Finite element model with equivalent beam elements of single-walled carbon nanotubes

Graphite sheet and single-walled carbon nanotube areintegrated through Carbon-Carbon (C---C) covalent bonds. Under the assumption ofsmall deformation, the potential of C---C bonds can be described by a harmonicfunction, with the same form as the strain energy function of beamelements, so beam elements can be used to describe C---C bonds. This paperpresents a finite element model with equivalent beam elements, which canperfectly replace the harmonic potential to describe the bond stretching,bond angle variance, inversion angle variance and torsion of the C---C bonds.By the analysis of graphite sheet under typical loads, the parameters of theequivalent beam elements and the relation of the parameters of theequivalent beam elements vs the C---C bonds are obtained. By using the model,the elastic properties for achiral nanotubes are calculated. The results arein good agreement with the existing results.