Thermal buckling and postbuckling analysis of FG-CNTRC cylindrical shells stiffened by helical FG-CNTRC stiffeners with temperature-dependent material properties

Abstract

This study presents an analytical investigation on the thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) cylindrical shells reinforced by FG-CNTRC stiffeners. The shell is subjected to a uniform temperature rise, and the material properties of both the shell and stiffeners are assumed to be temperature-dependent. Three stiffening configurations, including orthogonal and helical stiffeners, are considered within a unified formulation based on the smeared stiffener technique. The governing nonlinear equilibrium equations are established using the Donnell shell theory with von Kármán geometric nonlinearity. A Ritz-based energy approach is employed to derive the analytical expressions for the critical buckling temperature and postbuckling equilibrium paths. The effects of CNT distribution patterns, CNT volume fraction, stiffener configuration, and geometric parameters on the thermal stability of the shells are systematically examined. The results indicate that stiffeners significantly enhance the thermal buckling resistance of FG-CNTRC cylindrical shells, with helical stiffeners providing a markedly higher improvement compared to orthogonal stiffeners. Among the considered CNT volume fractions, an intermediate value provides the highest thermal buckling resistance, while a further increase in CNT content may reduce the thermal stability. In addition, the spacing and arrangement of stiffeners play a crucial role in determining the buckling temperature and postbuckling response.