This article aims to evaluate the geometrical nonlinear behavior of toroidal shell segments surrounded by elastic medium under two types of axial edge-loading and external pressure, including the thermal effects. The considered shells are assumed to be made of some composite plies incorporating three constituents: carbon nanotubes (CNTs) and graphene nanoplatelets (GPLs) as nanocomposites, fibers and polymeric resin. The considered nanocomposites are assumed to be randomly oriented and functionally distributed in the resin. The governing equations are extended based the first-order shear deformation theory (FSDT) for the moderately thick shells. Also, an analytical solution using Galerkin method is proposed which yields to a closed-form load–deflection relationship. The present formulation has two important advantages which justify its novelty. It provides a robust tool for geometrical nonlinear static analysis of hybrid GPL/CNT/fiber/resin composite shallow toroidal shells with no computational efforts. Although the present method incorporates thin and moderately thick shells with a complicated thermo-mechanical specifications, it has been extended simpler than the other related formulations proposed in the previous studies. In order to validate the applicability of the extended formulation, some benchmark examples from the existing literature are considered and the corresponding equilibrium paths are compared with those are obtained by using the present method. Also, the parametric studies incorporate the effects of various geometrical, mechanical, and thermal parameters on the nonlinear equilibrium path of the proposed shells. The verification procedure and the performed parametric studies show that the proposed method and extended formulation enable a strong tool for the geometrical nonlinear analysis of such shells.
