Nonlinear thermoelastic analysis of FGM thick plates

In this paper, a new application of a four variable refined plate theory to analyze the nonlinear bending of functionally graded plates exposed to thermo-mechanical loadings, is presented. This recent theory is based on the assumption that the transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces, and similarly, the shear components do not contribute toward bending moments. The derived transverse shear strains has a quadratic variation across the thickness that satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The material properties are assumed to vary continuously through the thickness of the plate according to a power-law distribution of the volume fraction of the constituents. The solutions are achieved by minimizing the total potential energy. The non-linear strain–displacement relations in the von Karman sense are used to derive the effect of geometric nonlinearity. It is concluded that the proposed theory is accurate and simple in solving the nonlinear bending behavior of functionally graded plates.