Tangential differential calculus and the finite element modeling of a large deformation elastic membrane shell problem

TL;DR

This paper introduces a finite element method for large deformation elastic membrane shells using tangential differential calculus, simplifying geometric complexity and enabling applications to form finding problems.

Contribution

It presents a novel finite element approach based on tangential differential calculus that avoids classical differential geometry for membrane shell modeling.

Findings

Effective modeling of large deformation membranes

Application to form finding problems demonstrated

Simplified geometric approach without classical differential geometry

Abstract

We develop a finite element method for a large deformation membrane elasticity problem on meshed surfaces using a tangential differential calculus approach that avoids the use of classical differential geometric methods. The method is also applied to form finding problems.