Three-dimensional static analysis of thick functionally graded plates by using meshless local Petrov–Galerkin (MLPG) method

Abstract

In this paper, a version of meshless local Petrov–Galerkin (MLPG) method is developed to obtain three-dimensional (3D) static solutions for thick functionally graded (FG) plates. The Young's modulus is considered to be graded through the thickness of plates by an exponential function while the Poisson's ratio is assumed to be constant. The local symmetric weak formulation is derived using the 3D equilibrium equations of elasticity. Moreover, the field variables are approximated using the 3D moving least squares (MLS) approximation. Brick-shaped domains are considered as the local sub-domains and support domains. In this way, the integrations in the weak form and approximation of the solution variables are done more easily and accurately. The proposed approach to construct the shape and the test functions make it possible to introduce more nodes in the direction of material variation. Consequently, more precise solutions can be obtained easily and efficiently. Several numerical examples containing the stress and deformation analysis of thick FG plates with various boundary conditions under different loading conditions are presented. The obtained results have been compared with the available analytical and numerical solutions in the literature and an excellent consensus is seen.