To the description of multi-layered nanotubes in models of cylindrically anisotropic elasticity

The atomic structure and mechanical behavior of multi-layered carbon nanotubes are in many ways similar to the structure and behavior of graphite single crystals. Therefore, just as various methods of discrete atomic simulation can successfully be applied to nanotubes, so also can methods of continuum mechanics be applied to carbon nanotubes with rather thick walls and diameters greater than several nanometers. In continual description of nanotubes, the model of a thin cylindrical shell has gained wide acceptance. An alternative analytical model in recent use is the model of cylindrically anisotropic hollow rods elaborated by S. Lekhnitskii in the framework of classical anisotropic elasticity. In the works based on the above model, torsion and tension problems for cylindrical tubes made of graphite-like materials with rhombohedral (in particular, hexagonal) symmetry were solved. In the paper, we perform a more thorough analysis of two different solutions of torsion and tension problems for nanotubes with two types of cylindrical anisotropy. Consideration is given to a strong dependence of the elastic characteristics of carbon nanotubes on the type of curvilinear anisotropy. In particular, it is shown that the discrepancy in the results found in relevant papers is due to the difference in the types of curvilinear anisotropy used.