Finite Element Analysis Over Tangled Meshes
Josh Danczyk, Krishnan Suresh · 2012
In finite element analysis (FEA), tasks such as mesh optimization and mesh morphing can lead to overlapping elements, i.e., to a tangled mesh. Such meshes are considered ‘unacceptable’ today, and are therefore untangled using specialized procedures. Here it is shown that FEA can be easily extended to handle tangled meshes. Specifically, by defining the nodal functional space as an oriented linear combination of the element shape functions, it is shown that the classic Galerkin formulation leads to a valid finite element formulation over such meshes. Patch tests and numerical examples illustrate the correctness of the proposed methodology.