有限板裂纹系问题

PROBLEMS OF FINITE PLATE WITH CRACKS

本文给出了有限板裂纹系问题的复应力函数的一般表达式,把有限平面裂纹系的第一、第二基本问题归结为求解一类奇异积分方程问题,解出了有限平面一共直线和一共圆周裂纹系问题的复应力函数,并利用幂级数展开,求出一圆盘中心处含有一条直线裂纹和含有一条圆弧裂纹的复应力函数中的待定常数以及应力强度因子的解析表达式。指出有限平面的共线裂纹问题的解也可适合无限平面的共线裂纹问题,并将这两类不同性质、互为独立的问题统一起来,简化了这两种平面裂纹问题的求解。

The general problems of the finite plate with cracks are discussed and thegeneral expressions of complex stress functions are presented in this paper. Theproblems are reduced to that of solving certain singular integral equations, therebyobtaining the complex stress functions of the problems of collinear cracks and co-cir-cular cracks. Finally, the remaining coefficients of the complex stress functions ofa disk containing an internal symmetric crack and a circular arc crack are computedby means of power series, and expressions of the stress intensity factors on thecrack tips are also obtained. As radius R→∞, the above mentioned solution tendsto that for the infinite plate with cracks.