中文摘要：

首先用分子结构力学方法导出单壁碳纳米管的几何参数,用有限元法（Ansys）分别计算扶手椅型和锯齿型单壁碳纳米管（single-walled carbon nanotubes,SWCNTs）的弹性模量,并分析它们与碳纳米管半径和长度的关系;以有效弹性性能较为稳定的扶手椅型单壁碳纳米管为例,利用能量等效原理证明用连续圆筒代替原子结构碳纳米管的可行性;进而建立包含界面相的三维非贯穿连续碳纳米管圆筒增强复合材料实体模型,用纳微观均质化法计算复合材料整体有效弹性模量,分别讨论强界面结合、弱界面结合情况下界面层的长厚比、体积比、弹性模量等的变化对有效弹性模量的影响,应用含空洞、筒体、界面相、基体四相介质的经典Halpin-Tsai、Mori-Tanaka方法验证纳微观均质化计算方法的有效性。同时计算强弱界面情况沿碳纳米管长度方向碳纳米管及界面层的正应力和剪应力分布规律,阐述界面结合的强弱对复合材料承载能力的影响。

英文摘要：

The geometry parameters are determined by the molecular structural mechanics,so the relationship between effective elastic modulus and the radius and the length of nano-tube can be analyzed for armchair and zigzag single-wall nano-tube（SWNT）.The energy method is applied to prove that it is effective to instead the armchair SWNT by using the continuum hollow cylinder model.The effective elastic moduli of three-dimensional composites reinforced by the nonpenerative continuum hollow cylinder with interphase region are calculated by using the nano-microscopic homogenization method,and the effect of length-thickness ratio,volume fraction and elastic modulus of the strong and weak interfaces on effective elastic moduli are discussed,and the results are compared well with the classical Halpin-Tsai and Mori-Tanaka method with four phases medium（hollow,continuum tube,interface and matrix）.The normal stresses and shear stresses along the nano-tube are calculated to describe the influence of strong and weak interface on the loading capability for nano-composites.