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In structural optimization, both parameters and shape are relevant for themodel performance. Yet, conventional optimization techniques usually considereither parameters or the shape separately. This work addresses this problem byproposing a simple yet powerful approach to combine parameter and shapeoptimization in a framework using Isogeometric Analysis (IGA). The optimizationemploys sensitivity analysis by determining the gradients of an objectivefunction with respect to parameters and control points that represent thegeometry. The gradients with respect to the control points are calculated in ananalytical way using the adjoint method, which enables straightforward shapeoptimization by altering of these control points. Given that a change in asingle geometry parameter corresponds to modifications in multiple controlpoints, the chain rule is employed to obtain the gradient with respect to theparameters in an efficient semi-analytical way. The presented method isexemplarily applied to nonlinear 2D magnetostatic simulations featuring apermanent magnet synchronous motor and compared to designs, which wereoptimized using parameter and shape optimization separately. It is numericallyshown that the permanent magnet mass can be reduced and the torque ripple canbe eliminated almost completely by simultaneously adjusting rotor parametersand shape. The approach allows for novel designs to be created with thepotential to reduce the optimization time substantially.

Combined Parameter and Shape Optimization of Electric Machines with Isogeometric Analysis