The RMVT- and PVD-based finite layer methods for the three-dimensional analysis of multilayered composite and FGM plates

The Reissner mixed variational theorem (RMVT)- and principle of virtual displacements (PVD)-based finite layer methods (FLMs) are developed for the three-dimensional (3D) analysis of simply-supported, multilayered composite and functionally graded material (FGM) plates subjected to mechanical loads. The material properties of the FGM layers are assumed to obey either an exponent-law exponentially varied with the thickness coordinate or the power-law distributions of the volume fractions of the constituents. In these formulations, the plate is divided into a number of finite layers, where the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the field variables of each individual layer, respectively. Because an h-refinement instead of a p-refinement process is adopted to yield the convergent solutions in this analysis, the layerwise either linear or parabolic function distribution through the thickness coordinate is assumed for the related field variables. The unified formulations of these two kinds of FLMs with freely-chosen orders for the in- and out-of-plane field variables are presented. The accuracy and convergence rate of a variety of RMVT- and PVD-based FLMs developed in this paper are assessed by comparing their solutions with the exact 3D solutions available in the literature.