Large deflection geometrically nonlinear analysis of functionally graded multilayer graphene platelet-reinforced polymer composite rectangular plates

Abstract

A large deflection geometrically nonlinear analysis of functionally graded (FG) multilayer graphene platelet-reinforced polymer composite (GPL-RPC) rectangular plates subjected to uniform and sinusoidal transverse mechanical loadings is performed in this article. Based on the sinusoidal shear deformation plate theory and von Kármán nonlinear strain-displacement relations, the nonlinear governing equilibrium equations and boundary conditions are developed by using the principle of virtual work. It is assumed that the weight fraction of GPL nanofillers layer-wisely changes across the thickness of plate. The effective Young’s modulus of FG-GPL-RPCs is approximately calculated via the modified Halpin-Tsai model. Also, the effective Poisson’s ratio and mass density are determined by employing the rule of mixture. The investigation is performed by using a numerical solution approach. To evaluate the nonlinear bending stiffness of FG multilayer GPL-RPC plate, the discretization of governing equations and boundary conditions is carried out using the generalized differential quadrature (GDQ) method, and the pseudo arc-length continuation technique is employed to solve the set of nonlinear algebraic discretized equations to obtain the load-deflection curve. Numerical problems are given to reveal the influences of GPL distribution pattern, weight fraction, geometry of GPL nanofillers, length-to-thickness and edge conditions on nonlinear bending responses of the GPL-RPC plates.