Multimaterial filtering applied to the topology optimization of a permanent magnet synchronous machine

This study aims to propose a general methodology to handle multimaterial filtering for density-based topology optimization containing periodic or antiperiodic boundary conditions, which are expected to reduce the simulation time of electrical machines. The optimization of the material distribution in a permanent magnet synchronous machine rotor illustrates the relevance of this approach. Design/methodology/approach The optimization algorithm relies on an augmented Lagrangian with a projected gradient descent. The 2D finite element method computes the physical and adjoint states to evaluate the objective function and its sensitivities. Concerning regularization, a mathematical development leads to a multimaterial convolution filtering methodology that is consistent with the boundary conditions and helps eliminate artifacts. Findings The method behaves as expected and shows the superiority of multimaterial topology optimization over bimaterial topology optimization for the chosen test case. Unlike the standard approach that uses a cropped convolution kernel, the proposed methodology does not artificially reflect the limits of the simulation domain in the optimized material distribution. Originality/value Although filtering is a standard tool in topology optimization, no attention has previously been paid to the influence of periodic or antiperiodic boundary conditions when dealing with different natures of materials. The comparison between the bimaterial and multimaterial topology optimization of a permanent magnet machine rotor without symmetry constraints constitutes another originality of this work.