Analytical Solutions for the Thermo-Elastic Analysis of FGM Plates Using Higher Order Refined Theories

Abstract

Analytical formulations and solutions are presented for the thermo-elastic analysis of Functionally Graded Material (FGM) plates based on a set of higher order refined shear deformation theories. The displacement components in these computational models are based on Taylor’s series expansions, which incorporates parabolic variation of transverse strains across the plate thickness. The displacement model with twelve degrees of freedom considers the effects of both transverse shear and normal strain/stress while the other model with nine degrees of freedom includes only the effect of transverse shear deformation. Besides these, a higher order model and a first order model with five degrees of freedom that are developed by other investigators and are reported in the literature are also used in the present investigation for evaluation purposes. A simply supported FGM plate subjected to thermal load is considered throughout as a test problem. The material properties are mathematically modeled based on power law function. The temperature is assumed to vary nonlinearly and obey one-dimensional steady state heat conduction equation throughout the plate thickness while in-plane is sinusoidal. Along with this constant and linearly varying temperatures are also considered in the study. The equations of equilibrium are derived using the Principle of Minimum Potential Energy (PMPE) and closed form solutions are obtained using Navier’s solution technique. Firstly, numerical results obtained using various displacement models are compared with the three-dimensional elasticity solutions available in the literature inorder to establish the accuracy of higher order models considered in the study. After establishing the accuracy of the solution method benchmark results and comparison of solutions are presented for Monel/Zirconia, Titanium-Alloy/Zirconia and Aluminium/Alumina FGM plate by varying edge ratio, slenderness ratio and power law parameter. Numerical and graphical results are presented for in-plane, transverse displacements and stresses for all the models by considering different temperature profiles.