Sensitivity Analysis Using the Virtual Work Principle for 2-D Magnetostatic Problems

The sensitivity analysis of electromagnetic quantities such as the magnetic force and torque is a crucial step when optimizing electromagnetic devices with gradient-based optimizers. This article provides an analytical derivation of those two quantities using the virtual work principle in a finite element package. It is suitable for any kind of optimization. A focus on the particular use of this sensitivity on shape optimization is presented. The development and validation of the method is detailed in this case. Finally, it is applied to the shape optimization of a switch reluctance motor (SRM) to improve its performances.