Closed-form solution for nonlinear buckling analysis of FG-CNTRC cylindrical shells with initial geometric imperfections

The circular cylindrical shells have been widely used in modern engineering structures, especially in the aerospace industry such as the oil pipeline, the missile, spacecraft hull, storage tanks. In recent years, functionally graded carbon nanotube composites (FG-CNTRCs) have emerged, as a promising type of composites. Due to the increasing demands for high structures performance, this research paper proposes a closed-form solution to investigate the nonlinear buckling behavior of the FG-CNTRC cylindrical shells subjected to compressive load. The small initial imperfections of the FG-CNTRC cylindrical shells are also considered through analytical modeling. Effective properties of materials of the shells reinforced by single-walled carbon nanotubes (SWCNTs) are estimated through a micro-mechanical model based on the extended rule of mixtures. The Donnell shell theory and von-Karman nonlinear kinematics are used for nonlinear equilibrium equations. The novelty of this work is to exploit an exact solution via Galerkin procedure and term of the Airy stress function in order to reveal the impacts of the imperfection parameter, different types of CNTs distribution, the volume fraction of CNTs on nonlinear behavior and compressive equilibrium paths of FG-CNTRC cylindrical shells.