Nonlinear Thermomechanical Transient Response of FGM Circular Plates and Shallow Spherical Caps with Porosities and Tangentially Restrained Edges

The present study aims to examine the nonlinear thermomechanical transient behavior of functionally graded material (FGM) circular plates and shallow spherical caps loaded by suddenly applied uniform external pressure taking into account the effects of pores, meridional restraints of periphery, and raised temperatures. Unlike previous studies, boundary edges are hypothesized to be elastically restrained against meridional displacements. The voids are assumed to scatter in FGM via even and uneven types. The material properties of constituents are hypothesized to be temperature dependent and overall properties of porous FGM are estimated by means of a modified mixture rule. Motion and compatibility equations are formulated on the basis of first-order shear deformation theory (FSDT) incorporating von Kármán–Donnell nonlinear terms and initial geometric imperfection. Basic equations are resolved by means of an analytical procedure along with the Galerkin technique for a clamped boundary condition to obtain a time ordinary differential equation that is of quadratic and cubic nonlinearities. Dynamical deflection–time curves are traced by taking up a fourth-order Runge–Kutta iteration scheme. After verifying for particular conditions of meridional constraints of edges with the literature, numerical examinations are implemented to rate various impacts on the nonlinear thermomechanical temporal behavior of FGM circular plates and spherical caps. It is found that the meridional constraints of the periphery strongly affect the nonlinear dynamical behavior of FGM circular plates and spherical caps with voids, especially at high temperatures. The analyses also reveal that the geometry properties and geometric imperfection size significantly influence the behavior tendency and the amplitude of dynamical deflection.