An Exact Solution for Combined Loading of a Double Walled Carbon Nanotube

An exact closed form solution is presented for a case of combined loading of an initially imperfect double walled carbon nanotube. A continuum mechanics based thin shell model is used which accounts for the presence of Van der Waals forces between the walls in an approximate way. This exact solution is used to investigate the effects of axial load distribution, initial imperfections, and the transverse loading on axisymmetric buckling. It is found that the axisymmetric buckling behaviors of single walled and double walled carbon nanotubes are qualitatively similar.