Analysis of laminated composites and sandwich structures by trigonometric, exponential and miscellaneous polynomials and a MITC9 plate element

This paper proposes some advanced plate theories obtained by expanding the unknown displacement variables along the thickness direction using trigonometric series, exponential functions and miscellaneous polynomials. The used refined models are Equivalent Single Layer (ESL) theories. They are obtained by means of the Unified Formulation by Carrera (CUF), and they accurately describe the displacement field and the stress distributions along the thickness of the multilayered plate. The governing equations are derived from the Principle of Virtual Displacement (PVD), and the Finite Element Method (FEM) is employed to solve them. The plate element has nine nodes, and the Mixed Interpolation of Tensorial Components (MITC) method is used to contrast the membrane and shear locking phenomenon. Cross-ply plates with simply-supported edges and subjected to a bi-sinusoidal load, and sandwich plates with simply-supported edges and subjected to a constant transverse uniform pressure are analyzed. Various thickness ratios are considered. The results, obtained with different theories within CUF, are compared with the elasticity solutions given in the literature and the layer-wise solution. It is shown that refined kinematic theories employing trigonometric or exponential terms are able to accurately describe the displacement field and the mechanical stress fields. In some cases, the reduction of computational costs is particularly relevant respect to the layer-wise solution.