Effect of omitting terms involving tube radii difference in shell models on buckling solutions of DWNTs

Continuum cylindrical shell models have been widely applied in the buckling analysis of carbon nanotubes. An explicit expression for the critical buckling strain of double-walled carbon nanotubes (DWNTs) may be obtained based on cylindrical shell models. The expression is usually simplified by neglecting the terms involving outer and inner tube radii difference. In this brief note, we present the critical buckling strains of DWNTs with the inclusion of these terms and investigate the quantitative effect of neglecting these terms on the critical strain. It was found that the omission of the terms related to outer and inner tube radii difference leads to an overprediction of the critical buckling strain as well as a possible change in the buckling mode shape. It is also observed that the effect of the terms is especially significant for DWNTs with small inner radius but is negligible when the inner radius is relatively large.