Thermal buckling of multi-walled carbon nanotubes based on a rigorous van der waals interaction

This paper reports the result of an investigation on the axially compressed buckling of multi-walled carbon nanotubes under thermal load, based on a rigorous van der Waals interaction which is dependent on the change of interlayer spacing and the radii of tubes. From the point of view of continuum modeling, each of the concentric tubes of multi-walled carbon nanotubes is considered as an individual elastic shell and coupled with any two tubes through a rigorous van der Waals interaction force. Based on this model, some example calculations are carried out to describe the effect of temperature changes and van der Waals interaction models on the axially critical load of multi-walled carbon nanotubes. Some results obtained show that the axial buckling stress of multi-walled carbon nanotubes under thermal environment is dependent on the wave number of axially buckling modes, and the wave numbers corresponding to the minimum axial stress are not unique for the multi-walled carbon nanotubes under thermal environments. On the other hand, a rigorous van der Waals interaction force can make the axially critical load of multi-walled nanotubes under thermal loading increase. The effect of thermal environments on the axially critical stress of multi-walled nanotubes gradually increases as the axial half wavenumber (m) of buckling modes increases.