2个正交异性半平面周期焊接的界面共线裂纹问题

The periodic welding problem by two orthotropic semi-planes with collinear cracks on the welding curve

为解决2个正交异性半平面周期焊接界面共线裂纹问题,采用复变方法和解析函数边值问题的基本理论,将正交异性弹性体内的应力和位移用2个解析Φ(z1)、Φ(z2)表示;并将定义于半平面Z+,Z-中的应力函数Φ1k(z1),Φ2k(z2)分别按照应力连续法则进行全平面扩张,则平面周期焊接界面共线裂纹问题转化为X上的Riemann边值问题.进一步根据Riemann边值问题的基本理论,利用plemelj积分公式及积分方程理论,即可以求出弹性体应力分布封闭形式解和弹性体内应力函数的解析表达式.计算实例表明,该方法简单易行且较为精确.

In order to solve the collinear crack problem of periodic welding on two orthotropic semi-planes,the complex variable method and theory of boundary value are used.The stress and displacement in the orthotropic elastic body can be expressed by two analytic functions,namely Φ（z1）,Φ（z2）,and the stress functions Φ1k（z1）,Φ2k（z2） defined in the semi-plane Z＋,Z-can be enlarged to full plane according to the law of stress continuity,and thus the collinear crack problem can be converted into the Riemann boundary value problem on X axis.Furthermore,according to the theory of Riemann boundary value,and using the formula of integration and complex variable method,the analytic functions of the stress distribution is given.The result shows that the method is simple and accurate.