Post-buckling of multilayer PSFG cylindrical shells with two-layered FGP cores resting on elastic foundation

In this research, the post-buckling analyses of multilayer porous sigmoid functionally graded (PSFG) cylindrical shells with two-layered FG porous (FGP) cores resting on elastic foundations (EF) exposed to external excitation are examined using an analytical method. The research focuses on two distinct variations of FG layers: those with evenly distributed porosities (FG-EPD) and those with unevenly distributed porosities (FG-UEPD). Additionally, the FGP cores are explored in two forms: one with uniform porosity distribution (UPD) and another with non-symmetric porosity distribution (NSPD). This analysis includes eight different configurations of these layers. The equilibrium equations have been formulated using the classical shell theory, incorporating geometrical nonlinearity in the von Kármán-Donnell framework. An approximate solution for deflection, involving three terms, has been selected for greater accuracy. Additionally, explicit formulas for determining the post-buckling load-deflection relationships and the critical load are provided through the use of Galerkin's method. The influences of various parameters, including geometry, EF coefficients, and material properties, on post-buckling behaviors of the multilayer PSFG cylindrical shells with two-layered FGP cores resting on EF are investigated.