A high‐order enrichment strategy for the finite cell method

Abstract

Thanks to the application of the immersed boundary approach in the finite cell method, the mesh can be defined independently from the geometry. Although this leads to a significant simplification of the mesh generation, it might cause difficulties in the solution. One of the possible difficulties will occur if the exact solution of the underlying problem exhibits a kink inside an element, for instance at material interfaces. In such a case, the solution turns out less smooth -and the convergence rate is deteriorated if no further measures are taken into account. In this paper, we explore a remedy by considering the partition of unity method. The proposed approach allows to define enrichment functions with the help of a high-order implicit representation of the material interface.

The hierarchical finite cell method for nonlinear problems: Moment fitting quadratures, basis function removel, and remeshing

“…Since its introduction, the FCM has been successfully applied in various fields, e.g. applications to elastic and plastic problems in small and large strain [19,20,[23][24][25][26][27][28][29][30][31][32][33], homogenization of heterogeneous and cellular materials as well as foams [34][35][36][37][38][39][40], topology optimization [41,42], problems including material interfaces [43][44][45][46][47], contact problems [40,[48][49][50][51][52][53][54], multi-physic problems [55][56][57][58][59][60][61][62], fracture simulation [63,64], or simulation of wave propagation [65][66][67]…”