Buckling Temperature of a Single-Walled Carbon Nanotube Using Non local Timoshenko Beam Model

The thermal buckling of single-walled carbon nanotube (SWCNT) subjected to a uniform temperature rise is studied using Timoshenko beam model, including the effects of transverse shear deformation and rotary inertia. The governing buckling equations of SWCNT are established on the basis of nonlocal continuum theory. An analytical solution to the equations is derived for the determination of critical buckling temperature. The solution can be further reduced to obtain the results of Euler beam model. According to the analysis, for mode 4, the Euler beam model overpredicts the critical buckling temperature by 57%, 13% and 3.5% for L/d = 10, 30 and 60, respectively. The Timoshenko beam model is able to predict the buckling temperature of the SWCNT at higher-order modes with small length-to-diameter ratios. In addition, the critical buckling temperature decreases with increasing the nonlocal value.