A closed-form solution for critical buckling temperature of a single-walled carbon nanotube

In this paper, Timoshenko beam model, including the effects of transverse shear deformation and rotary inertia, is employed to study the critical buckling temperature of armchair and zigzag single-walled carbon nanotubes (SWCNTs) subjected to a uniform temperature rise. A closed-form solution for the determination of critical buckling temperature is derived. The solution can be further reduced to obtain the results of the Euler beam model. The results show that the Euler beam model overpredicts the critical buckling temperature of SWCNTs, especially at relatively small length-to-diameter ratios and higher-order modes. In addition, the critical buckling temperature of armchair and zigzag SWCNTs for the first ten modes with different length-to-diameter ratios is compared.