Thermo-torsional postbuckling of CNT-reinforced composite toroidal shell segments with surrounding elastic media and tangentially restrained edges

An analytical investigation on the nonlinear stability of toroidal shell segment (TSS) made of carbon nanotube (CNT)-reinforced composite, surrounded by an elastic medium, exposed to elevated temperature and subjected to uniform torsion is presented in this paper. The properties of constituents are assumed to be temperature dependent and effective properties of composite are determined using an extended rule of mixture. CNTs are embedded into matrix phase according to functionally graded or uniform distributions. Basic equations in terms of deflection and stress function are established within the framework of classical shell theory including geometrical nonlinearity in von Karman-Donnell sense and interactive pressure from surrounding elastic medium. Two boundary edges of the shell are assumed to be simply supported and tangentially restrained. Multi-term analytical solutions are assumed and Galerkin method is used to derive expressions of buckling load and nonlinear relation between torsional load and deflection. Parametric studies are carried out to analyze the effects of material and geometry properties, in-plane boundary condition, elevated temperature and surrounding elastic medium on the buckling resistance and postbuckling behavior of torsionally loaded TSS. Novel finding of this study is that tangential edge constraints have no and negative effects on critical torsional loads at room and elevated temperatures, respectively, and profoundly beneficial influences on postbuckling load capacity of TSSs.