Stress analysis of functionally graded plates subjected to thermal and mechanical loadings

A two-dimensional (2D) higher-order deformation theory is presented for the evaluation of displacements and stresses in functionally graded (FG) plates subjected to thermal and mechanical loadings. The modulus of elasticity of plates is assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. By using the method of power series expansion of continuous displacement components, a set of fundamental governing equations which can take into account the effects of both transverse shear and normal stresses is derived through the principle of virtual work. Several sets of truncated Mth order approximate theories are applied to solve the static boundary value problems of a simply supported FG plate. In order to assure the accuracy of the present theory, convergence properties of the displacements and stress components are examined in detail. A comparison of the present results of isotropic plates is also made with previously published results. The transverse stresses have been obtained by integrating the three-dimensional (3D) equations of equilibrium in the thickness direction starting from the top or bottom surface of a plate. The distributions of transverse shear and normal stresses in the thickness direction are obtained accurately by satisfying the surface boundary conditions of a plate. The present numerical results are also verified by satisfying the energy balance of external and internal works are considered to be sufficient with respect to the accuracy of solutions. It is noticed that the present 2D higher-order approximate theories can predict accurately the stresses and displacements of simply supported FG plates subjected to thermal and mechanical loadings.