Robust layerwise C-0 finite element approach based on a variable separation method for the modeling of composite and sandwich plates

摘要

This paper deals with a new approach using both the variable separation and a robust C-0 eight-node finite element for the modeling of composite plates. The displacement field is approximated as a sum of separated functions of the in-plane coordinates x, y and the transverse coordinate z. This choice yields to an iterative process that consists of solving a 2D and 1D problem successively at each iteration. In the thickness direction, a fourth-order expansion in each layer is considered. For the in-plane description, the main novelty consists in the formulation of a field compatible approximation for the transverse shear strain field, referred to as the CL8 interpolation. This latter has to be adapted to the particular framework of the separated representation. It allows us to eliminate the shear locking pathology by constraining only the z-constant transverse shear strain terms. Numerical assessments show the absence of locking problems as well as the enhanced robustness with respect to distorted element shapes in comparison to classical isoparametric approaches. This new CL8 plate element provides excellent convergence rates under different boundary and loading conditions, and it yields accurate displacements and stresses for both thick and thin composite and sandwich plates.