Nonlinear Thermomechanical Transient Response of Initially Stressed FGM Shallow Shell Panels Including Porosity and Geometric Imperfection

This paper aims to investigate the simultaneous effects of initial stresses, porosities, geometrical imperfections, elastic foundations, and high temperatures on the nonlinear transient response of spherical and cylindrical shell panels made up of functionally graded material (FGM) and that have undergone suddenly applied uniform transverse loads. Initial thermomechanical stresses are caused by reactive forces produced at tangentially restrained edges or active axial compressive loads applied at movable curved edges of cylindrical panels. The pores are distributed in FGM via even and uneven distribution patterns. Due to the presence of pores, the effective properties of porous FGM are evaluated by employing a modified mixture rule. Mathematical derivations governing the dynamic behavior of shallow shell panels are performed on the basis of first-order shear deformation theory incorporating von Kármán–Donnell nonlinearity, initial geometric imperfection, and interactive pressure from two-parameter foundations. Analytical solutions are adopted to satisfy simply supported boundary conditions and the Galerkin method is utilized to obtain a time-variable ordinary differential equation of quadratic and cubic nonlinearities. This differential equation is solved using the fourth-order Runge–Kutta integration method to trace temporal response paths. Through parametric studies, numerous effects on the nonlinear temporal response and findings are analyzed and discussed.