Buckling analysis of carbon nanotubes modeled using nonlocal continuum theories

In this paper, the buckling of carbon nanotubes, modeled as nonlocal one dimensional continua within the framework of Euler–Bernoulli beams, is considered. Both a stress gradient and a strain gradient approach are considered and a variational approach is adopted to obtain the variationally consistent boundary conditions. The dependence of the buckling load on the nonlocal parameter has been determined using the boundary conditions obtained from the variational analysis. Results indicate significant dependence of nonlocal parameter on buckling load for particular types of boundary conditions. These findings are important in mechanical design considerations of devices that use carbon nanotubes.