Effects of FG-GRC auxetic core on the nonlinear torsional buckling of FG-GRC toroidal shell segments in thermal environment

Abstract

This paper presents an analytical study on the thermo-mechanical nonlinear buckling behavior of toroidal shell segments composed entirely of functionally graded graphene-reinforced composite (FG-GRC), including both the facesheets and the auxetic core. In contrast to conventional sandwich configurations with polymer-based cores, the present model introduces an auxetic core with a honeycomb lattice structure also made of FG-GRC, ensuring material continuity and enhanced stiffness performance. The effective material properties of the FG-GRC constituents are evaluated using an extended Halpin-Tsai model, while the auxetic core is homogenized as an equivalent orthotropic medium with functionally graded characteristics. The governing equations are formulated based on the nonlinear Donnell shell theory, incorporating von Kármán geometric nonlinearity and thermal strains induced by environmental temperature variations. A Ritz energy method is employed to derive the equilibrium equations by minimizing the total potential energy, leading to a closed-form solution for the critical torsional buckling load and postbuckling response. Parametric analyses are performed to investigate the influences of temperature change, graphene distribution patterns, geometrical parameters, and auxetic core configuration on the stability behavior. The results reveal that the fully FG-GRC configuration significantly enhances structural stiffness and thermal resistance compared to conventional sandwich shells, while thermal effects markedly reduce the critical buckling load.