In this paper, the mechanical properties, such as the axial and radial Young’s moduli, shear
moduli, buckling loads and natural frequencies, of single-walled carbon nanotubes, are estimated by a
finite element approach. Each carbon nanotube is simulated as a frame-like structure and the primary
bonds between two nearest-neighboring atoms are treated as isotropic beam members with a uniform
circular cross-section. In the modeling work, the BEAM4 element in commercial code ANSYS is
selected to simulate the carbon bonds and the atoms are nodes. As to the input parameters of the
BEAM4 element, they are determined via the concept of energy equivalence between molecular
dynamics and structural mechanics, and represented in terms of the force constants of the carbon
bonds found in molecular mechanics. Based on this modeling concept, finite element models of both
armchair and zigzag types of carbon nanotubes with different sizes are established and the mechanical
properties of these tubes are then effectively predicted. Most of the computed results which can be
compared with existing results show good agreement. Moreover, the effects of tube diameter, length
etc., on the mechanical properties are also investigated.
Free Vibration Analysis of Single-Walled Carbon Nanotubes Based on the Continuum Finite Element Method