For finite element (FE) analysis of no-insulation (NI) high-temperature superconducting (HTS) pancake coils, the high aspect ratio of the turn-to-turn contact layer (T2TCL) leads to meshing difficulties which result in either poor quality mesh elements resulting in a decrease of the solution accuracy or a high number of degrees of freedom. We proposed to mitigate this issue by collapsing the T2TCL volume into a surface and using a so-called thin shell approximation (TSA). Previously, two TSA have been introduced, one to solve the heat equation and the other for an $\vec{H}-\phi$ magnetodynamic formulation. In this work, we propose to combine the magnetodynamic and thermal TSA to create a coupled magneto-thermal TSA for three-dimensional FE analysis. Particular attention is paid to the detailed derivation of the coupling terms. In the context of NI HTS pancake coils, the TSA represents the electric and thermal contact resistance of the T2TCL. For the HTS coated conductor (CC) itself, an anisotropic homogenization is used which represents its multi-layered structure. In axial and azimuthal direction, it resolves the current sharing between the HTS and other layers of the CC. The coupled TSA formulation is verified against a reference model with volumetric T2TCL. The coupled TSA is shown to significantly reduce the solution time as well as the manual effort required for high-quality meshes of the T2TCL. The implementation is open-source and a reference implementation is made publicly available.

翻译：针对无绝缘高温超导饼式线圈的有限元分析，匝间接触层的高纵横比会导致网格划分困难，进而产生低质量网格单元降低求解精度或导致自由度数量激增。为解决该问题，我们提出将匝间接触层体积坍缩为曲面并采用所谓的薄壳近似方法。此前已有两种TSA分别用于求解热传导方程和基于$\vec{H}-\phi$的磁动力学公式。本工作提出将磁动力学与热学TSA相结合，构建适用于三维有限元分析的耦合磁热薄壳近似方法，并特别关注耦合项的详细推导过程。在无绝缘高温超导饼式线圈背景下，TSA表征了匝间接触层的电接触电阻与热接触电阻。对于高温超导涂层导体本身，采用各向异性均质化方法表征其多层结构，在轴向和环向方向上解析了超导层与其他层之间的电流分配。通过具有体积化匝间接触层的参考模型验证了耦合TSA公式的准确性。研究表明，耦合TSA可显著缩短求解时间，并减少对匝间接触层高质量网格划分的人工投入。本方法的开源实现及参考代码已公开发布。