Intrinsic finite element modeling of a linear membrane shell problem

TL;DR

This paper develops an intrinsic finite element method for membrane elasticity problems on surfaces, extending 2D elements into 3D to improve modeling accuracy for thin shell structures.

Contribution

It introduces a novel intrinsic finite element approach for membrane shells based on boundary differential equations, enhancing existing methods.

Findings

Effective modeling of membrane elasticity on meshed surfaces

Extension of 2D elements into three dimensions for thin shells

Improved accuracy over traditional methods

Abstract

A Galerkin finite element method for the membrane elasticity problem on a meshed surface is constructed by using two-dimensional elements extended into three dimensions. The membrane finite element model is established using the intrinsic approach suggested by [Delfour and Zol\'esio, A boundary differential equation for thin shells. J. Differential Equations, 119(2):426--449, 1995].