  In the present paper, a temperature-dependent meshless numerical framework
based on the thermo-related quasi-continuum constitutive model is developed for
predicting the thermal mechanical properties of single-walled carbon nanotubes
(SWCNTs) at finite temperature. The extended thermal-related higher order
Cauchy-Born (THCB) rule included second order deformation gradient relates the
deformation of bond vectors of the atomic system and that of the continuous
medium, which can capture the curvature effect of carbon nanotubes (CNTs)
conveniently. Helmholtz free energy is employed to allow for the thermal effect
of SWCNTs. In the meshless numerical implementations of the theory, the Newton
iteration method is applied to find the equilibrium configuration of a SWCNT
subjected to large deformation at a prescribed temperature only with the nodal
displace parameters as optimization variables. The finite deformation behaviors
of armchair and zigzag SWCNTs under axial compression and torsion are tested.
It is shown that the simulation results are in good agreement with those
obtained by molecular dynamic methods even with fewer meshless nodes used.
