Exact solution for thermoelastic deformations of functionally graded thick rectangular plates

An exact solution is obtained for three-dimensional deformations of a simply supported functionally graded rectangular plate subjected to mechanical and thermal loads on its top and/or bottom surfaces. Suitable temperature and displacement functions that identically satisfy boundary conditions at the edges are used to reduce the partial differential equations governing the thermomechanical deformations to a set of coupled ordinary differential equations in the thickness coordinate, which are then solved by employing the power series method. The exact solution is applicable to both thick and thin plates. Results are presented for two-constituent metal-ceramic functionally graded rectangular plates that have a power law through-the-thickness variation of the volume fractions of the constituents. The effective material properties at a point are estimated by either the Mori-Tanaka or the self-consistent schemes. Exact displacements and stresses at several locations for mechanical and thermal loads are used to assess the accuracy of the classical plate theory, the first-order shear deformation theory, and a third-order shear deformation theory for functionally graded plates. Results are also computed for a functionally graded plate with material properties derived by the Mori-Tanaka method, the self-consistent scheme, and a combination of these two methods.