Fourier mode analysis of layers in shallow shell deformations

Abstract

We investigate here the length scales of the boundary or interior layer effects in shell deformation. Quantitative information on the layers is obtained by considering two (simplified) “shallow” shell models corresponding to the “classical” three-field Love–Novozhilov–Koiter (LNK), respectively five-field Reissner–Naghdi (RN) shell models. We start by analysing the layers as functions of the thickness of the shell, while keeping the other geometric parameters fixed. Having found the four limit Fourier modes we complete the analysis investigating systematically the layers length scales under more general assumptions, particularly when also the wave parameter is variable. Scaling properly the energy expressions, as indicated by the layer mode analysis, shell deformation energies characteristic to shell layers are found. These show how the layer is effectively seen by the finite element solver and can be useful in the analysis of numerical locking effects in the FEM approximation of shell layers.