二维编织复合材料几何结构的平面群分析

由10个平面点群与5个平面点阵组合,推导出与二维编织复合材料几何结构有密切关系的17个平面群. 叙述了二维编织复合材料纱线段的点符号简化方法及其组合、交叉原则,以及由点符号组成的无对称单元、基本对称单元构建的方法. 阐述了从无对称单元到基本对称单元最终形成编织织物的过程. 将二维编织织物分为4种编织系,每种编织系包括若干个平面群,每个平面群对应一类编织结构,每类结构包括一种或几种编织形式,交织方法类似. 举例说明了多数平面群可能对应的编织几何结构.

Plain group analysis of 2D braided composites geometry

Seventeen plain groups, which were associated with 2D braided geometry of composites, were deduced from the combination of ten plain point groups and five plain dot lattices. The simplified method, combination and crossover principle of the point symbol on a 2D braided composites yarn segment were proposed. The construction methods of non-symmetry unit and basic symmetry unit were investigated, and the fabric-braided procedure from non-symmetry unit to basic symmetry unit was discussed. The 2D braided fabric of composites was classified four braided families, each braided family included several plain groups, each plain group was corresponding a group of braided structures, and each group of braided structures had one or several braided modes whose interwoven methods were homologous. The possible 2D braided composites geometry of majority plain groups was illustrated.