Shape optimization for maximizing ferromagnetic repulsive force using shape sensitivity and adaptive level set method

It is known that the magnetic attractive force generally occurs between the magnetic materials in the magnetic field. However, the recent study reports that the ferromagnetic bodies in the magnetic field can experience the repulsive force by changing the surface shape of them. In this paper, the repulsive electromagnet in the magnetic system is optimized to generate the maximum repulsive force. Continuum design sensitivity analysis and adaptive level set method are employed for the shape optimization. Continuum design sensitivity analysis is used to derive the sensitivity formula as a closed form and to calculate the sensitivity value on the boundary of the magnetic materials for using finite element method (FEM). Adaptive level set method is used to express complicated evolving geometry because it has an advantage to reduce numerical errors of sensitivity value compared with the results of the conventional method.