We establish the uniformity of stresses inside both a non-parabolic open inhomogeneity and a non-elliptical closed inhomogeneity interacting with a nearby circular Eshelby inclusion undergoing uniform anti-plane eigenstrains when the surrounding matrix is subjected to uniform remote anti-plane stresses. Our procedure involves the introduction of a conformal mapping function for the doubly connected domain occupied by the matrix and the circular Eshelby inclusion. Two conditions are established in order to achieve the uniformity property inside each of the two inhomogeneities. Our results indicate that: (a) the internal uniform stresses are independent of the specific shapes of the two inhomogeneities and the existence of the nearby circular Eshelby inclusion; (b) the open and closed shapes of the respective inhomogeneities are significantly affected by the presence of the circular Eshelby inclusion. We also consider the two more complex cases involving: (a) an arbitrary number of circular Eshelby inclusions undergoing uniform eigenstrains; (b) a circular Eshelby inclusion undergoing linear eigenstrains. Detailed numerical results demonstrate the feasibility and effectiveness of the proposed theory.

当周围的矩阵受到均匀的远程反平面应力时，我们建立了与附近的圆形Eshelby夹杂物相互作用的非抛物线形开放非均质性和非椭圆形封闭非均质性内部应力的均匀性。我们的过程涉及为矩阵和圆形Eshelby包含所占据的双连接域引入保形映射函数。建立两个条件是为了在两个不均匀性的每一个内部实现均匀性。我们的结果表明：（a）内部均匀应力与两种不均匀性的特定形状以及附近的圆形埃舍尔比夹杂物的存在无关；（b）圆形埃舍尔比夹杂物的存在显着影响了各自不均匀性的打开和闭合形状。我们还考虑了两个更复杂的情况，其中包括：（a）任意数量的圆形Eshelby夹杂物经历均匀的本征应变；（b）经历线性特征应变的圆形Eshelby夹杂物。详细的数值结果证明了该理论的可行性和有效性。