Design sensitivity and LSM for topology and shape optimization in electromagnetic system

Abstract

Purpose

The purpose of this paper is to propose a level set method (LSM) for topology optimization of an electromagnetic system.

Design/methodology/approach

The classical shape optimization method has a meshing problem for shape changes and so the level set method is employed to overcome this difficulty, due to its efficient representation of evolving geometry. The velocity field is required to solve the level set equation of the Hamilton‐Jacobi equation. It is obtained using the continuum shape sensitivity in a closed form by the material derivative concept. The optimization problem is modeled as a coupled system of Poisson's equation and the level set equation. They are solved using a standard FEM in the time domain.

Findings

Numerical examples are shown to test an optimization problem in the electric and magnetic field system. The design goal is to obtain the maximum torque for an operating electrostatic actuator and synchronous reluctance motor (SynRM), respectively. The results of the optimal shape and topology for electromagnetic system are presented.

Originality/value

This paper presents a theoretical algorithm and numerical techniques for topology optimization of an electromagnetic system to generate the maximum torque using the level set method and design sensitivity analysis.

Citation

Sun Kim, Y., Ki Baek, M. and Han Park, I. (2012), "Design sensitivity and LSM for topology and shape optimization in electromagnetic system", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 31 No. 3, pp. 803-815. https://doi.org/10.1108/03321641211209717