In this paper, to investigate the buckling characteristics of carbon nanotubes, an equivalent beam model is first constructed. The molecular mechanics potentials in a C-C covalent bond are transformed into the form of equivalent strain energy stored in a three dimensional (3D) virtual beam element connecting two carbon atoms. Then, the equivalent stiffness parameters of the beam element can be estimated from the force field constants of the molecular mechanics theory. To evaluate the buckling loads of multi-walled carbon nanotubes, the effects of van-der Waals forces are further modeled using a newly proposed rod element. Then, the buckling characteristics of nanotubes can be easily obtained using a 3D beam and rod model of the traditional finite element method (FEM). The results of this numerical model are in good agreement with some previous results, such as those obtained from molecular dynamics computations. This method, designated as molecular structural mechanics approach, is thus proved to be an efficient means to predict the buckling characteristics of carbon nanotubes. Moreover, in the case of nanotubes with large length/diameter, the validity of Euler's beam buckling theory and a shell model with the proper material properties defined from the results of present 3D FEM beam model is investigated to reduce the computational cost. The results of these simple theoretical models are found to agree well with the existing experimental results.

Japan Atomic Energy Research Institute is constructing the International Thermonuclear Experimental Reactor common test facility for the Central Solenoid Model Coil which is around 180 tons, a forced-flow cooled magnet with the maximum pulsed operation of 2 T/s and generates the rated magnetic field of 13 T at 48 kA with stored energy of 668 MJ. The test facility consists of a coil vacuum chamber, a cryogenic system with the 5-kW refrigerator and 500-g/s cryogenic pump, two pairs of 50-kA current leads, two DC power supplies (50kA and 60kA) and two JT-60 pulsed power supplies (50 kA, k4.5 kV and k40 kA, k1.5 kV). The facility will be demonstrating the refrigeration and operation of a fusion pulsed magnet and the design and construction mill accumulate experience towards the construction of ITER.

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Based on both molecular mechanics and computational structural mechanics, a three-dimensional (3D) equivalent beam element is developed to model a C-C covalent bond on carbon nanotubes (CNTs) whereas the van der Waals forces between atoms in the different walls of multi-walled CNTs are described using a rod element. The buckling characteristics of CNTs are conveniently analyzed by using the traditional finite element method (FEM) of a 3D beam and rod model, termed as molecular structural mechanics approach (MSMA). Moreover, to model the CNTs with large length or large diameter, the validity of Euler’s beam buckling theory and a shell model with proper properties defined from the results of MSMA is investigated. The predicted results by this simple continuum mechanics approach agree well with the reported experimental data.