Cut finite element modeling of linear membranes

TL;DR

This paper develops a cut finite element method for simulating membrane elasticity problems on embedded meshes, incorporating membrane-3D elasticity coupling using tangential calculus and Galerkin discretization.

Contribution

It introduces a novel cut finite element approach for membranes, including coupling with 3D elasticity, using surface restriction of 3D basis functions.

Findings

Effective discretization of membrane problems on embedded meshes

Coupling membranes with 3D elasticity enhances model accuracy

Method applicable to free and coupled membrane scenarios

Abstract

We construct a cut finite element method for the membrane elasticity problem on an embedded mesh using tangential differential calculus. Both free membranes and membranes coupled to 3D elasticity are considered. The discretization comes from a Galerkin method using the restriction of 3D basis funtions (linear or trilinear) to the surface representing the membrane. In the case of coupling to 3D elasticity, we view the membrane as giving additional stiffness contributions to the standard stiffness matrix resulting from the discretization of the three-dimensional continuum.