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 Lagr ange multipliers by penalizing the geometric constraints and the finit e element field equations. The direction of optimization is determined by a newly developed closed form evaluation of the Hessian matrix. Re luctivity curves of nonlinear iron materials are taken into account an d modeled by two types of exponential functions so that at least their second-order derivatives are piece-wise continuous across the boundar y of low and high magnetization regions. The algorithm has been tested on pole face optimization of a salient pole synchronous machine opera ting in saturation.