毛东雪, 汪文帅, 谢军. 远场载荷下含椭圆孔热电薄板的热电力耦合解析解[J]. 工程力学, 2023, 40(4): 21-34. DOI: 10.6052/j.issn.1000-4750.2021.10.0763
引用本文: 毛东雪, 汪文帅, 谢军. 远场载荷下含椭圆孔热电薄板的热电力耦合解析解[J]. 工程力学, 2023, 40(4): 21-34. DOI: 10.6052/j.issn.1000-4750.2021.10.0763
MAO Dong-xue, WANG Wen-shuai, XIE Jun. THERMOELECTRIC COUPLED ANALYTICAL SOLUTION OF THERMOELECTRIC PLATE WITH ELLIPTICAL HOLE SUBJECTED TO FAR FIELD LOAD[J]. Engineering Mechanics, 2023, 40(4): 21-34. DOI: 10.6052/j.issn.1000-4750.2021.10.0763
Citation: MAO Dong-xue, WANG Wen-shuai, XIE Jun. THERMOELECTRIC COUPLED ANALYTICAL SOLUTION OF THERMOELECTRIC PLATE WITH ELLIPTICAL HOLE SUBJECTED TO FAR FIELD LOAD[J]. Engineering Mechanics, 2023, 40(4): 21-34. DOI: 10.6052/j.issn.1000-4750.2021.10.0763

远场载荷下含椭圆孔热电薄板的热电力耦合解析解

THERMOELECTRIC COUPLED ANALYTICAL SOLUTION OF THERMOELECTRIC PLATE WITH ELLIPTICAL HOLE SUBJECTED TO FAR FIELD LOAD

  • 摘要: 该文研究了含椭圆孔的无限热电薄板在均匀电流和均匀总能量通量作用下的二维热电力耦合问题。采用复变函数法和保角映射技术,推导了电流密度和能量通量的解析解,并将椭圆孔退化为圆孔后的理论结果与均匀材料带圆孔的结果进行对比,进而验证了该文理论推导的正确性。通过已建立的二维热应力问题的复变函数方法,求解了绝缘椭圆孔干扰均匀热流引起的热应力并进行了数值分析。结果表明:在椭圆孔口轴端处出现电流密度和能量通量集中现象,当加载电流方向与长轴方向平行时,电流密度和能量通量随着椭圆孔口轴比的增大而减小;当加载电流方向与椭圆孔长轴方向不平行时,电流密度和能量通量随着椭圆孔口轴比的增大而增大,并且随着电流加载方向与椭圆孔长轴方向的夹角的增大而增大。由均匀热流引起的热应力也在椭圆孔口轴端出现应力集中现象,且随着椭圆孔口轴比以及电流加载方向与椭圆孔长轴方向的夹角的增大而增大。

     

    Abstract: The two-dimensional thermoelectric coupling problem of an infinite thermoelectric plate with elliptical hole subjected to the action of uniform electric current and uniform total energy flux is studied. The analytical solutions of the electric current density and total energy flux are derived by the complex variable function method and the conformal mapping technique. The theoretical results of the degradation of elliptical hole to circular hole are compared with the results of uniform material with circular hole, and the theoretical derivation is verified. The thermal stress caused by the interference of elliptical hole in insulation with uniform heat flow is analyzed numerically by the method of complex function. The results show that the electric current density and energy flux concentration appear at the axial end of the elliptical hole. When the loaded current direction is parallel to the long axis direction, the electric current density and energy flux decrease with the increase of the axis ratio of the elliptical hole. When they are not parallel, the electric current density and energy flux increase with the increase of the axial ratio of the elliptical hole, and increase with the increase of the angle between the direction of the loaded electric current and the long axis direction of the elliptical hole. The thermal stress caused by uniform heat flow is concentrated at the axial end of the elliptical hole. The thermal stress increases with the increase of the axial ratio of the elliptical hole and the angle between the direction of the loaded electric current and the long axis direction of the elliptical hole.

     

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