A Novel Derivative Free Methodology for Multi-Material Topology Optimization Based on Projective Transformations and Boolean Operations

A variety of topology optimization (TO) studies have been carried out for the design of a multi-material magnetic system including permanent magnet (PM) and back-iron structures. However, most conventional methodologies update the material distribution iteratively according to the sensitivity information, which is of low accuracy and even unavailable in some cases. Moreover, in reality, the fabrication of PMs with intricate geometries poses significant challenges. However, a limited number of the existing methodologies incorporate geometric controls within the optimization process to guarantee the manufacturability of the optimized topologies. To address the aforementioned issues, a novel derivative free multi-material TO method based on the projective transformations (PTs) and Boolean operations (BOs) is proposed. Specifically, some elementary components (ECs) are constructed and then evolved by using PT and BO to generate new topologies. Also, the mechanism that can deal with the interaction of multiple materials is developed. According to the numerical results, the proposed methodology is capable of effectively enhancing the objective function and ensuring the manufacturability of the optimized results.