含对称裂纹与孔洞的有界弹性圆盘的第一基本问题

The First Problem of the Elastic Disk Which Has Symmetric Holes and Cracks

主要研究了既含有裂纹又含有孔洞的有界弹性圆盘的循环对称断裂问题.运用平面弹性复变方法把满足已知边界条件的弹性平衡问题转化为解析函数边值问题,再通过引入Sherman变换,把边值问题转化为Cauchy核的奇异积分方程组.最后,利用高斯切比雪夫数值计算方法求出了此奇异积分方程组的数值解,并给出了应力强度因子的数值结果.

The circular symmetric problem which have symmetric holes and cracks in the elastic disk is discussed. By using plane elasticity complex variable method, the mathematical model can be established on boundary value problem of analytic functions. Furthermore, it can be changed into singular integral equations with Cauchy kernel by introducing Sherman transformation. Then, the numerical example is given, and the stress intensity factors can be obtained.