无限域多椭圆孔多裂纹反平面问题

Antiplane Multiple Elliptical Holes and Multiple Cracks Problem of Infinite Region

运用复变函数及积分方程方法 ,求解了无限域中的多椭圆孔多裂纹反平面问题 .建立了两种类型的基本解 .利用叠加原理和所得的基本解 ,并沿椭圆孔和裂纹表面取待定的基本解密度函数 ,可得一组以基本解密度函数为未知函数的 Fredholm积分方程 .通过该方程组的数值求解可以得到密度函数的离散值 ,进而得到裂纹尖端的应力强度因子 .

By using of complex variable and integral equation methods, the antiplane multiple elliptical holes and multiple cracks problem of infinite region was considered. In order to solve the proposed problem, two kinds of elementary solution were presented. Utilizing the proposed elementary solutions and taking density functions of elementary solutions along elliptical holes and cracks surface as undetermined functions, a group of Fredholm integral equations can be established. After the numerical solution of the integral equations, the SIF values at the crack tips can be calculated.