Assessing the effect of stiffeners on the stability of sandwich metacomposite toroidal shells under axial compression

This research explores the effect of stiffeners on the stability of sandwich toroidal shell segments (TSSs) featuring the recently developed graphene origami (GOri)-enabled auxetic metamaterial core and carbon nanotube (CNT)-reinforced face sheets supported by elastic foundations and subjected to axial compression. The shells are stiffened circumferentially or longitudinally with CNT-reinforced rings or stringers, which are internally embedded and modeled using an innovative smeared stiffener approach. CNTs are distributed throughout the thickness of the shell-stiffener structure, following either a uniformly distributed (UD) or functionally graded (FG) distribution model. The nonlinear equilibrium equations for the longitudinally shallow shells are derived using the von Kármán shell theory and Stein and McElman approximations while considering a Winkler-Pasternak elastic foundation to model the interaction between the shell and the elastic foundation. A deflection solution under simply supported boundary conditions is employed, and the Galerkin method is applied to obtain the nonlinear load-deflection relationship. This relationship is subsequently used to calculate the buckling loads and analyze the postbuckling behavior. The numerical analysis addresses the effects of stiffeners, considering the CNT volume fraction, distribution models, geometrical parameters, and the impact of the elastic foundation on the stability of auxetic-core TSSs.