Semianalytical Solution for Buckling Analysis of Variable Thickness Two-Directional Functionally Graded Circular Plates with Nonuniform Elastic Foundations

Abstract

In the current study, a semianalytical closed-form solution is presented for the first time for buckling analysis of two-directional, functionally graded (FG) circular plates with variable thickness supported by both constrained edges and two-parameter elastic foundations. It is assumed that the material properties of the functionally graded material (FGM) vary in the transverse and radial directions, simultaneously. While variations of the elasticity modulus in the transverse direction is described by a power-law, variations of the material properties and the thickness in the radial direction are assumed to obey exponential laws. Mindlin’s shear deformation plate theory and the differential transform technique are employed to develop the governing equations. A sensitivity analysis including evaluation of effects of various edge conditions, geometric parameters, coefficients of the elastic foundation, and material heterogeneity is performed. Results reveal that the strength degradation caused by the radial thickness reduction may be compensated by an appropriate increasing of the elasticity modulus in the radial direction. Furthermore, the elastic foundation may significantly affect the buckling load in some circumstances.