Thermoelastic fields for a heat exchanger of arbitrary shape in a bi-material infinite plane
Thermoelastic fields for a heat exchanger of arbitrary shape in a bi-material infinite plane
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DOI：
10.1016/j.ijsolstr.2023.112167
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发表时间：
2023-02
影响因子：
3.6
通讯作者：
Chunling Wu;H. Yin
中科院分区：
文献类型：
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作者：
Chunling Wu;H. Yin
当含有任意形状的多边形夹杂物的双材料具有两个节理的不同半平面时，热弹性场包括温度和位移，可以用格林函数技术用源对夹杂物的积分来推导。首先利用Hadamard正则化方法，从三维格林函数中导出两节理非相似半平面的二维热格林函数、弹性格林函数和热弹性格林函数作为相应的基本解。通过调整材料常数可以恢复半无限域和无限域的基本解。Eshelby张量是由双调和、调和和两个Boussinesq位移势函数导出的。将任意形状的换热器嵌入具有不同热、力学性能的基体中，结合连续分布的特征温度梯度和特征应变场，采用双等效夹杂法（DEIM）分别处理材料导热系数、刚度和热膨胀系数的失配问题。因此，整个热弹性场只需要在换热器上积分即可得到。本征场在指向粒子中心的泰勒级数中展开，与无限域中圆非均匀性的解析解相比，在均匀项、线性项或二次项上表现出可定制的精度。给出了嵌在无限域中的圆形非均匀性的精确热弹性解。以混凝土砌块内电热电缆为例，验证了该模型的正确性。该方法可用于包含任意形状的热交换器作为散热器或热源的薄膜。
When a bi-material with two jointed dissimilar half-planes containing an arbitrarily shaped polygonal inclusion is subjected to heat flow, the thermoelastic fields, including temperature and displacement, can be derived by the Green’s function technique with the integral of the source over the inclusion. Using Hadamard’s regularization, the two-dimensional (2D) thermal, elastic, and thermoelastic Green’s functions of two-jointed dissimilar half-planes are firstly derived from the 3D Green’s functions as the corresponding fundamental solutions. The fundamental solutions for semi-infinite and infinite domains can be recovered by adjusting the material constants. Eshelby’s tensors are derived in terms of the biharmonic, harmonic, and two Boussinesq’s displacement potential functions. When a heat exchanger of arbitrary shape is embedded in a matrix with different thermal and mechanical properties, combining a continuously distributed eigen-temperature gradient and eigenstrain field, the dual equivalent inclusion method (DEIM) is applied to handle the material mismatch of thermal conductivity, stiffness, and thermal expansion coefficient, respectively. Therefore, the full thermoelastic fields can be obtained by the integral over the heat exchanger only. The eigen-fields are expanded in the Taylor series referred to the center of the particle, which exhibits tailorable accuracy with uniform, linear or quadratic terms in comparison with the analytical solution for a circular inhomogeneity in the infinite domain. An exact thermoelastic solution of a circular inhomogeneity embedded within the infinite domain is present. The case study of an electric heat cable in the concrete block demonstrates the capability and exactness of the model. The method can be used for a thin film containing a heat exchanger of arbitrary shape as either a heat sink or source.