Shape sensitivity analysis of magnetic forces

This paper presents a shape sensitivity analysis of magnetic forces evaluated using the Maxwell stress tensor and the finite element method. The formulation is based upon a discrete approach which takes the analytical derivatives of the finite element equations with respect to the shape variables and also on the adjoint variable method in order to carry out the derivation procedure. Sensitivity analysis is developed in the context of the axisymmetrical nonlinear magnetostatic field problem with a modified magnetic vector potential as state variable. Numerical results are presented to validate this methodology. Shape sensitivity analysis is then applied to the optimization of the force-displacement characteristic of a linear actuator. A sequential quadratic programming method is used in the optimization process.