两个各向异性半平面不完全周期焊接的数学问题

THE MATHEMATICAL PROBLEMS OF INCOMPLETE PERIODIC WELDING FOR TWO HALF-PLANES WITH ANISOTROPIC MEDIA

本文利用平面复变方法讨论裂纹周期分布于焊接线上的两个各向异性弹性半平面的焊接问题。将所讨论问题化为一组解析函数的边值问题,进而转化为沿焊接线的奇异积分方程组。并在焊接材料相同或为正交各向异性材料的情况下的得到了封闭形式的解。

The incomplete periodic welding problems for two half-planes with different anisotropic materials are discussed by means of method of analytic functions, Snch problems are transferred to a pair of singular integral equations. We get their solutions in closed form if the materials are orthogonal anisotropic or have the same elastic constants.