This paper presents the research on the stability analysis of carbon nanotubes (CNTs) via elastic continuum beam and shell models. The estimation of the flexural stiffness of a single-walled nanotube (SWNT) via the elastic beam model is proposed based on the postulate analyzed and provided in the paper. The validation of the stiffness is conducted with the ab initio calculations of the vibration of a SWNT. Based on the stiffness proposed, the stability analysis of CNTs is further conducted and validated with the well-cited research results by Yakobson and his collaborators. In addition, more predictions of various buckling phenomena of carbon nanotubes by beam and shell models are provided and studied. Finally, the kink phenomenon in a SWNT under pure bending is discussed via the continuum model. It is hoped that this paper will pave the way toward a better understanding of the application of continuum models in the stability and dynamics analysis of carbon nanotubes.
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