A refined multilayered finite-element model applied to linear and non-linear analysis of sandwich plates

Abstract

This paper presents a computationally efficient and mechanically accurate finite-element formulation for linear and non-linear analysis of flat sandwich panels. Computational efficiency is guaranteed by preserving C 0-continuity as in the Reissner–Mindlin model. Mechanical accuracy is acquired by allowing a zig-zag in-plane displacement field in the thickness direction and by fulfilling interlaminar equilibrium at the interface between the core and skins for the transverse shear stress components. The resulting mixed model is reduced to the standard displacement formulation by writing a weak form of Hooke’s Law. The model is denoted by the acronym RMZC, Reissner–Mindlin, zig-zag, interlaminar continuity. The principle of virtual displacement is employed to write finite element equations governing the linear and non-linear static response, free vibration, buckling and postbuckling behaviour. Non-linear equations are solved iteratively by Newton–Raphson linearization accounting arc-length type strategies. The numerical investigation assesses the proposed model by comparing it to classical lamination theory (CLT), First-order shear deformation theory (FSDT) and other available results. The efficiency and accuracy of the RMZC model is then demonstrated by solving several problems dealing with linear and non-linear bending, natural frequencies, in-plane buckling and postbuckling. Appendices quote details of the most interesting points of the models presented.