Buckling of a Double-Walled Carbon Nanotube

In this study we present the buckling behavior of the double-walled carbon nanotubes under various boundary conditions. First we study the case of the simply supported double-walled carbon nanotubes at both ends which is amenable to exact solution. Then we utilize approximate methods of Bubnov-Galerkin and Petrov-Galerkin to check the efficacy of these approximations for the simply supported double-walled carbon nanotubes. Once the extreme accuracy is demonstrated for this study we apply the approximate techniques to two other cases of the boundary conditions, namely to clamped-clamped and simply supported-clamped double-walled carbon nanotubes. For the first time in the literature approximate expression for the buckling loads are given for these boundary conditions.