Structural optimization in magnetic fields using the homogenization design method

This dissertation is purposed to study the optimal topology design of structures in magnetic fields using the homogenization design method. The applications are classified into two parts: frequency response optimization of a structure which is excited by magnetic forces and magnetic energy optimization of a structure to maximize the magnetic energy/vector potential.; For the topology optimization of a structure using the homogenization design method, the accuracy of the finite element analysis is important since the homogenization design method is based on the results of the finite element analysis. A new hexahedral eight node element is formulated based on the displacement method to overcome shear and volumetric locking for the three dimensional elastic analysis. Also, another hexahedral eight node element is formulated to perform a simple, static electromagnetic analysis. The examples verifies that these formulations are effective for elastic structural analysis and magnetic field analysis.; The topology optimization of a structure which is excited by magnetic forces is an important issue to minimize the vibration/noise level of an electric machine. In this dissertation, the magnetic force is computed using the Maxwell stress method based on the finite element analysis of magnetic fields. The optimization problem is formulated to minimize the frequency response based on the homogenization design method. The examples shows that this method successfully decreased the vibration level of a structure excited by magnetic forces.; To improve the performance of electric machinery, it is necessary to obtain an optimal topology of a structure in magnetic fields to maximize the magnetic energy. In this dissertation, a design process is formulated to achieve this goal based on the homogenization design methodology. The application is possible not only for simple linear cases but also for nonlinear cases when saturation effect is considered. The examples shows that the homogenization design method can be extended to obtain the optimal topology of a structure in magnetic fields considering magnetic energy.