Post-buckling analysis of functionally graded material (FGM) plates resting on Winkler and Pasternak elastic foundations subjected to thermomechanical loadings with circular cut-outs at centre and random material properties is presented. The material properties of each constituent’s materials, volume fraction index, thermal expansion coefficients, foundation stiffness parameters and thermal conductivities are taken as independent basic random input variables. The basic formulation is based on applying Reddy’s higher order shear deformation theory, which requires C1 continuous element approximation. A modified form C0 continuity is applied in the present investigation. A serum-free expansion medium with mean-centred first-order regular perturbation technique for composite plates is extended for FGM plates to solve the random eigenvalue problem. Typical numerical results are presented to examine the second-order statistics for effect of the volume fractions index, plate length-to-thickness ratios, plate aspect ratios, types of loadings, amplitude ratios, support conditions and various shape and size of holes with random thermomechanical properties. The results obtained by the present solution approach are validated with published papers and the robust method of simulation. It is found that the laminates with round cuts (FGM plates resting on Winkler and Pasternak elastic foundations) have a significant influence on the post-buckling response under Thermomechanical loading conditions. Present investigations are useful for the applications and further research.
