含圆形弹性夹杂的反平面问题级数解法  

The solution of series of the anti-plane problem on a circular elastic inclusion in an infinite body

作　　者：王明斌[1] 王兆清[1] 任宗强[2] 

机构地区：[1]山东建筑大学理学院,山东济南250101 [2]南昌大学经济与管理学院,江西南昌330031

出　　处：《山东建筑大学学报》2006年第5期442-444,454,共4页Journal of Shandong Jianzhu University

摘　　要：研究了含一个圆形弹性夹杂的纵向剪切问题。运用复变函数的级数展开技术,将问题转化为线性方程组的求解。数值结果表明:界面径向应力随两相材料剪切模量之比呈单调递增的关系;基体界面环向应力随两相材料剪切模量之比也呈单调递增的关系;夹杂界面环向应力随两相材料剪切模量之比呈单调递减的关系;根据两相材料剪切模量之比不同的,基体的最大径向应力和环向应力随距离圆心距离的不同呈现相反的趋势;而夹杂内的应力和到圆心的距离无关。An infinite solid containing a circular elastic inclusion under longitudinal shear is dealt with. By using the technique of the complex series expansion, the problem can be converted to solve a set of linear algebraic equations. The numerical results indicate that the values of the interfacial radial stresses increase with the increase of the ratio of the shear modulus between matrix and inclusion, the interfacial tangential stresses of the matrix conform to the above law, the interfacial tangential stresses of the inclusion are opposite to the above law, the values of the maximum radial and tangential stresses of the matrix with the distance from the center of a circular have different change law. The stresses in the inclusion are irrelevant to the distance from the center of a circular.

关 键 词：圆形弹性夹杂 反平面问题 界面应力 复势方法 

分 类 号：O343.2[理学—固体力学]