针对小尺度碳纳米管在多物理场下的轴压屈曲问题，提出了基于非局部弹性理论耦合场作用下的力学模型．首先采用弹性壳体模型，考虑热－电－力多场耦合作用，同时计及多壁碳纳米管层间范德华力和周边弹性介质的影响，得到基于非局部弹性理论多场耦合作用下多壁碳纳米管的屈曲控制方程．并且以双壁管为例，可以得到双壁碳纳米管轴向屈曲的临界载荷的解析解，而且对其进行了数值分析，讨论了尺度效应对轴向临界屈曲载荷的影响．发现当尺度效应参数 e₀a 较大时，基于非局部弹性理论下的临界屈曲载荷与经典弹性理论得到的临界屈曲载荷相差很大，说明在小尺度范围内，经典弹性理论已经不再适用．

Aiming at the problem of the axially- compressed buckling of the small- scale carbon nanotubes in multi-physical fields,a mechanical model for the coupled fields is proposed based on the nonlocal elasticity theory.First,a buckling governing equation of the multi- walled carbon nanotubes subjected to thermo- electro- mechanical loadings is obtained based on the nonlocal elasticity theory and by using the elastic shell model,which considers the van der Waals forces between adjacent nanotubes and the effects of the surrounding elastic medium.Then,the analytical solution to the axially critical buckling load of double- walled carbon nanotubes is derived.Finally,the small- scale effects on the axially critical buckling load are discussed by means of numerical analysis.It is found that,with a large coefficient of the small- scale effects,the critical buckling load based on the nonlocal elasticity theory is markedly different from that based on the classical elasticity theory,which indicates that the classical elasticity theory is no longer applicable in a small- scale range.