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.

Abstract We propose a novel topology optimization method to efficiently minimize the maximum compliance for a high‐resolution model bearing uncertain external loads. Central to this approach is a modified power method that can quickly compute the maximum eigenvalue to evaluate the worst‐case compliance, enabling our method to be suitable for large‐scale topology optimization. After obtaining the worst‐case compliance, we use the adjoint variable method to perform the sensitivity analysis for updating the density variables. By iteratively computing the worst‐case compliance, performing the sensitivity analysis, and updating the density variables, our algorithm achieves the optimized models with high efficiency. The capability and feasibility of our approach are demonstrated over various large‐scale models. Typically, for a model of size 512×170×170 and 69934 loading nodes, our method took about 50 minutes on a desktop computer with an NVIDIA GTX 1080Ti graphics card with 11 GB memory.