Axial buckling analysis of single-walled carbon nanotubes in thermal environments via the Rayleigh–Ritz technique

Axial buckling characteristics of single-walled carbon nanotubes (SWCNTs) including thermal environment effect are studied in this paper. Eringen’s nonlocal elasticity equations are incorporated into the classical Donnell shell theory to establish a nonlocal elastic shell model which takes small-scale effects into account. The Rayleigh–Ritz technique is implemented in conjunction with the set of beam functions as modal displacement functions to consider the four commonly used boundary conditions namely as simply supported–simply supported, clamped–clamped, clamped–simply supported, and clamped-free in the buckling analysis. Selected numerical results are presented to demonstrate the influences of small scale effect, aspect ratio, thermal environment effects and boundary conditions in detail. It is found that the value of aspect ratio has different effects on the critical axial buckling loads of SWCNTs in low and high temperature environments. Also, it is observed that the difference between the thermal axial buckling responses of SWCNTs relevant to various boundary conditions is more prominent for higher values of nonlocal elasticity constant.

► Development of the nonlocal Donnell shell model for buckling of single-walled carbon nanotubes in thermal environment.
► Implementation of the Rayleigh-Ritz method to analytically solve the stability problem.
► Construction of the new variational form of the field equations according to a semi-inverse method.
► Consideration of different boundary conditions and temperature fields.
► Investigation of nonlocality effects on the stability characteristics.