Thermal response of functionally graded sandwich plates using a semi-analytical approach

This paper presents a semi-analytical method for analysing the through-thickness stress and displacement distributions in simply supported functionally graded (FG) sandwich plates under thermal loading. The formulation is based on theory of elasticity equations leading to ordinary differential equations (ODEs) with a two-point boundary value problem approach. In this method ad-hoc assumptions are not made on displacements and stresses. The material properties (modulus of elasticity, coefficient of thermal expansion and thermal conductivity) vary according to a power law in the thickness direction, while the Poisson's ratio is kept constant throughout the depth of the plate. The plate is subjected to a temperature gradient across its thickness using Fourier heat conduction law, and the thermal response of the FG sandwich plate is evaluated in terms of stresses and displacements. Semi-analytical formulation in this study is validated for pure FGM plate under thermal load and results are compared with those of higher order theory to establish the efficacy and efficiency of the presented method. The study provides a comprehensive behaviour of FG sandwich plates under thermal loading, highlighting the importance of accurate modelling and analysis. The results presented in this theory can be served as benchmark solutions in absence of exact solutions.