Coupling effects in elastic analysis of FGM composite plates by mesh-free methods

In this paper we shall investigate the static response of thin and/or thick elastic functionally graded (FG) plates. The spatial variation of material coefficients in the FG composite structures is determined by distribution of volume fractions of particular constituents. The attention is devoted to derivation of the special formulation of governing equations in FGM plates, which includes the Kirchhoff–Love theory (KLT) as well as the 1st and 3rd order shear deformation plate theory (SDPT). The power-law gradations across the plate thickness and along in-plane coordinates yield two different problems. To facilitate the numerical solution of rather complex governing equations, we propose the strong formulation combined with Moving Least Square (MLS) approximation for field variables. Several numerical examples are presented to investigate the accuracy, convergence of accuracy and computational efficiency of studied mesh-free formulation for boundary value problems with existing benchmark solutions. The coupling effects are studied via the response of FGM square plate to static loading within the KLT as well as the 1st and 3rd order SDPT.