余永强, 韩文哲, 王超.可铸造性十字板式节点拓扑优化设计研究[J].河南理工大学学报（自然科学版）,2025,44(4):170-178.

YU Y Q, HAN W Z, WANG C. Topology optimization design of castable cross-plate joints [J]. Journal of Henan Polytechnic University (Natural Science) , 2025, 44(4): 170-178.

可铸造性十字板式节点拓扑优化设计研究

余永强1, 韩文哲1, 王超2

1.河南理工大学 土木工程学院， 河南 焦作  454000；2.河南大学 土木建筑学院，河南 开封  475000

摘要: 目的 采用传统结构拓扑优化方法对十字板式节点构型进行优化设计后，所得优化结果几何构型复杂，铸造困难。 方法 考虑铸造约束的结构拓扑优化，在密度法框架下，本文以结构柔顺度最小化为目标，建立同时考虑材料体积和铸造约束条件的结构拓扑优化模型；利用密度过滤和阈值投影相结合的优化技术减少优化设计中的中间密度单元；采用P-norm函数解决铸造约束函数面临的可微性问题。在此基础上，分别进行基于典型2D和3D十字板式节点的可铸造性结构拓扑优化设计对比研究。 结果 结果表明：采用集成铸造约束条件的结构拓扑优化方法，可有效解决传统十字板式节点拓扑优化设计面临的铸造困难问题；不同脱模方向和材料体积均会导致不同的节点设计，合理的脱模方向和充足的材料有利于获取高性能节点设计；过滤半径和网格密度主要影响节点的优化设计质量，过滤半径越小，节点设计越精细，网格密度越细密，节点设计越光滑。 结论 本文优化设计构型创新，满足可铸造性要求，可为可铸造性铸钢节点优化设计提供有益参考。 

关键词:拓扑优化;十字板式节点;可铸造性;铸钢节点;空间结构

doi: 10.16186/j.cnki.1673-9787.2023110038

基金项目:国家自然科学基金资助项目（11872311）；中国博士后科学基金资助项目（2022M721019，2023T160189）；河南省自然科学基金资助项目（242300421673）；河南省高等学校重点科研项目（24A130001）

收稿日期:2023/11/17

修回日期:2024/03/04

出版日期:2025/06/19

Topology optimization design of castable cross-plate joints

Yu Yongqiang1, Han Wenzhe1, Wang Chao2

1.School of Civil Engineering， Henan Polytechnic University， Jiaozuo  454000， Henan， China；2.School of Civil Engineering and Architecture， Henan University， Kaifeng  475000， Henan， China

Abstract: Objectives Cross-plate joints are widely used in spatial structures. However， traditional topology optimization methods often produce geometrically complex results that are difficult to cast. This study introduces a topology optimization approach that incorporates casting constraints to improve the castability of such joints. Methods A density-based topology optimization framework is adopted， aiming to minimize structural compliance （i.e.， maximize stiffness） while considering both material volume and casting constraints. To mitigate intermediate density issues， a combination of density filtering and threshold projection is employed. The P-norm function is introduced to address the differentiability of the casting constraint function. Optimization designs are conducted for typical 2D and 3D cross-plate joints. Results The results demonstrate that integrating casting constraints into the optimization process effectively addresses the casting challenges associated with conventional methods. Variations in demoulding direction and material volume significantly influence joint design-appropriate demoulding directions and sufficient material availability lead to high-performance outcomes. Additionally， filter radius and mesh density affect design quality： smaller filter radii yield finer designs， and denser meshes result in smoother configurations. Conclusions The proposed method produces innovative joint configurations that satisfy castability requirements. This work offers practical guidance for the castability-aware design of cast-steel joints in spatial structures. 

Key words: topology optimization; cross-plate joint; castability; cast-steel joint; spatial structure