Mechanical and thermal nonlinear buckling analysis of FGM shallow spherical caps with porosity and elastically restrained edge

This paper investigates the buckling and postbuckling behavior of functionally graded material (FGM) shallow spherical caps (SSCs) with porosity and elastically restrained edge subjected to uniform external pressure and elevated temperature. For the first time, the occurrence possibility and type of thermally induced buckling response of porous FGM SSCs are scrutinized. Pores are distributed into FGM via even and uneven distributions. The properties of constituent materials are assumed to temperature dependent and the effective properties of porous FGM are estimated using a modified rule of mixture. Equilibrium and strain compatibility equations are established using the first order shear deformation theory taking into account the von Kármán–Donnell nonlinearity and initial geometric imperfection. These equations are solved using analytical solutions and Galerkin method to derive a nonlinear relation between loads and deflection of clamped SSCs. In the thermal postbuckling analysis, an iteration procedure is adopted to determine critical temperatures and postbuckling temperature–deflection paths. The study detects that bifurcation–type buckling behavior of thermally loaded SSC may occur in case the SSC is sufficiently shallow and the size of its imperfection satisfies a definite value. It is also found that in‐plane edge constraint dramatically affects the nonlinear buckling behavior of pressure–loaded SSCs, especially at elevated temperatures.