Thermoelastic analysis of infinite space containing ellipsoidal inhomogeneities

This article conducts a thermoelastic analysis of an infinite space embedded with multiple ellipsoidal inhomogeneities, which exhibit different thermal conductivity, stiffness, and thermal expansion ratios. Using the dual equivalent inclusion method (DEIM), the inhomogeneities are replaced by a matrix containing two continuously distributed eigen-fields: eigen-temperature-gradient (ETG) and eigenstrain. Unlike conventional numerical methods that rely on the volume integrals of temperature, the thermo-mechanical fields are expressed by volume integrals of eigen-fields and three Green’s functions over the inhomogeneity domains only, which exhibit significant improvement in computational efficiency. Through the DEIM, this article proves that the uniform ETG and linear eigenstrain, and linear ETG and quadratic eigenstrain are the exact solutions when an ellipsoidal inhomogeneity is subjected to a uniform far-field temperature gradient and a uniform volumetric heat source, respectively. The accuracy of the DEIM is verified <i>via</i> the finite element method through comparisons of thermoelastic fields.

本文针对内嵌多个椭球形异质体的无限大空间开展热弹性分析，这些异质体具有各不相同的热导率、刚度及热膨胀系数。借助对偶等价夹杂法（Dual Equivalent Inclusion Method，DEIM），本文将异质体等效替换为基体中包含两类连续分布的本征场的介质：本征温度梯度（Eigen-Temperature-Gradient，ETG）与本征应变。与传统依赖温度体积分的数值方法不同，本文仅需通过异质体域内本征场与三类格林函数的体积分，即可表征热-力学场，该方法在计算效率上具有显著提升。借助DEIM，本文证明了当椭球形异质体分别承受均匀远场温度梯度与均匀体热源作用时，均匀本征温度梯度与线性本征应变、线性本征温度梯度与二次本征应变分别为其精确解。本文通过有限元法对比热弹性场分布，验证了DEIM的计算精度。