颗粒增强复合材料的椭圆形刚性夹杂呈双周期分布模型的反平面问题研究

THE ANTI-PLANE PROBLEM OF PARTICLE-REINFORCED COMPOSITE MATERIALS WITH DOUBLY PERIODIC ELLIPTICAL RIGID INCLUSIONS

在遵循复合材料中各夹杂相互影响的重要条件下 ,构造呈双周期分布且相互影响的椭圆形刚性夹杂模型的复应力函数 ,采用坐标变换和复变函数的依次保角映射方法 ,达到满足各个夹杂的边界条件 ,利用围线积分将求解方程化为线性代数方程 ,推导出了在无穷远双向均匀剪切 ,椭圆形刚性夹杂呈双周期分布的界面应力解析表达式 ,最后的算例分析给出了夹杂的形状对界面应力最大值 (应力集中系数 )的影响规律 。

According to the principle of interaction among the i nclusions in composites,complex stress functions, which reflect the interaction of doubly periodical elliptical rigid inclusions distributed in the isotropic matrix and satisfy the boundary condition of every inclusion, are con structed by means of coordinate transformation an d conformal mapping. By circulatio n integral, the linear algebraic equations are solved. Under the load of anti-plane shear in the infinite plane of isotropic elastic matrix, the interface stress formula , the numerical results and the graph, which ref le ct the variation of the interface stress maximum with the shape of inclus ions , have been obtained.