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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.

This paper uses the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-order theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates.