Buckling analysis of double-walled carbon nanotubes embedded in an elastic medium under axial compression using non-local Timoshenko beam theory

Using the non-local elasticity theory, Timoshenko beam model is developed to study the elastic buckling of double-walled carbon nanotubes (DWCNTs) embedded in an elastic medium under axial compression. The non-local effects in the normal and transverse shear stress components are considered. The effects of the surrounding elastic medium based on a Winkler model and van der Waals' (vdW) force between the inner and outer nanotubes are taken into account. Considering the small-scale effects, the governing equilibrium equations are derived and the critical buckling loads under axial compression are obtained. The numerical results are reported using the non-local Timoshenko beam theory and compared with those obtained using the non-local Euler-Bernoulli beam theory. The results show that the critical buckling load can be overestimated by the local beam model if the small-scale effect is overlooked for long nanotubes. Furthermore, in order to estimate the non-local critical buckling load of DWCNTs under axial compression, a simplified analysis is carried out and the results are compared with those obtained using molecular mechanics.