An inhomogeneity embedded in a continuum medium is a classical problem in solids that dates back to Maxwell, and the fields within an ellipsoidal inhomogeneity governed by temperature-independent constitutive law are well known to be uniform, rendering them important applications in composite analysis. The thermoelastic problem of an inhomogeneity in temperature-dependent medium, on the other hand, is much more difficult to analyze. Using the generalized complex variable method, the thermoelastic problem of an elliptic inhomogeneity embedded in an infinite medium has been analyzed, and the temperature and thermoelastic fields have been obtained analytically. The analytical and Numerical results show that the thermal flux within the inhomogeneity is uniform, while the thermal stress within the inhomogeneity is a quadratic function with respect to the coordinates. At the right tip of this elliptic inhomogeneity, both ${\sigma }_x$ and ${\sigma }_y$ vary nonlinearly with respect to the remote thermal loads, while ${\sigma }_{xy}$ is proportional to $J_{Qy}^{\infty }$. These results provide a powerful tool to analyze the effective behavior of temperature-independent composites.

嵌入在连续介质中的不均匀性是固体中的一个经典问题，可以追溯到麦克斯韦，并且众所周知，由温度无关本构定律控制的椭球不均匀性内的场是均匀的，这使得它们在复合分析中具有重要应用。另一方面，温度相关介质中不均匀性的热弹性问题更难以分析。利用广义复变量法，分析了无限大介质中椭圆不均匀性的热弹性问题，解析得到了温度场和热弹性场。分析和数值结果表明，不均匀性内的热通量是均匀的，而不均匀性内的热应力是关于坐标的二次函数。在这种椭圆不均匀性的右端，${\sigma }_X$ 和 ${\sigma }_{是}$ 相对于远程热负荷呈非线性变化，而 ${\sigma }_{X是}$ 正比于 $J_{问是}^{\infty }$. 这些结果为分析与温度无关的复合材料的有效行为提供了强大的工具。