An analytical approach for nonlinear thermo-mechanical buckling behavior of Porous FG-GPLRC circular plates and spherical caps

This paper presents an analytical approach for the nonlinear thermo-mechanical stability analysis of porous functionally graded graphene platelets reinforced composite (Pr-FG-GPLRC) circular plates (CPs) and shallow spherical caps (SCs) resting on nonlinear elastic foundation. Pr-FG-GPLRC is considered to have three different types of foam distribution. The applied load includes uniform external pressure and uniform thermal loads. The governing formulations are established by the first-order shear deformation theory (FSDT) and the von Kármán geometrical nonlinearities. The deformation compatibility equations are established and the stress function is introduced to reduce the equilibrium equation system into three equations with three function variables (deflection, rotation, and stress function). The chosen solution form approximately satisfies the clamped boundary conditions and the Ritz energy method is applied to obtain the equilibrium equation system in nonlinear algebraic form. The explicit expressions of buckling loads and thermo-mechanical post-buckling curves can be obtained. Numerical investigations are performed to discuss the remarkable effects of nonlinear foundation stiffness, material, and geometrical properties imperfection on the nonlinear thermo-mechanical buckling behavior and load-carrying capacity of CPs and SCs.