In this paper, an atomic-scale finite-element (AFE) model is proposed for single-walled carbon nanotubes (SWCNTs), which are considered to behave like space-frame structures when subjected to loadings. To create the AFE models, three-dimensional beam elements are used to model the bonds between carbon atoms as loading-carrying elements, while the nodes are placed at the locations of carbon atoms to connect the loading-carrying elements. The material properties of beam elements can be determined by using a linkage between molecular and continuum mechanics. In order to evaluate the AFE model and its performance, the influence of tube wall thickness on Young's modulus of SWCNTs is investigated. It is found that the selection of wall thickness significantly affects the magnitude of the Young's modulus. For the values of wall thickness used in this study, the obtained values of Young's modulus agree well with the corresponding theoretical results. Furthermore, the results also illustrate that Young's modulus is inversely proportional to the wall thickness. The presented results demonstrate that the proposed AFE model can be used as a valuable tool for studying the mechanical behaviour of carbon nanotubes.
Free Vibration Analysis of Single-Walled Carbon Nanotubes Based on the Continuum Finite Element Method
