Moving frames applied to shell elasticity

TL;DR

This paper applies exterior calculus and moving frames to model the elasticity of curved shells, deriving kinematics from Lie derivatives and dynamics from stress-forms, offering a geometric approach to shell elasticity.

Contribution

It introduces a novel geometric framework using exterior calculus and moving frames for analyzing shell elasticity, linking kinematics and dynamics through differential forms.

Findings

Provides a new geometric formulation for shell elasticity

Derives shell kinematics from Lie derivatives of forms

Models shell dynamics using stress-forms

Abstract

Exterior calculus and moving frames are used to describe curved elastic shells. The kinematics follow from the Lie-derivative on forms whereas the dynamics via stress-forms.