【作者】 马文锁；

【导师】 冯伟；

【作者基本信息】 上海大学 ， 固体力学， 2006， 博士

【摘要】 三维编织复合材料的品种还比较少,用于描述编织几何结构的理论和系统的分类方法有待于深入研究,本文用对称群理论解决了这些问题。编织几何结构的对称性可以用对称群加以描述。用点群描述编织几何结构的点对称性,根据点对称性特征可将编织材料进行粗略分类,同时获得相应几何结构的单胞形式。用空间群描述三维编织几何结构,可以将其进行详细分类,从而推导出系列全新的编织材料几何结构。本文首先论述了与编织材料几何结构有关的对称群理论。定义了与编织材料几何结构对称群有关的对称操作和对称元素等概念;阐述了编织几何结构的对称操作的类型和表达方法;通过编织几何结构的对称性定义了编织点群、编织点阵和编织空间(平面)群;用编织材料几何结构对称操作的矩阵表示推导了编织空间点群、空间群的矩阵表示;归纳了对应编织几何结构的平面点阵和空间点阵。为了用平面点群研究二维编织几何结构的点对称性,本文定义了代表纱线段的点符号和基本对称单元等概念。在此基础上,论述了对称单元的构建方法,从而将二维编织(包括平面机织)材料按几何结构合理分类。用平面点对称操作构建相应的平面对称单元图案,得到对应不同几何结构的单胞。在分析二维编织几何结构的简化方法及与平面点阵阵点对应关系的过程中,对编织平面点阵进行总结分类。根据不同编织平面点阵的特点,归纳了二维编织几何结构惯用单胞的形状。用编织平面群分析二维编织几何结构,将二维编织几何结构进行有效分类,系统推导了二维编织几何结构。同时推导二维编织材料几何结构对应点群的矩阵表示,矩阵表示可用于编织复合材料的力学性能研究。用空间点群将三维编织几何结构分类,并将其单胞的对称性用点群进行了描述。推导了编织空间点群的矩阵表示,为将对称群变换应用到三维编织复合材料的力学性能研究打下基础。通过验证得出编织空间点群不含有纯镜面对称群元素的结论。将具有点对称性的纱线段组合用一个阵点表达,三维编织材料的几何结构就可以对应的不同空间点阵。根据不同编织空间点阵的特点,归纳了三维编织几何更多还原

【Abstract】 There are a few varieties of 3D braided structural composites, the theory of braided geometric structures and systematic classification method of 3D braided structural composites should be approached deeply. Such problems have been solved by the theory of symmetry group in this paper. The symmetries of braided geometric structure can be described with symmetry group. When point symmetries of braided geometric structures are described with point group, the braided materials are briefly classified according to their point symmetries, thereby unit-cells of braided geometric structure are derived. Space group is applied to classify 3D braided geometric structures at length, which derives fully novel geometric structures of braided structural composites.In the dissertation, the symmetry group theory of braided geometric structure has been generalized. Symmetric operations and symmetric elements of braided geometric structures are defined. Then we describe the type and expression of the symmetric operations. Braid point group, lattice and space (plane) group are defined according to the related symmetries of braided geometric structure. The matrix representations of space point group and space group on braid are derived from the matrix representations, which are symmetric operations to describe braided geometric structures. The related plane and space lattices are deduced.To describe the point symmetries of 2D braided geometric structures with plane point group,the constructional method of symmetric unit is studied by setting up point symbols representing yarn segment and applying the idea of a basic symmetric unit,therefore 2D braided geometric structures(including plain woven) are rationally classified. We obtained unit cells that satisfy various point symmetries by constructing various plane symmetry unit patterns with plane point symmetric operations.The Simplified methods of 2D braided geometric structures and their relations with plane lattice point are investigated. The braided plane lattices are summarized up and classified. According to specialties of various braided plane lattices, the shape of the regular unit cells of 2D braided geometric structures are reduced.更多还原