ABSTRACT
The investigations on carbon nanotubes behavior have been mainly focused on the experimental description and molecular dynamics simulations such as classical molecular dynamics, tight-binding molecular dynamics and the AB initio method. However, the researchers have been seeking more efficient computational methods with which it is possible to analyze the large scale of CNTs in a more general manner. Yakobson [12] found that the continuum shell model could predict all changes of buckling patterns in atomic molecular-dynamics simulations. The analogousness of the cylindrical shell model and CNTs leads to extensive application of the shell model for CNT structural analysis. Ru [57, 81] used the CM approach and stimulated the effect of van der Waals forces by applying a uniformly distributedpressure field on the wall, the pressure field was adjusted so as to give the same resultant force on each wall of the tube. It has verified that the mechanical responses of CNTs can be efficiently and reasonably predicted by the shell model provided that the parameters, such as Young’s modulus and effective wall thickness, are judiciously adopted. Wang et al. [82] studied buckling of double-walled carbon nanotubes under axial loads, by modeling CNTs using solid shell elements. Han et al. [83, 84] investigated Torsional buckling of a DWNT and MWNT embedded in an elastic medium. Han et al. [85]also studied bending instability of double-walled carbon nanotubes. Yao and Han [84]analyzed the thermal effect on axially compressed and Torsional buckling of a multi-walled carbon nano tube. Some conclusions were drawn that at low and room temperature the critical load for infinitesimal buckling of a multi-walled carbon nanotubes increases as the value of temperature change increases, while at high temperatures the critical load for infinitesimal buckling of a multi-walled carbon nanotubes decreases as the value of temperature change increases. Nonlinear post buckling behavior of carbon nanotubes under large strain is significant to which great attention is paid by some researchers [86, 87]. The Torsional post buckling behavior of single-walled or multi-walled carbon nanotubes was discussed in details by Yiao and Han [88]The problems encountered in the numerical modeling of pristine and defective carbon nanotubes were demonstrated in details by Muc [89-91]. In the mentioned references, the linear and non-linear (iterative) approaches were illustrated.
