发表机构
School of Mechanical Engineering, Southwest Jiaotong University; Technology and Equipment of Rail Transit Operation and Maintenance Key Laboratory of Sichuan Province, Southwest Jiaotong University; State Key Laboratory of Bridge Intelligent and Green Construction, Southwest Jiaotong University; School of Mechanical Engineering, University of Leeds（西南交通大学机械工程学院; 四川省轨道交通运营维护关键技术实验室，西南交通大学; 西南交通大学桥梁智能绿色建造全国重点实验室; 利兹大学机械工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于水平集负映射插值的多材料拓扑优化方法，通过交替活动相位算法与进化策略，消除灰色单元与材料重叠，其柔度性能与经典SIMP方法相当，可应用于二维和三维结构优化。
AI 中文摘要
为解决灰色单元和材料重叠等挑战，本文将基于水平集的负映射插值方法扩展到二维和三维宏观结构的多材料比例拓扑优化。该方法采用交替活动相位算法，将M相问题分解为用水平集函数描述的简化两相子问题；通过整合进化策略，避免了复杂的灵敏度计算；随后利用负映射插值消除界面处的材料重叠。对二维悬臂梁、MBB梁及三维悬臂梁的数值实验表明，该方法可消除灰色单元、生成光滑边界，确保材料分布无重叠，且其柔度与经典SIMP方法相当：在8个二维测试案例中，4个案例的柔度低于SIMP值，另外4个案例分别高0.3%、0.4%、4.8%和12.7%；本文还讨论了材料属性、界面处理及迭代次数对结果的影响。
英文摘要
Gray elements and material overlaps at the interfaces limit density-based multi-material topology optimization. This article extends the level set-based negative-mapping interpolation to the multi-material proportional topology optimization of macro-scale structures in two and three dimensions. An alternating active-phase algorithm decomposes M-phase problems into two-phase sub-problems described by level set functions; an evolutionary strategy removes the need for sentitivity analysis; and the negative-mapping interpolation eliminates the overlaps of the phases in the interface elements. Cantilever and half-MBB beams in two dimensions and a cantilever beam in three dimensions, with three and four material phases, give smooth boundaries, no gray elements and overlap-free designs. The compliance lies below the SIMP value in four of the eight two-dimensional cases and 0.3%, 0.4%, 4.8% and 12.7% above it in the other four. The influence of the material properties, of the interface treatment and of the algorithmic parameters is also examined.
Comments39 pages, 16 figures, 11 tables
DOI：10.1080/0305215X.2026.2746638
