An accurate two-dimensional theory for deformation and stress analyses of functionally graded thick plates

Abstract

A displacement-based, higher order shear and normal deformations theory (HOSNT) is used to analyse the thick functionally graded (FG) plates in which mechanical properties are changing smoothly with the plate’s thickness coordinate. A more realistic parabolic distribution of transverse shear strains through thickness of plate is ensured in the presented formulation. The influence of transverse normal strain on bending responses of FG plates is examined in this study. Functionally graded materials (FGMs), although heterogeneous, are idealized as continua with their mechanical properties changing smoothly with respect to spatial coordinates. The material properties of FG plates are assumed to be varying through thickness of plate in a continuous manner. Poisson’s ratio of FG plates is assumed to be constant, but their Young’s modulii are considered to vary continuously in thickness direction according to the volume fraction of its constituents which is mathematically modelled as an exponential function. The governing equations of equilibrium for static analysis of FG plates are obtained using principle of minimisation of potential energy (PMPE) employing HOSNT. Navier solution method is used to solve the governing differential equations of equilibrium. It is thought that the presented results would be a reference for other researchers to compare their results.