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

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.