Nonlinear stability analysis of shear-deformable sandwich meta-composite shell with arc-type auxetic core

This paper introduces analytical solutions to study the nonlinear buckling and postbuckling behavior of shear-deformable, arc-type auxetic-core sandwich composite toroidal shell segments (TSSs) with carbon nanotube (CNT)-reinforced face sheets surrounded by Kerr-type foundation and subjected to external pressure. CNTs are incorporated into a polymer matrix with a uniform (UD) or functionally graded (FG) distribution across the shell thickness. Inspired by the traditional concave hexagonal design, the arc-type auxetic core includes curved ribs and allows for a smooth transition between adjacent unit cells, effectively mitigating stress concentrations. The Kerr-type three-parameter elastic foundation is modeled with a central shear layer and two spring layers on both the top and bottom sides. The governing equations for the TSSs are derived using Reddy's third-order shear deformation theory (TSDT), incorporating von Kármán-type geometric nonlinearity. A three-term deflection solution under simply supported boundary conditions is employed, with the Galerkin method used to establish the nonlinear load-deflection relationship. The effectiveness of the current approach is confirmed through comparative analysis with existing literature, demonstrating good agreement with theoretical results. The numerical results examine the effects of geometric parameters of the arc-type auxetic metamaterial structure—specifically the inclined angle of the auxetic core and circular arc radius—along with Kerr-type elastic foundation parameters, CNT distribution, and geometric characteristics on the critical buckling loads and postbuckling paths of sandwich TSSs.