Topology Optimization of Self-supporting Structures for Additive Manufacturing via Implicit B-spline Representations

Owing to the rapid development in additive manufacturing, the potential to fabricate intricate structures has become a reality, emphasizing the importance of designing structures conducive to additive manufacturing processes. A crucial consideration is the ability to design structures requiring no additional support during manufacturing. This paper employs implicit B-spline representations for self-supporting structure design by integrating a topology optimization model with self-supporting constraints derived analytically from the implicit representation. This analytical derivation for detecting overhang regions enables accurate and efficient calculation of constraints, outperforming other B-spline-based methods. Compared to the traditional voxel-based methods, the implicit B-spline representation significantly expedites the optimization process by reducing the number of design variables. Additionally, several acceleration techniques are implemented to enhance the efficiency of our method, allowing simulations of 3D models with millions of finite elements to be completed within one and half an hour, excelling other B-spline-based methods and voxel-based methods. Various numerical experiments validate its excellent performance, confirming the effectiveness and efficiency of the proposed algorithm.