三维正交机织复合材料单胞特征单元及其应用

Unit Cell Eigen-element of 3-D Orthogonal Woven Composites and Its Applications

基于三维正交机织复合材料,提出了一种特征单元均匀化分析方法。用“特征单元”来表示能够反映单胞的几何构造细节和材料构造细节的单元。首先用一般有限元方法对三维正交机织复合材料单胞进行分析得到总体刚度矩阵,利用该矩阵的特征向量建立了单胞的特征单元。通过比较特征单元的刚度矩阵元素和利用传统均匀化方法得到的刚度矩阵元素,说明了特征单元能够反应单胞的几何构造和材料构造细节。为了验证特征单元的有效性,分别用特征单元、传统均匀化方法和一般有限元方法计算了三维正交机织复合材料梁的固有频率,结果表明特征单元精度比传统均匀化方法高,而计算量比一般有限元方法大幅度降低。

As for 3 D orthogonal woven composite, a new homogenized eigen-element method is proposed in this paper. The term ‘eigen-element’means that the element can depict the characteristics of geometry and material configurations. The global stiffness matrix of 3 D orthogonal woven composite unit cell is obtained using the ordinary finite element method with the eigenvectors of the global stiffness matrix and the eigen-element of the unit cell is constructed. After comparing the stiffness matrix elements of the eigen-element with those obtained by conventional homogenization method, it＇s shown that the eigen element can depict the details of geometric and material configuration of the unit cell. In order to validate the eigen-element, the inherent frequencies of 3-D woven composite beam are computed by eigen-element method, conventional homogenization method and ordinary finite element method respectively, the results demonstrate that the eigen-element is more precise than the conventional homogenization method, and the amount of computational work reduce greatly comparing with the ordinary finite element method.