Stability analysis of carbon nanotubes based on a novel beam model and its comparison with Sanders shell model and molecular dynamics simulations

we study the effects of small-scale parameter on the buckling loads and strains of nanobeams, based on nonlocal timoshenko beam model. however, the lack of higherorder boundary conditions leads to inconsistencies in critical buckling loads. in this paper, we apply a novel approach based on nonlocal timoshenko kinematics, strain gradient approach and variational methods for deriving all classical and higher-order boundary conditions as well as governing equations. therefore, closed-form and exact critical buckling loads of nanobeams with various end conditions are investigated. moreover, the dependence of buckling loads on the small-scale parameter as well as shear deformation coefficient is studied using these new boundary conditions. then, numerical results from this new beam model are presented for carbon nanotubes (cnts). they illustrate a more accurate buckling response as compared to the previous works. furthermore, the critical strains are compared with results obtained from molecular dynamic simulations as well as sanders shell theory and are found to be in good agreement. results show that unlike the other beam theories, this model can capture correctly the small-scale effects on buckling strains of short cnts for the shell-type buckling. moreover, the value of nonlocal constant is calculated for cnts using molecular dynamic simulation results.