粘结平面对称分叉裂纹的奇异积分方程数值解

本文对一个含分叉裂纹的弹性半平面与另一不同材料的半平面粘结的问题用复势方法化为一组三个复Caucby型奇异积分方程。采用修正的Gauss-Legendre和修正的Lobatto-Legendre数值求积法则化成一代数方程组,裂纹尖端的应力强度因子值可从代数方程组的解求得。本文计算得到了弹性半平面、刚体与弹性半平面相粘结、两种不同材料的弹性半平面相粘结的三种问题的几种几何形状的对称分叉裂纹的应力强度因子。本文的结果扩充了“应力强度因子手册”的内容。

Numerical Solutions of Singular Integral Equations for Symmetrically Branched Cracks in Two Half-Planes Bonded Together

In this paper, the problem of a branched crack in an elastic half-plane which is bonded together with another half-plane made of different material can be solved by using the method of complex potentials and by reduction to a system of three complex Cauchy-type singular integral equations. This system can be reduced to a system of linear algebraic equations by using the modified Gauss-Legendre and modified Lobatto-Legendre numerical integration rules. The values of the stress intensity factors at the crack tips can be obtained from the solution of this system of linear algebraic equations. In this paper, the va- lues of the stress intensity factors for several geometries of symmetrically bran- ched cracks have been computed for three problems, one is in an elastic half- plane, one in an elastic half-plane bonded with a rigid half-plane and one in two half-planes, which are made of different materials, bonded together. The results obtained in this paper may expand contents of "Handbook of the Stress Intensity Factors"