探究了含有多个椭球夹杂的双材料和半无限大空间的稳态传热解. 双材料的界面由包 含连续性条件的双材料空间格林函数考虑, 通过调整参数, 该函数可退化为半无限大空间或者无限大空间格林函数. 利用 Eshelby 等效夹杂法 (equivalent inclusion method, EIM), 将椭球夹杂等效为基底材料和夹杂内连续分布的本征温度梯度场. 基于含多项式密度的椭球积分, 椭球夹杂的扰动作用由本征温度梯度场和双材料格林函数域积分精确描述. 本征场由夹杂形心展开的泰勒级数, 并通过各个夹杂形心建立的多项式等效热流方程求解, 求解精度由有限元法 (finite element method, FEM) 验证, 实现了无网格求解双材料和半无限大空间中多个椭球夹杂的稳态传热问题.

This study performed a steady-state thermal analysis of ellipsoidal inhomogeneities embedded in a bimaterial or semi-infinite domain. Because of the Green’s function of the bimaterial, the continuity conditions for the temperature and heat flux of the interface were mathematically involved. Through proper modification of the material properties, the Green’s function of the bimaterial could be reduced to semi-infinite and infinite. This study proposed the use of Eshelby’s equivalent inclusion method to simulate ellipsoidal inhomogeneities, which replaced the inhomogeneity of the matrix material containing a continuously distributed polynomial-form eigen-temperature gradient field. Based on the analytical ellipsoidal integral with polynomial density functions, the disturbance caused by inhomogeneities was analytically evaluated using the domain integrals of the eigentemperature gradient and Green’s function of the bimaterial. The eigen-temperature gradient for each inhomogeneity was described by a Taylor series expanded at the geometric center, which could then be evaluated by solving the equivalent heat flux conditions. A fi- nite element method (FEM) was used to verify the accuracy of the semi-analytical method.The study showed that mesh-free solutions to multiple ellipsoidal inhomogeneities in the bimaterial/semi-infinite domain could be achieved.