Closed-form solution for buckling analysis of thick functionally graded plates on elastic foundation

• Buckling analysis of functionally graded plate is presented using Reddy's theory.
• The position of neutral surface of functionally graded plate is determined.
• The governing equations based on neutral surface are derived.
• Closed-form solutions are obtained for Levy-type plates.

Closed-form solution for buckling analysis of thick functionally graded plate resting on elastic foundation is presented using the third-order shear deformation theory. It is assumed that the plate rests on Pasternak foundation and its material properties vary through the plate thickness as a power function. By decoupling the governing equations, the neutral surface position for such plate is determined, and the third-order shear deformation theory based on exact neutral surface position is employed to derive the governing equations. Comparing with the middle surface based formulations, the neutral surface based formulations do not exhibit the stretching–bending coupling; hence, the values of buckling load can be obtained by eigenvalue analysis. Closed-form solutions are obtained for rectangular with different boundary conditions. Numerical results are presented and discussed for a wide range of plate and foundation parameters.