Porosity effects on the buckling and post buckling of metamaterial sandwich toroidal shell segments

This article investigates the effect of porosity on the buckling and postbuckling characteristics of sandwich toroidal shell segments (TSSs) with graphene origami (GOri)-enabled auxetic core and porous functionally graded carbon nanotubes (FG-CNT)-reinforced face sheets. The TSSs are subjected to combined axial compression and radial pressure and supported by an elastic foundation. The auxetic property of the core layer can be effectively tuned by the content and folding degree of GOri, and the material characteristics are estimated using genetic programming (GP)-assisted micromechanical models. CNTs are embedded within a polymer matrix by uniform or FG distribution (UD, FG-X, and FG-O) throughout the shell thickness, and three distinct porosity distribution patterns are considered for the face sheets: uniform, symmetric, and asymmetric. The nonlinear equilibrium equations of the longitudinally shallow shells are formulated using the von Karman-Donnel shell theory in conjunction with Stein and McElman approximations while considering the Winkler-Pasternak type elastic foundation to simulate the interaction between the shell and elastic foundation. A three-term solution for deflection under simply supported boundary conditions is employed, with the Galerkin method utilized to derive the nonlinear load-deflection relation. The effectiveness of the proposed approach is confirmed through comparative analysis with existing literature, demonstrating good agreement with theoretical results. Extensive parametric studies are subsequently carried out to thoroughly investigate the impacts of various parameters such as the porosity coefficients and distribution patterns, load-proportional parameters, presence of an elastic foundation, and geometric properties on the buckling and postbuckling performance of TSSs under combined mechanical loads.