We prove that it is possible to maintain an internal uniform hydrostatic stress field within a non-elliptical inhomogeneity in the neighborhood of a non-circular inhomogeneity when the surrounding matrix is subjected to uniform remote in-plane stresses. The non-circular inhomogeneity and the matrix have a common shear modulus but distinct Poisson's ratios. The given non-circular shapes of the inhomogeneity include a Booth's lemniscate, a generalized Booth's lemniscate and a cardioid. Our analysis indicates that the uniform hydrostatic field inside the non-elliptical inhomogeneity is unaffected by the existence of the nearby non-circular inhomogeneity whereas the non-elliptical shape of the inhomogeneity is caused solely by the presence of the non-circular inhomogeneity. Numerical examples are presented to demonstrate the general solutions obtained in each of the three non-circular shapes of the inhomogeneity.

我们证明，当周围基体受到均匀远程面内应力时，可以在非圆形不均匀性附近的非椭圆不均匀性内保持内部均匀静水应力场。非圆形不均匀性和基体具有共同的剪切模量但不同的泊松比。不均匀性的给定非圆形形状包括布斯双线、广义布斯双线和心形。我们的分析表明，非椭圆不均匀内部的均匀流体静力场不受附近非圆形不均匀存在的影响，而不均匀的非椭圆形状仅由非圆形不均匀的存在引起。