics with integrable systems theory.

Findings

Infinitely many shear-free, twist-free deformations exist for integrable middle surfaces.

Symmetries from integrable systems are present in classical shell deformation theory.

The result bridges shell mechanics and integrable systems theory.

Abstract

In this paper, we show that symmetries, which are known in the theory of integrable systems, naturally appeared in the classical linear theory of deformations of thin shells. Our result shows that if the middle surface of a shell becomes `integrable', infinitely many deformations exist that have no shear strains and twisting of the coordinate lines.