Buckling analysis of short carbon nanotubes based on a novel Timoshenko beam model

In this paper, we present a novel method to investigate the buckling behavior of short clamped carbon nanotubes (CNTs) with small-scale effects. Based on the nonlocal Timoshenko beam kinematics, the strain gradient theory and variational methods, the higher-order governing equation and its corresponding boundary conditions are derived, which are often not considered. Then, we solve the governing differential equation and determine exact critical buckling loads using a linear polynomial plus trigonometric functions different from the purely trigonometric series. We also investigate the influences of the scale coefficients, aspect ratio and transverse shear deformation on the buckling of short clamped CNTs. Moreover, we compare the critical strains with the results obtained from the Sanders shell theory and validate them with molecular dynamic simulations which are found to be in good agreement. The 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.