This paper describes an investigation into elastic buckling of an embedded multi-walled carbon nanotube under combined torsion and axial loading, which takes account of the radial constraint from the surrounding elastic medium and van der Waals force between two adjacent tube walls. Depending on the ratio of radius to thickness, the multi-walled carbon nanotubes discussed here are classified as thin, thick, and nearly solid. Critical buckling load with the corresponding mode is obtained for multi-walled carbon nanotubes under combined torsion and axial loading, with various values of the radius to thickness ratio and surrounded with different elastic media. The study indicates that the buckling mode (m, n) of an embedded multi-walled carbon nanotube under combined torsion and axial loading is unique and it is different from that with axial compression only. New features for the buckling of an embedded multi-walled carbon nanotube under combined torsion and axial loading and the meaningful numerical results are useful in the design of nanodrive device, nanotorsional oscillator and rotational actuators, where multi-walled carbon nanotubes act as basic elements.

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This paper reports the results of an investigation on combined torsional buckling of an individual multi-walled carbon nanotube (MWNT) under combined torque and axial loading. Here, a multiple shell model is adopted and the effect of van der Waals forces between two adjacent tubes is taken into account. According to the ratio of radius to thickness, MWNTs discussed in this paper are classified into three types: thin, thick and nearly solid. The critical shear stress and the combined buckling mode are calculated for three types of MWNTs under combined torque and axial loading. Results carried out show that the buckling mode (m, n) corresponding to the critical shear stress is unique, which is obviously different from the purely axial compression buckling of an individual MWNT. Numerical results also show that the critical shear stresses and the corresponding buckling modes of MWNTs under combined torque and axial loading are dependent on the axial loading form and the types of MWNTs. The new features and meaningful numerical results in the present work on combined buckling of MWNTs under combined torque and axial loading may be used as a useful reference for the designs of nano-drive devices and rotational actuators in which MWNTs act as basic elements.

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