Nonlinear postbuckling behavior of auxetic-core toroidal shell segments with Graphene reinforced face sheets under axial loads

The main aim of this paper is to provide an analytical approach for the nonlinear buckling behaviors of toroidal shell segments made by three layers included honeycomb auxetic-core and two Graphene reinforced face sheets under axial compressive or tensile loads. The auxetic core is designed in a honeycomb form and three distribution laws of Graphene are considered for two symmetric face sheets. The homogenization technique for honeycomb auxetic plates and shells is applied to establish the stiffness formulations of the core. By approximating the doubly curved coordinate to the simpler coordinate with the Stein and McElman assumption, the nonlinear basic equations are formulated using the nonlinear Donnell shell theory and the model of the two-parameter foundation. The Galerkin method can be performed three times for three states of buckling responses and the expressions of the load-deflection postbuckling curves can be determined. The numerical examinations present that the bifurcation buckling occurs with both axial tensile and compressive loads for convex and concave shells and the significantly beneficial effects of auxetic core and functionally graded Graphene reinforced face sheets on nonlinear buckling responses of shell segments.