When an underground heat exchanger is subjected to a surface load on the ground and temperature change inside, the stress transfer between the thermal tank and the earth may cause the deformation and destruction of the tank. The bi-material thermoelastic fundamental solution of two-jointed dissimilar half-spaces is applied to elastic and thermal analysis of spherical heat storage tanks, where the continuity equations at the bi-material interface are satisfied. Using Hadamard’s regularization in the $x_3$ direction, the two-dimensional bi-material thermoelastic fundamental solution can be obtained. By changing the material constants, the fundamental solution for a semi-infinite domain or an infinite domain with a single material can be recovered. In general, the storage tanks and soil exhibits different thermal and mechanical properties. A dual equivalent inclusion method (DEIM) is proposed to simulate the material mismatch of thermal conductivity and elasticity with continuously distributed eigen-temperature-gradients and inelastic eigenstrains on the tanks, respectively. Using the analytical domain integrals, no mesh is required for inhomogeneities. Due to the boundary effects and inhomogeneity interactions, the eigen-fields are expanded at the center of each inhomogeneity using the Taylor series with tailorable accuracy. The DEIM is verified by the finite element method and demonstrated by the geothermal applications using uniform, linear, or quadratic orders of eigen-fields. For a spherical heat exchanger in an infinite homogeneous domain, DEIM provides the exact solutions of the thermoelastic fields for a uniform heat source and a uniform far-field heat flux field.

地下换热器在地面承受地表荷载和内部温度变化时，储热罐与大地之间的应力传递可能导致储罐变形和破坏。将双连接异种半空间的双材料热弹性基本解应用于球形储热罐的弹性和热分析，其中双材料界面处的连续性方程得到满足。在中使用 Hadamard 正则化$X_{\mathrm{3个}}$方向，可以获得二维双材料热弹性基本解。通过改变材料常数，可以恢复具有单一材料的半无限域或无限域的基本解。一般来说，储罐和土壤表现出不同的热和机械特性。提出了一种双等效包含方法 (DEIM) 来模拟热导率和弹性与连续分布的特征温度梯度和储罐上的非弹性特征应变的材料不匹配。使用分析域积分，不均匀性不需要网格。由于边界效应和非均匀性相互作用，使用泰勒级数以可定制的精度在每个非均匀性的中心扩展特征场。DEIM 通过有限元方法验证，并通过使用均匀、线性或二次特征场阶数的地热应用来证明。对于无限均匀域中的球形换热器，DEIM 提供了均匀热源和均匀远场热流场的热弹性场的精确解。