The present study has theoretically investigated the combined torsional buckling of double-walled carbon nanotubes (DWCNTs) with axial load in the multi-field coupled condition. The effects of torsion, axial load, thermal-electrical change, surrounding elastic medium and the Van der Waals forces are all taken into consideration. The governing equation of buckling for CNTs subjected to thermo-electro-mechanical loadings has been established based on an elastic shell model of continuum mechanics. Reasonable simplifications are made to get the explicit expression of the critical buckling shear stress of DWCNTs, and numerical experiments are conducted for further research. It is shown that under certain electric and temperature field the critical buckling shear stress of DWCNTs only depends on the wave number of buckling modes. On the other hand, all the related impact factors have enormous influence on the critical buckling shear stress under a certain buckling mode. The critical buckling shear stress changes linearly with the axial-to-shear stress ratio, as well as the thermal and electric change. Axial compression tends to make DWCNTs unstable, while axial tension benefits the buckling stability. The critical buckling shear stress is directly proportional to the applied voltage. At room or lower temperature, the critical shear stress for infinitesimal buckling increases as the temperature change increases, while it decreases at a higher temperature. The conclusions are useful for the design of nano-structures related to the buckling stability of DWCNTs.
