Shape optimization of nonlinear magnetostatic problems using the finite element method embedded in optimizer

This paper describes a second-order algorithm using the method of Lagrange multipliers by penalizing the geometric constraints and the finite element field equations. The direction of optimization is determined by a newly developed closed form evaluation of the Hessian matrix. Reluctivity curves of nonlinear iron materials are taken into account and modeled by two types of exponential functions so that at least their second-order derivatives are piece-wise continuous across the boundary of low and high magnetization regions. The algorithm has been tested on pole face optimization of a salient pole synchronous machine operating in saturation.