Cut finite element modeling of linear membranes
This work provides a numerical method for simulating thin membranes embedded in 3D continua, which is relevant for computational mechanics applications.
The paper develops a cut finite element method for linear membrane elasticity on embedded meshes, using tangential differential calculus. It handles both free membranes and membranes coupled to 3D elasticity, with the membrane adding stiffness to the 3D stiffness matrix.
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.