周期性单胞复合材料有效弹性性能的边界力方法

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。 

Boundary force method to predict effective elastic properties of periodical unit cell composite material

The homogenization method has been proved to be a validated and precise method which can be used to predict the effective properties of periodical unit cell composite materials. However due to the complication of the control equation of homogenization method, the homogenization method can not be conveniently realized in commonly used finite element software. The paper describes the boundary force method based on the homogenization method. The homogenization equations were converted to a general three dimension stress problem using Gauss theory in the boundary force method. The surface distributed force of heterogenous material interface is given and the homogenization method control equation is solved by applying the surface boundary force. The effective properties of unidirectional composite material and three dimension four direction braided composite material were calculated by the boundary force method, and the results show that the predictions compare well with theoretical and experimental results.