Nanotubes are the most important structural elements of nanomaterials used in nanotechnological applications and are also used in the production of nanocomposite materials. In the reinforcement (in the fibers) of the structure of composite materials, the initial curvature occurring due to structural reasons or technological processes causes the appearance of self-balancing stresses. The magnitudes of these stresses can lead to exceeding of the safety limits of the material. Therefore, theoretical investigation of the mechanical behaviors of the material, under tension and compression in the direction of the strengthening (fibers), is important for engineering. In this study, composite materials containing the double-walled nanotube are investigated in the scope of the piecewise homogeneous body model with the use of the geometric nonlinear exact equations of the three-dimensional theory of elasticity. The investigation involves stress analysis on the outer surface of the outer layer of the carbon nanotube (CNT) and on the matrix intersection, and non-ideal contact conditions between CNT and the matrix are used. Van der Waals forces which exist between the CNT walls are considered. The results include the impact of the geometric linearity and geometric nonlinearity on the parameters of the problem at the interface of the study. Numerical results on the influence of the problem parameters on the stress distribution are presented and discussed. The effect of van der Waals force on the stresses is shown by comparison with the case where the interlayer gap is disregarded and full contact between the CNT is assumed. It is seen that the maximum absolute values of the stress increase significantly when there is no van der Waals force. In addition, it has been observed that the values of the stress change monotonically with the increase of the thickness of the nanotube. Moreover, it is established that the increase of elasticity constants significantly affects the stresses.

纳米管是用于纳米技术应用的纳米材料的最重要的结构元素，也用于纳米复合材料的生产。在复合材料结构的增强（在纤维中）中，由于结构原因或工艺过程而产生的初始曲率会导致出现自平衡应力。这些应力的大小可能导致超出材料的安全极限。因此，对材料在拉伸和压缩作用下沿增强方向（纤维）的力学行为进行理论研究对于工程至关重要。在这个研究中，使用三维弹性理论的几何非线性精确方程，在分段均质体模型的范围内研究了包含双壁纳米管的复合材料。研究涉及对碳纳米管（CNT）外层的外表面以及基体相交处的应力分析，并使用了CNT与基体之间的非理想接触条件。考虑存在于CNT壁之间的范德华力。结果包括几何线性和几何非线性对研究界面问题参数的影响。给出并讨论了问题参数对应力分布影响的数值结果。与忽略层间间隙并假设CNT之间完全接触的情况相比，显示了范德华力对应力的影响。可以看出，当没有范德华力时，应力的最大绝对值显着增加。另外，已经观察到，应力的值随着纳米管的厚度的增加而单调变化。此外，已经确定，弹性常数的增加显着影响应力。已经观察到，应力的值随着纳米管的厚度的增加而单调变化。此外，已经确定，弹性常数的增加显着影响应力。已经观察到，应力的值随着纳米管的厚度的增加而单调变化。此外，已经确定，弹性常数的增加显着影响应力。