Buckling Analysis of Cantilever Carbon Nanotubes Using the Strain Gradient Elasticity and Modified Couple Stress Theories

In this paper, higher-order continuum theories are proposed for the buckling analysis of single walled carbon nanotubes (SWCNT). Modified strain gradient elasticity and modified couple stress theories are proposed. The governing equations for buckling and related boundary conditions are obtained in conjunctions with the strain gradient elasticity and variational principle. Detailed formulations and analytical solutions are presented for cantilever boundary conditions. Some new results are computed for buckling analysis of carbon nanotubes in order to show the scale effect.