圆形界面刚性线夹杂的平面问题

Plane Elastic Problem on the Rigid Lines Along a Circular Inclusion

研究了圆弧形界面刚性线夹杂的平面弹性问题.集中力作用于夹杂或基体中的任意点,并且无穷远处受均匀载荷作用.利用复变函数方法,得到了该问题的一般解答.当只含一条界面刚性线夹杂时,获得了分区复势函数和应力场的封闭形式解答,并给出刚性线端部奇异应力场的解析表达式.结果表明,在平面荷载下界面圆弧形刚性线夹杂尖端应力场和裂纹尖端相似具有奇异应力振荡性.对无穷远加载的情况,讨论了刚性线几何条件、加载条件和材料失配对端部场的影响.

The plane elastic problem of circular rigid line inclusions is considered. The model is subjected to remote general loads and concentrated force which is applied at an arbitrary point inside either the matrix orthe circular inclusion. Based on complex variable method, the general solutions of the problem were derived. The dosed form expressions of the sectionally holomorphic complex potentials and the stress fields were derived for the case of the interface with a single rigid line. The exact expressions of the singular stress fields at the rigid line tips were calculated which show that they possess a pronounced oscillatory character similar to that for the corresponding crack problem under plane loads. The influence of the rigid line geometry, loading conditions and material mismatch on the stress singularity coefficients is evaluated and discussed for the case of remote nuifonu load.