Optimization of a magnetic pole face using linear constraints to avoid jagged contours

Optimum design problems, with an unknown boundary which has to be optimized may not converge to any solution if no regularity constraints are imposed on that boundary. To impose these regularity conditions for finite element analysis the solution region is subdivided into subregions. Then the interior nodes or the subregion which contains the unknown boundary are constructed from the nodes of the unknown boundary using a continuous mapping, even though that boundary is not explicitly known. During the optimization process using gradient techniques the finite element model changes. Maintaining the topological properties of the mesh with the continuously changing finite element model is important to obtain accurate derivatives of the finite element solution with respect to the parameters. In some applications, the use of the above mentioned regularity constraints and topological properties may result in unrealistic solutions and shapes which cannot be practically implemented. In this paper we analyze how the application of some linear constraints on the parametrized nodes of an electromagnet pole face improve the unrealistic shape resulted from the shape optimization of the magnet for a constant flux density in the air gap