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                <term xml:lang="en">Wachspress’ shape functions</term>
                <term xml:lang="en">Nonlinear magnetostatics</term>
                <term xml:lang="en">Multimaterial topology optimization</term>
                <term xml:lang="en">Electrical machine</term>
                <term xml:lang="en">Density methods</term>
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              <p>This work uses multi-material topology optimization (MMTO) to maximize the average torque of a 3-phase permanent magnet synchronous machine (PMSM). Eight materials are considered in the stator: air, soft magnetic steel, three electric phases, and their three returns. To address the challenge of designing a 3-phase PMSM stator, a generalized density-based framework is used. The proposed methodology places the prescribed material candidates on the vertices of a convex polytope, interpolates material properties using Wachspress shape functions, and defines Cartesian coordinates inside polytopes as design variables. A rational function is used as penalization to ensure convergence towards meaningful structures, without the use of a filtering process. The influences of different polytopes and penalization parameters are investigated. The results indicate that a hexagonal-based diamond polytope is a better choice than the classical orthogonal domains for this MMTO problem. In addition, the proposed methodology yields high-performance designs for 3-phase PMSM stators by implementing a continuation method on the electric load angle.</p>
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