Mechanical and thermal buckling analysis of functionally graded plates resting on elastic foundations: An assessment of a simple refined nth-order shear deformation theory

Abstract

In present study, a refined nth-order shear deformation theory is proposed, formulated and validated for a variety of numerical examples of functionally graded (FG) plates resting on elastic foundation for the mechanical and thermal buckling responses. The present refined nth-order shear deformation theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components, in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The most interesting feature of this theory is that it accounts for a parabolic 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. Governing equations are derived from the principle of minimum total potential energy. A Navier type closed form solution methodology is also proposed for simply supported FG plates resting on elastic foundation which provides accurate solution. The accuracy of the present theory is verified by comparing the obtained results with those predicted by classical plate theory (CPT), first-order shear deformation theory (FSDT), higher-order shear deformation theory (HSDT) and refined plate theory (RPT). Moreover, results show that the present theory can achieve the same accuracy of the existing higher-order shear deformation theories which have more number of unknowns.