Cylindrical shells are usually buckled under complex and combined loading conditions. This article presents an analytical approach to investigate the buckling and postbuckling behaviors of cylindrical shells reinforced by single-walled carbon nanotubes, surrounded by an elastic medium, exposed to thermal environments, and subjected to combined axial compression and lateral pressure loads. Carbon nanotubes (CNTs) are imbedded into matrix phase by uniform distribution or functionally graded distribution along the thickness direction. The properties of constituents are assumed to be temperature dependent, and effective properties of CNT-reinforced composite (CNTRC) are determined by an extended rule of mixture. Governing equations are based on the classical shell theory (CST) taking von Karman–Donnell nonlinearity and surrounding elastic foundations into consideration. Three-term form of deflection is assumed to satisfy simply supported boundary conditions, and Galerkin method is applied to obtain nonlinear load–deflection relations from which buckling loads and postbuckling equilibrium paths are determined. Numerical examples are carried out to show the effects of CNT volume fraction, distribution types, thermal environments, preexisting nondestabilizing lateral pressure and axial compression loads, and elastic medium on the buckling and postbuckling behaviors of CNTRC cylindrical shells.
