A two variable refined plate theory for the bending analysis of functionally graded plates

Bending analysis of functionally graded plates using the two variable refined plate theory is presented in this paper. The number of unknown functions involved is reduced to merely four, as against five in other shear deformation theories. The variationally consistent theory presented here has, in many respects, strong similarity to the classical plate theory. It does not require shear correction factors, and gives rise to such transverse shear stress variation that the transverse shear stresses vary parabolically across the thickness and satisfy shear stress free surface conditions. Material properties of the plate are assumed to be graded in the thickness direction with their distributions following a simple power-law in terms of the volume fractions of the constituents. Governing equations are derived from the principle of virtual displacements, and a closed-form solution is found for a simply supported rectangular plate subjected to sinusoidal loading by using the Navier method. Numerical results obtained by the present theory are compared with available solutions, from which it can be concluded that the proposed theory is accurate and simple in analyzing the static bending behavior of functionally graded plates.