Axial buckling analysis of vertically aligned ensembles of single-walled carbon nanotubes using nonlocal discrete and continuous models

摘要

Several novel models, based on the nonlocal stress theory, on the lateral buckling of two-and three-dimensional (2D and 3D) ensembles of vertically aligned single-walled carbon nanotubes (SWCNTs) are developed. The existing van derWaals forces between the constitutive atoms of the neighboring SWCNTs are modeled by an elastic layer, and each individual SWCNT is modeled using the nonlocal Rayleigh beam theory. The governing equations for lateral buckling of both 2D and 3D SWCNTs ensembles due to axial compressive loads are derived. These are called discrete models since the lateral deformations of each SWCNT only express in terms of the longitudinal coordinate of the SWCNT. It will be revealed that the lateral deformation of SWCNTs can be also stated in terms of two and three coordinates for 2D and 3D ensembles of SWCNTs, respectively. The resulting models are called continuous models. Based on both discrete and continuous models, the critical axial buckling loads for both 2D and 3D ensembles of SWCNTs for a special case, when the outer SWCNTs are prohibited from any lateral movement, are obtained. A reasonably good agreement between the results of the discrete model and those of the continuous model is reported. Subsequently, the roles of small-scale parameter, intertube distance, and number of SWCNTs on the critical buckling loads are examined. The obtained results and the proposed models in the present work would be very helpful in design and fabrication of 2D and 3D groups of vertically aligned SWCNTs, particularly those whose main duties are to transfer securely the applied axial forces.