Structural and equivalent continuum properties of single-walled carbon nanotubes

Single-walled carbon nanotubes are treated as cylindrical structures of which their extensional, torsional, and bending rigidities are investigated. Using the potential energy for interatomic forces of the molecular mechanics model, pin-jointed truss models for single-walled carbon nanotubes were created. These truss models were then used to determine the extensional, torsional, and bending rigidities for both armchair and zigzag tubes. New stiffness parameters were introduced that are independent of the cross sectional area of the nanotube. Subsequently, by treating a single-walled nanotube as an equivalent thin-walled continuum hollow cylinder, and, in addition, requiring the structural rigidities of the continuum cylinder to be equal to that of the truss model, the effective Young's modulus of the nanotube is determined after choosing the wall thickness to be 0.34 nm.