Buckling and postbuckling of single-walled carbon nanotubes based on a nonlocal Timoshenko beam model

In this research, the axial buckling and postbuckling configurations of single-walled carbon nanotubes (SWCNTs) under different types of end conditions are investigated based on an efficient numerical approach. The effects of transverse shear deformation and rotary inertia are taken into account using the Timoshenko beam theory. The nonlinear governing equations and associated boundary conditions are derived by the virtual displacements principle and then discretized via the generalized differential quadrature method. The small scale effect is incorporated into the model through Eringen's nonlocal elasticity. To obtain the critical buckling loads, the set of linear discretized equations are solved as an eigenvalue problem. Also, to address the postbuckling problem, the pseudo arc-length continuation method is applied to the set of nonlinear parameterized equations. The effects of nonlocal parameter, boundary conditions, aspect ratio and buckling mode on the critical buckling load and postbuckling behavior are studied. Moreover, a comparison is made between the results of Timoshenko beam model and those of its Euler-Bernoulli counterpart for various magnitudes of nonlocal parameter.