Design sensitivity for skin effect and minimum volume optimization of grounded and ungrounded shields

The aim of the present work is twofold: (a) to extend the design sensitivity analysis of finite-element eddy current formulations to the situation of constraining the total induced current by applying Ampere´s law, and (b) to present a formulation for the minimum weight optimization of magnetic shields. In the first step an existing finite-element formulation is implemented and validated with test measurements. In the second step, design sensitivity analysis is derived for this formulation. The formulation of the optimal design of a shield is based on these sensitivity calculations and solved by nonlinear programming methodologies. The formulation presented results in a large number of explicit and nonlinear constraints, which require the utilization of appropriate nonlinear programming methods. The optimization examples presented demonstrate that grounded shields are far more effective than ungrounded ones