Buckling and post-buckling analyses were made of a double-walled carbon nanotube subjected to axial compression in thermal environments. The analysis was based upon a continuum mechanics model in which each tube of a double-walled carbon nanotube was described as an individual orthotropic shell with van der Waals interaction forces. The interlayer friction was negligible between the inner and outer tubes. The governing equations were based upon higher-order shear deformation shell theory with a von Kármán-Donnell type of kinematic non-linearity, and included thermal effects. Temperature-dependent material properties, which came from molecular dynamics simulations, and an initial point defect which was simulated as a dimple on the tube wall, were taken into account. A singular perturbation technique was used to determine the buckling loads and post-buckling equilibrium paths. Numerical examples concerned the post-buckling response of perfect and imperfect axially loaded armchair and zig-zag nanotubes in various thermal environments. The results revealed that a temperature change had a significant effect upon the post-buckling behavior of the single-walled carbon nanotube, but had a small effect upon the post-buckling behavior of the double-walled carbon nanotube. The single-walled nanotube had an unstable post-buckling path, and the structure was imperfection-sensitive. The double-walled carbon nanotube had a very weak snap-through post-buckling path, and the structure was essentially imperfection-insensitive.

Postbuckling Prediction of Axially Loaded Double-Walled Carbon Nanotubes with Temperature Dependent Properties and Initial Defects. H.S.Shen, C.L.Zhang: Physical Review B, 2006, 74[3], 035410. See also: International Journal of Solids and Structures, 2007, 44[5], 1461-87