Compressive study of functionally graded plates resting on Winkler-Pasternak foundations under various boundary conditions using hyperbolic shear deformation theory

Equilibrium equations of a functionally graded plate resting on two-parameter elastic foundations are derived using hyperbolic shear deformation theory. This theory takes into account the hyperbolic distribution of transverse shear deformation and satisfies that the corresponding shear stresses equal to zero on upper and lower surfaces of the plate without requiring any shear correction factors. Eight different types of boundary conditions are considered. Governing equations are obtained including the plate-foundation interaction. The present results are compared well with the corresponding available in the literature. Effects of boundary conditions, linear (Winkler) modulus and shear foundation (Pasternak) modulus, gradient index, plate aspect ratio, side-to-thickness ratio on the stresses and deflections are all discussed. It is established that the present model is more accurate than some theories developed previously.