Benchmark computations on point-loaded shallow shells: Fourier vs. FEM

In this paper, we study experimentally the performance of the finite element method when approximating the characteristic shell layers that arise from boundaries and load irregularities in a thin shell. For that purpose we introduce a set of model problems where the shell is under a certain periodic and self-balancing point load distribution. We use a simplified shallow shell model with constant coefficients for a thin, linearly elastic shell and apply Fourier techniques to obtain the “exact” displacement and strain fields in different geometries.