Nonlinear postbuckling of double-walled carbon nanotubes induced by temperature changes

Different from the linear thermal buckling of carbon nanotubes with small deformation, nonlinear postbuckling induced by the temperature change can present more applicable result because of the postbuckling after the linear status. In this investigation, the nonlinear postbuckling of double-walled carbon nanotubes is studied by the nonlocal continuum model. The nonlinear large deformation is taken into account, and the thermal effects are considered. The explicit solution for the critical temperature is derived, which has the relation to the transverse deflection. From the numerical results, it can be observed that different from the linear thermal buckling, the normalized critical temperature for the nonlinear postbuckling depends on the deflection of the nanotubes and can bear more thermal loads. The small-scale effects can be enhanced by the large mode numbers, and the small-scale effects on the nonlinear postbuckling properties are significant for the short nanotubes. Moreover, the nonlinear postbuckling behaviors of short carbon nanotubes are more sensitive to the maximum deflection and mode number.