An analytical approach of nonlinear buckling behavior of torsionally loaded auxetic core toroidal shell segments with graphene reinforced polymer coatings

Abstract

The buckling and nonlinear postbuckling analysis of toroidal shell segments with auxetic-core layer and Graphene-reinforced polymer coatings under torsional loads is reported in the present research. The functionally graded Graphene-reinforced polymer coatings are considered with three distribution laws, and the auxetic cores are designed in the honeycomb lattice forms. An auxetic homogenization technique is applied to establish the stiffness terms of the auxetic core. The combination of nonlinear von Karman Donnell shell theory and the Stain and McElman approximate is applied to formulate the nonlinear equilibrium equations of shells with the shallow longitudinal curvature considering the two-parameter foundation model. The deflection of shells is assumed to be a three-term form corresponding to the pre-buckling, linear and nonlinear postbuckling behaviors, and the Galerkin method is employed for three terms of defection. The torsion-deflection and torsion-twist angle postbuckling behaviors can be obtained in explicit forms. The numerical examinations validate the large effects of honeycomb lattice auxetic core, the functionally graded Graphene-reinforced polymer coatings, the parameters of shell’s geometric and foundation on the nonlinear buckling behaviors of shells.