考虑范德华力曲率效应的双壁碳纳米管外压屈曲

针对双壁碳纳米管外压屈曲问题，研究了层间范德华力的曲率效应对临界外压的影响。应用弹性双层圆柱壳模型，考虑层间范德华力不仅与层间距有关而且与挠度曲率的变化有关，导出了外压屈曲临界压力解析公式。计算得出在不同半径、不同长细比下，外压屈曲临界压力的数值结果，并与经典壳的结果和忽略范德华力曲率效应的结果做了比较。结果显示，对于小半径的双壁碳纳米管曲率效应对外压屈曲有效明显的影响。

Curvature Effect of Van Der Waals Forces on Buckling of Double-Walled Carbon Nanotubes under External Pressure

The curvature effects of interlayer van der Waals(vdW) forces on external pressure-induced buckling of a double-walled carbon nanotubes(DWNTs) were studied. The analysis was based on a double elastic shell model and assumed that the interlayer vdW pressure at a point between the inner and outer tubes depends not only on the change of interlayer spacing, but also on the change of the curvatures of inner and outer tubes at that point. An explicit formula was obtained for the external buckling pressure of DWNTs. The critical external pressure was calculated for various internal-to-external pressure ratios with various radii, with detailed comparison to the classical results and the results which neglect the curvature effects of the interlayer vdW forces. It showed that the curvature effects play a significant role in buckling problems under external pressure for small radii DWNTs.