Abstract: Presents an exact solution to the problem of an ellipsoidal inhomogeneity embedded in an infinitely extended body with imperfect interface subject to uniform shear stress at infinity. A kind of new boundary condition similar to the dislocation-like model is used. The tractions are assumed continuous across the interface, and the displacements may be discontinuous from one side to the other. With the help of Lamé functions, Papkowich-Neuber displacement potential functions are introduced. In the end, the displacements fields inside and outside the ellipsoid are obtained in explicit form, respectively. Then the stress field in the whole do main will be concluded relevantly.

Key words: ellipsoidal inhomogeneity, imperfect interface, Lamé's function

摘要： 给出了下述问题的精确解：包含椭球夹杂的无限大基体，在无限远作用剪切力的问题。文中采用了类位错型边界条件，即在边界上应力是连续的，而位移可以是不连续的。利用Lamé函数，构造了Papkowich-Neuber通解中的势函数，从而得到了椭球内外的位移场，全空间的应力场可随之导出。

关键词: 椭球夹杂, 非完善界面, Lamé函数