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均匀化方法是一种适应于周期性构造复合材料有效性能预测的有效方法。然而均匀化方程数学表达形式复杂,均匀化方法很难直接应用通用有限元软件进行计算,因此本文中提出一种便于求解均匀化方程的边界力方法,利用高斯定理将原均匀化问题转化为普通的三维应力问题,给出了单胞中不同材料交界面上作用的面分布力形式。运用有限元软件求解了均匀化系数,预报了单向复合材料和三维四向编织复合材料的有效性能,计算结果与实验吻合很好。
Homogenization method is an effective method to predict the effective performance of periodic composite materials. However, the mathematical expression of the homogenization equation is complicated and the homogenization method is difficult to be calculated by the general finite element software directly. Therefore, a boundary force method that is easy to solve the homogenization equation is proposed in this paper. The homogenization problem is transformed into the normal The problem of three-dimensional stress is given, and the distribution of surface distributed force acting on the interface of different materials in the cell is given. Finite element software was used to solve the homogenization coefficient, and the effective performance of unidirectional composites and three-dimensional four-directional braided composites was predicted. The calculated results are in good agreement with the experimental results.