Stability of Compressed Carbon Nanotubes Using Shell Models

Abstract

This paper presents some remarks on the use of shell models to analyse the stability behaviour of single-walled NTs under compression. It is shown that there are three different categories of critical buckling modes of NTs under compression: while the axi-symmetric mode is critical for very short NTs, the flexural buckling mode is critical for long tubes. While the former exhibits cross-section contour deformation but no warping deformation, the later is characterised by the opposite situation (warping deformation but no contour deformation). Additionally, a third category exists (distortional buckling): it takes place for NTs with moderate length, it is related to the transitional buckling behaviour between the shell (axi-symmetric mode) and the rod (flexural mode) and it is characterised by both cross-section contour deformation and warping deformation. Concerning the distortional buckling behaviour of moderately long NTs, it is also shown that the well known Donnell-type theory of shells leads to erroneous results.