Derivation of a general sensitivity formula for shape optimization of 2-D magnetostatic systems by continuum approach

This paper presents a generalized sensitivity formula that is applicable to any objective function of the optimization problems in two-dimensional (2-D) linear magnetostatic systems. For the objective function defined on an interface boundary as well as in a region, the shape design sensitivity expression is derived in a closed form from the augmented Lagrangian method, the material derivative concept and the adjoint variable method. The resultant sensitivity formula is expressed as a line integral along the interface boundary undergoing shape modification. Three shape design problems, whose objective functions are defined on an interface boundary or in a region, are tested to validate the derived sensitivity formula.