Bernoulli-Euler beam theory of single-walled carbon nanotubes based on nonlinear stress-strain relationship

Recent experiments and density functional tight-binding (DFTB) calculations indicated the nonlinear elastic properties of graphene. However, this nonlinear stress-strain relationship has not been applied to the carbon nanotubes (CNTs) that can be viewed as graphene sheets that have been rolled tubes. In this paper, using the nonlinear stress-strain relationship of graphene, a new Bernoulli-Euler beam model of single-walled carbon nanotubes (SWCNTs) is presented for the first time. The static bending and the first-order mode forced vibrations of SWCNTs are investigated according to the new model. The results indicate that the nonlinear stress-strain relationship has a significant influence on the mechanical properties of SWCNTs.