The refined sinusoidal theory for FGM plates on elastic foundations

Using the refined sinusoidal shear deformation plate theory and including plate-foundation interaction, a thermoelastic bending analysis is presented for a simply supported, rectangular, functionally graded material plate subjected to a transverse uniform load and a temperature field, and resting on a two-parameter (Pasternak model) elastic foundation. The present shear deformation theory is simplified by enforcing traction-free boundary conditions at the plate faces. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain is given. Material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The equilibrium equations of the present plate are given based on various plate theories. A number of examples are solved to illustrate the numerical results concerning bending response of homogeneous and functionally graded rectangular plates resting on two-parameter elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The influences played by transversal shear deformation, plate aspect ratio, side-to-thickness ratio, volume fraction distributions, and elastic foundation parameters are studied.