Remeshing in the finite cell method for different types of geometry descriptions

Abstract

The numerical structural analysis of problems with complex geometries can be challenging, especially if standard finite elements are used. In contrast, immersed methods, such as the finite cell method, relieve the mesh generation such that simply shaped elements/cells can be used. Then, the domain boundary is considered during the numerical integration. In finite strain analysis, the elements/cells face large distortions, especially the cells that are intersected by the boundary. When the solution fails, remeshing can be applied to continue the simulation. This process is currently limited to geometries described by a triangulated surface. Therefore, the present work shows an alternative way of describing the deformed geometry by interpolating the displacement field. In this work, the inverse distance approach, and radial basis functions (RBF) with and without a constant extension are applied. It turns out that RBF with constant extension leads to the most robust results compared to the other methods. Moreover, different geometry description types are tested, and the present approach leads to promising results.