A refined plate theory for functionally graded plates resting on elastic foundation

► A refined theory is proposed for functionally graded plates on elastic foundation. ► The theory contains four unknowns and does not require shear correction factor. ► Closed-form solutions are derived for rectangular plates. ► The theory can accurately predict the deflection, buckling load, and frequency. A refined plate theory for functionally graded plates resting on elastic foundation is developed in this paper. The theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The number of independent unknowns of present theory is four, as against five in other shear deformation theories. The material properties of plate are assumed to vary according to power law distribution of the volume fraction of the constituents. The elastic foundation is modeled as two-parameter Pasternak foundation. Equations of motion are derived using Hamilton’s principle. The closed-form solutions of rectangular plates are obtained. Numerical results are presented to verify the accuracy of present theory.