Nonlinear Snap-Through Stability Behavior of Long Sandwich Cylindrical Panels with a Metal-Based Foam Porous Core

A porosity-dependent model is formulated in this research to investigate the snap-buckling resistance in infinite-length sandwich cylindrical shell panels. The sandwich shell is made of a metal-based foam porous core reinforced by graphene platelets (GPLs) and titanium alloy face sheets. It is assumed that the porous metal core consists of six layers each of them have different values of porosity to achieve a piece-wise functionally graded (FG) pattern. The porous sandwich shell is supported on a three-parameter nonlinear foundation and is subjected to uniformly distributed pressure loading. In the mathematical modeling, sinusoidal shear strain function coupling with the von Kármán kinematic nonlinearity is taken into account. The equilibrium equations of the sandwich shell are obtained utilizing the generalized principle of virtual work. The systems of nonlinear differential equations are analytically solved for the shell with immovable simply-supported and clamped-clamped boundaries by a perturbation-based technique. Novel numerical results are provided to investigate the effects of material properties, geometrical characteristics, and foundation stiffnesses on the snap-buckling resistance of the infinite-length sandwich cylindrical shell.