# Design Optimization of Electric Machines Using Shape Optimization and Sensitivity-Based Topology Optimization

## Dipl.-Ing. Peter Gangl

**Jan. 14, 2014, 12:45 p.m. S2 059**

Topological sensitivities are a very useful tool for determining optimal designs. The topological derivative of a domain-dependent functional represents the sensitivity with respect to the insertion of an infinitesimally small hole.

In the gradient-based ON/OFF method, proposed by M. Ohtake, Y. Okamoto and N. Takahashi in 2005, sensitivities of the functional with respect to a local variation of the material coeffcient are considered. We show that, in the case of a linear state equation, these two kinds of sensitivities coincide. For the sensitivities computed in the ON/OFF method the generalization to the case of a nonlinear state equation is straightforward, whereas the computation of topological derivatives in the nonlinear case is more involved. We will show numerical results obtained by applying the ON/OFF method in the nonlinear case to the optimization of an electric motor.

Moreover, we will address the same problem by means of shape optimization where the geometry is modified by moving a material interface along a velocity field which guarantees a decrease in the objective functional.