Topology and Shape Optimization with Application to Electrical Machines
- 1 Introduction
- 2 Physical Background
- I Topology Optimization
- II Shape Optimization
- III Interface Handling
- IV Combined Topology and Shape Optimization with Interface Handling
The performance of an electric motor depends on the electromagnetic fields in its interior, which, among other factors, also depend on the geometry of the motor via the solution to Maxwell‘s equations. This thesis is concerned with the question of how to determine a motor geometry which is optimal with respect to a given criterion.
On the one hand, we perform shape optimization based on the concept of the shape derivative, i.e., the sensitivity of the objective function with respect to a smooth perturbation of the shape of some part of the motor. On the other hand, based on the concept of the topological derivative, we can also alter the topology of the motor by introducing new holes at points in its interior where it is beneficial for the performance. Finally, we combine these two design optimization approaches and, together with a special numerical treatment of the material interfaces, apply them to the optimization of electric motors.