The aim of this work is to introduce a thermo-electromagnetic model for calculating the temperature and the power dissipated in cylindrical pieces whose geometry varies with time and undergoes large deformations; the motion will be a known data. The work will be a first step towards building a complete thermo-electromagnetic-mechanical model suitable for simulating electrically assisted forming processes, which is the main motivation of the work. The electromagnetic model will be obtained from the time-harmonic eddy current problem with an in-plane current; the source will be given in terms of currents or voltages defined at some parts of the boundary. Finite element methods based on a Lagrangian weak formulation will be used for the numerical solution. This approach will avoid the need to compute and remesh the thermo-electromagnetic domain along the time. The numerical tools will be implemented in FEniCS and validated by using a suitable test also solved in Eulerian coordinates.

这项工作的目的是引入一种热电磁模型，用于计算圆柱形部件的温度和功耗，该圆柱形部件的几何形状随时间变化并发生大变形；该运动将是已知数据。这项工作将是建立适合模拟电辅助成形过程的完整热电磁机械模型的第一步，这是这项工作的主要动机。电磁模型将从具有面内电流的时谐涡流问题获得；源将以边界某些部分定义的电流或电压给出。基于拉格朗日弱公式的有限元方法将用于数值求解。这种方法将避免随着时间的推移计算和重新划分热电磁域的网格。数值工具将在 FEniCS 中实施，并通过使用也在欧拉坐标中求解的合适测试进行验证。