Nonlinear Buckling and Postbuckling Response of Porous FGM Shallow Spherical Caps and Circular Plates with Nonlinear Elastic Foundation Effects Using the Ritz Energy Method

A new analytical study for nonlinear buckling and postbuckling behavior of porous functionally graded material (FGM) circular plates and shallow spherical caps resting on nonlinear elastic foundation was carried put using the nonlinear Reddy’s higher-order shear deformation theory (HSDT). The spherical caps/circular plates under thermo-mechanical loadings were considered, and the nonlinear elastic foundation was used to model the behavior of hardening and softening foundations. The total potential energy expressions of caps/plates were established, and the Ritz energy method was applied. The analytical expressions of load-deflection relationships were obtained. The critical buckling loads and postbuckling behavior of shells/plates were determined and analyzed. The remarkable influences of geometrical parameters, material parameters, and nonlinear foundation stiffnesses on the nonlinear static stability behavior of caps and circular plates were noted.