Clustering-based topology optimization of periodic structures with variable orientations of unit cells

In recent years, topology optimization of periodic structures has become an effective approach to generating efficient designs that meet a variety of practical considerations, including manufacturability, transportability, replaceability, and ease of assembly. Traditional periodic structural optimization typically restricts designs to a uniform assembly configuration utilizing only one type of unit cell. This study proposed a novel clustering-based approach for periodic structural optimization, which allows variable orientations of individual unit cells. A dynamic k-means clustering strategy is introduced to categorize all unit cells into distinct groups and gradually eliminate less efficient unit cells from the optimized design. Meanwhile, a novel technique is introduced to identify and select more efficient orientations of unit cells during the optimization process. Several numerical examples are presented to demonstrate the effectiveness of the proposed approach. The results show that periodic structures with clustered oriented unit cells can significantly outperform their traditional periodic counterparts. This study not only incorporates assembly flexibility into periodic topology optimization but also utilizes multiple types of unit cells in a design, thereby further enhancing its structural performance.