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

Dipl.-Ing. Peter Gangl

Jan. 14, 2014, 1:45 p.m. S2 059

Topological sensitivities are a very useful tool for determining optimal de-
signs. The topological derivative of a domain-dependent functional represents
the sensitivity with respect to the insertion of an in nitesimally 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 lo-
cal variation of the material coecient 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 modi ed by moving a material interface along a velocity
eld which guarantees a decrease in the objective functional.