Analytical study on nonlinear buckling of spiral-stiffened FG-CNTRC toroidal shells segments with piezoelectric layers and generalized curvature under external pressure

Abstract

This paper presents an analytical investigation into the nonlinear stability of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) toroidal shell segments with piezoelectric layers and generalized curvature subjected to external pressure. The analysis incorporates several typical meridian shapes, including circular, parabolic, and half-sinusoid geometries. The paper uses Donnell shell theory (DST), combined with von Kármán geometric nonlinearity and an improved Lekhnitskii smeared stiffener technique to study the behavior of stiffened spiral or orthogonal FG-CNTRC shells. The carbon nanotube (CNT) distributions in the shells and stiffeners are designed to satisfy material continuity conditions. Thermal effects and elastic foundation interactions are also incorporated into the analysis, providing a comprehensive framework for understanding their influence on structural stability. To examine large deformation behavior, three-term deflection functions fulfilling the simply supported boundary conditions are adopted, whereas the Ritz energy approach is utilized to derive the load-deflection relationship under external pressure. The numerical results indicate that the critical buckling loads and postbuckling responses are significantly affected by the spiral stiffener system, elastic foundation, temperature variations, and CNT distributions.