Buckling Behavior Of Carbon Nanotubes

Carbon nanotubes(CNTs), discovered in 1991 by Iijima of Japan with the high order electron microscope CNTs have very amazing mechanical, electronic, thermal and optical properties, which have been a hot topic for nano techno logy researches. Due to the large ratio of length to diameter and the hollow geometry, in particular, bulking or structure instability of CNTs has become a major topic of research among the CNTs community.Based on the minimum potential energy principle, this dissertation deals with the deformation and buckling behavior of CNTs under mechanical loads by using SQP algorithm. In order to calculate the search direction everytime, SQP algorithm just calculate the first-order partial derivatives, and calculate the second-order partial derivatives by BFGS algorithm automatically, compared with existing work, the use of memory and computational efficiency get a more optimal balance. This dissertation deals with the deformation and buckling behavior of CNTs under simple mechanical loads fistly,such as axial compression, torsion, pure bending and shear. In addition, this dissertation also investigates the deformation and buckling behavior of CNTs under combined loads, such as axial compression and torsion and axial compression and bending. The SQP algorithm is used to analyses the variation of energies with strain and the typical buckling modes.For the buckling of single-walled carbon nanotubes (SWCNTs) under simple loads, the strain energies in both states of before and after the critical point are monitored. Four typical buckling modes under different loads are presented. According to comprehensive numerical results, differences of buckling properties under axial compression, torsion, pure bending and shear are investigated in detail.For the buckling of SWCNTs under combined loads, the strain energies in both states of before and after the critical point are monitored. The buckling modes under axial compression and torsion are presented. The mechanical properties under combined loads are compared with those under corresponding pure loads.