Group Theory Analysis Of 3D Braided Structural Composites

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.