Abstract

The numerical analysis of electrical devices by means of Finite Element Methods (FEM) is often hindered by the need to incorporate the surrounding air. Next to the complexity of the discretisation of the air region, this exterior region has to be truncated by artificial boundaries and thereby incurring a modelling error. Even more problematic are moving parts which require tedious remeshing and remapping techniques. As an example, consider the numerical analysis of snapping magnets where an air mesh between the objects would become severely deformed. In this work, we take an alternative approach by using the Boundary Element Method (BEM) in conjunction with FEM. Whereas the solid parts of the electrical device are discretized by the FEM, which can easily account for material non-linearities (e.g., ferromagnetism, permanent magnets), the surrounding domain is represented by BEM via a surface-only discretisation. This approach significantly reduces the modelling time and avoids mesh entanglement due to large deformation or movement of the considered parts. To overcome the overall quadratic complexity of the Boundary Element Method, we have developed a massively parallel Fast Multipole Method (FMM). The formulation is capable of accurately predicting nodal forces, which are then used subsequently for an assessment of the mechanical behaviour of the devices. We have implemented the FEM-BEM coupling approach into LS-DYNA in order to simulate a wide range of multiphysic applications which involve eddy-current or magnetic effects. Taking advantage of LS-DYNA's sophisticated structural analysis capabilities and without the need to mesh the surrounding air, the simulation of magnetic metal forming processes, electromagnetic welding, inductive heating and moving magnets becomes feasible. In this work we discuss the advantages and drawbacks of the method and show how a robust, scaling implementation has been achieved. Finally, we present some benchmarks and practical examples which demonstrate the accuracy and wide range of applicability of the method.