Novel Semi-Analytical Solutions for the Transient Behaviors of Functionally Graded Material Plates in the Thermal Environment

Abstract

The primary objective of this article is to present a semi-analytical algorithm for the transient behaviors of Functionally Graded Materials plates (FGM plates) considering both the influence of in-plane displacements and the influence of temperature changes. Based on the classical plate theory considering the effect of in-plane displacements, the equilibrium equations of the motion system are derived by Hamilton’s principle. Here, we propose a novel, accurate, and efficient semi-analytical method that incorporates the Fourier series expansion, the Laplace transforms, and its numerical inversion and the Differential Quadrature Method (DQM) to simulate the transient behaviors. This paper validates the proposed method by comparisons with semi-analytical natural frequency results and those from the literature. Expressly, the results of dynamic response also agree well with those generated by the Navier’s method and Finite Element Method (FEM). A convergence study that utilizes the different numbers of sampling points shows that the process can converge quickly, and a few sampling points can achieve high accuracy. The effects of various boundary conditions at the ends, material graded index, and temperature change are further investigated. From the detailed parametric study, it is seen that the peak displacement increases as the edge degrees of freedom, the gradient index of the material, and temperature change increase.