Derivation of Hole Sensitivity Formula for Topology Optimization in Magnetostatic System Using Virtual Hole Concept and Shape Sensitivity

In this paper, hole sensitivity formula is analytically derived for topology optimization in magnetostatic system. With the concept of virtual hole, the hole sensitivity is obtained using continuum shape sensitivity. To demonstrate the validity of the hole sensitivity, topology optimization of synchronous reluctance motor is tested. Since the hole sensitivity formula is represented only with electromagnetic field, it is easily implemented for topology optimization.

I. Introduction

In this paper, a hole sensitivity formula for electromagnetic system is analytically derived so that we can raise a possibility to arrive at the global optimal design. The hole sensitivity formula is employed as a basic information to optimize its topology. When a hole is generated inside a material region, the hole sensitivity is derived using a virtual hole concept and the continuum shape sensitivity on the surface boundary of the hole. Since this hole sensitivity formula is represented in a simple closed form and has generality for any electromagnetic system, it can be usefully applied to various problems, such as shape/topology optimizations and inverse problems in the electromagnetic system.