The nonlinear post-buckling behavior of FG cylindrical copper shell reinforced with carbon nanotubes with a polymer core

Abstract

This research analyzes the buckling and post-buckling behavior of composite cylindrical shells with a polymer core and carbon nanotube-reinforced inner and outer copper layers with functional distribution under axial compressive loading. For this purpose, the differential equations governing the nonlinear buckling behavior of these shells were extracted while considering large deformations. Employing the Ritz energy method and considering the Airy function, analytical relations for the buckling load and the critical stress of the structure are extracted. In the following, considering different distributions, the equivalent mechanical properties of the composite structure have been calculated using the law of mixtures. Finally, the effect of different parameters, such as distribution types and volume fraction of nanotubes, on nonlinear buckling loads and post-buckling behavior of these materials is investigated. Results show that increasing the volume fraction of carbon nanotubes reduces the change in the critical length of the cylindrical shell, which happens as a result of increasing Young's modulus and the equivalent stiffness of the shell.