Nonlinear Thermomechanical Static and Dynamic Buckling Responses of FG-GPLRC Spherical Caps and Circular Plates with Two-Step Spiderweb Stiffeners and a Piezoelectric Layer

Nonlinear thermomechanical static and dynamic buckling responses of functionally graded graphene platelets-reinforced composite (FG-GPLRC) circular plates and spherical caps with two-step spiderweb stiffeners and piezoelectric layer are presented in this paper. An improved technique for two-step spiderweb stiffeners is successfully established and applied to the FG-GPLRC stiffeners. The circular plates and spherical caps are placed on the nonlinear elastic foundation under pressure and thermal loads that increase linearly with time. The Donnell shell theory with nonlinearities in von Karman sense, large deflection nonlinearities, and electrical effects of the piezoelectric layer are also considered. The total potential energy expression of structures is established and the Euler–Lagrange equations are applied to achieve the motion equation system. The Runge–Kutta method is applied to solve the motion equation system and dynamic buckling behavior of plates and shells. The static postbuckling behaviors of stiffened plates and shells are obtained in explicit forms. The remarkable discussions of the effects of graphene volume fraction and distribution, piezoelectric layers, and spiderweb stiffeners on the static and dynamic buckling behaviors are investigated by numerical examples.