A modified density approach for topology optimization in magnetic fields

Topology optimization has been widely used for the optimal structure design not only in elastic fields but also in electric/magnetic fields. The homogenization design method and the density approach are the representative methods in topology optimization. The purpose of this work is to suggest a modified density approach for the topology optimization in magnetic fields considering the characteristics in magnetic fields. In this work, a hole is assumed in an element based on the concept of the homogenization design method, and the density and the magnetic permeability of the element are obtained according to the size of the hole at each element while only one design variable, the element density, has been considered in the ordinary density method. It is also addressed that the appropriate value of the penalization parameter is quite different in magnetic optimization problems comparing to the value in elastic optimization problems. Numerical results according to the element density and the design domain are also discussed.