Nonlocal Flügge shell model for the axial buckling of single-walled Carbon nanotubes: An analytical approach

In this paper, the stability characteristics of single-walled carbon nanotubes (SWCNTs) under the action of axial load are investigated. To this end, a nonlocal Flügge shell model is developed to accommodate the small length scale effects. The analytical Rayleigh-Ritz method with beam functions is applied to the variational statement derived from the Flügge-type buckling equations. Molecular dynamics (MD) simulations are performed to obtain the critical axial buckling loads of (8,8) armchair SWCNTs with different types of end conditions. Through comparison of the results obtained from the present analytical solution and the ones from molecular dynamics simulations, the appropriate values of nonlocal parameter are proposed for SWCNTs with different kinds of boundary conditions. The effects of nonlocal parameter and boundary conditions on the critical buckling load are also examined. Moreover, in spite of the uncertainty that exists in defining the in-plane stiffness and bending rigidity of nanotube, by adjusting the nonlocal parameter, the present nonlocal shell model is shown to be capable of predicting the MD simulations results.