Torsional buckling of multi-walled carbon nanotubes under combined axial and radial loadings

Abstract

This paper investigates the torsional buckling of multi-walled carbon nanotubes under combined axial and radial loadings based on the continuum mechanics model. In particular, an explicit expression is obtained for the torsional buckling of double-walled carbon nanotubes (DWNTs) under combined loadings. Numerical results show that axial tensile stress or internal pressure will make DWNTs resist higher critical shear membrane force, while axial compressive stress or external pressure will lead to a lower critical shear membrane force. Further, for torsional buckling of DWNTs coupling with small axial stress and internal pressure or external pressure, the effect of the axial stress, internal pressure or external pressure on the critical shear membrane force is linear, and the associated buckling wave numbers are unique and the same as that under corresponding pure torque.