纤维增强复合材料的刚性圆柱夹杂双周期分布模型的平面问题

STUDY ON PLANE PROBLEMS OF THE FIBER-REINFORCED COMPOSITES WITH DOUBLY PERIODICAL CIRCULAR RIGID INCLUSIONS

对于硬夹杂—软基体的单向纤维增强复合材料 ,将纤维束看成刚性圆柱状夹杂 ,考虑夹杂间的相互影响 ,采用复变函数和坐标变换的方法 ,构造呈双周期分布且相互影响的刚性圆柱夹杂的复应力函数 ,同时满足夹杂的边界条件 ,利用围线积分将求解方程组化为线性代数方程组 ,推导出受到远场均匀拉应力的作用 ,双周期分布的刚性圆柱夹杂的界面应力表达式 ,算例给出双周期夹杂模型的界面应力值 。

The model of fiber-reinforced composites consisting of a continuous matrix with doubly periodical circular rigid inclusions is considered. The problem on interfacial stresses is solved accurately. By using the complex variable function integrated with the Laurent expansion method and coordinate transformation, the complex stress functions, which represent the interaction of doubly periodical circular rigid inclusions distributed in the isotropic matrix, are constructed, when boundary condition of every inclusion is satisfied. By circulation integral, the boundary equations are transformed into linear algebraic equations. Under the uniform load at infinity the interfacial stress formula and numerical results have been obtained. A comparison is made with interfacial stress maximum between different models to demonstrate the superiority of the proposed model and the accuracy of the solutions.