Nonlinear buckling analysis of FGP shallow spherical shells under thermomechanical condition

In this study, an analytical method is presented to investigate the nonlinear buckling analysis of functionally graded porous (FGP) shallow spherical shells exposed to external excitation in a thermal environment resting on elastic foundations. The elastic foundations of the FGP shell are consist of a two-term Winkler-Pasternak's model. Using the classical theory of shells and considering nonlinear von Karman-Donnell relations and Hook law, the governing equations of thin FG porous spherical shells are extracted. Galerkin's method is utilized to discretize the governing equation of shallow spherical shell. Regarding the discretized equations of motion, the explicit expressions for dynamic and static critical buckling loading are determined under thermomechanical effect. Two types of distributions for FG porous, including the uniform and symmetric porosity, are considered. To investigate the dynamic buckling exposed to external pressure and thermal effect, the equations of motion of FGP shallow spherical shells are examined via a numerical method named Runge-Kutta approach, and then with a procedure presented by Budiansky-Roth, the critical load for the nonlinear dynamic buckling is obtained. The influence of thermal environment changes, porosity coefficients, various porosity distributions, elastic foundations, and geometrical characteristics on the nonlinear static and dynamic buckling response of FGP shallow spherical shell is examined.