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)，doi:10.16186/j.cnki.1673-9787-2023110038.

YU Y Q,HAN W Z,WANG C.Topology optimization of cross-plate nodes with castability consideration[J].Journal of Henan Polytechnic University(Natural Science)，doi:10.16186/j.cnki.1673-9787-2023110038.

可铸造性十字板式节点拓扑优化设计研究(网络首发)

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 十字板式节点在空间结构工程中应用广泛，采用传统结构拓扑优化方法对其构型进行优化设计后，所得优化结果往往因具有复杂几何构型而面临铸造困难。为此，引入考虑铸造约束的结构拓扑优化方法，对这一典型空间结构节点进行可铸造性结构拓扑优化设计研究。方法 在密度法框架下，以结构柔顺度最小化（等价于结构刚度最大化）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；利用密度过滤与阈值投影相结合的优化技术来减少优化设计中的中间密度单元；采用P-norm函数来解决铸造约束函数面临的可微性问题。在此基础上，分别进行了基于典型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所面临的铸造困难问题；不同脱模方向与材料体积均会导致不同的节点设计，合理的脱模方向以及充足的材料有利于获取高性能节点设计；过滤半径与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，而网格密度越细密，节点设计则越光滑。结论 本文方法获得的优化设计不仅具有创新构型且满足可铸造性要求，将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

网络首发日期：2024-03-26

Topology optimization of cross-plate nodes with castability consideration

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 nodes are widely used in spatial structural engineering. Under traditional topology optimization methods, the optimized design of such structures often features complex geometric configurations, which can lead to casting difficulties. To this end, a structural topology optimization method considering casting constraint is introduced to investigate the design castability of this type of typical spatial structure nodes. Methods Under the framework of the density-based approach, an optimization model is established to minimize structural compliance (equivalent to maximizing structural stiffness), in which both the material volume and casting constraints are considered. Density filtering combined with threshold projection is used to reduce the intermediate densities of the optimized designs. The P-norm function is employed to solve the differentiability of the casting constraint function. Then, the optimized design of typical 2D and 3D cross-plate nodes is studied. Results The results show that the application of structural topology optimization with casting constraint is an effective way to solve the casting difficulties mentioned above. Different demoulding directions and material volumes will lead to different node designs. Reasonable demoulding directions and sufficient materials will be conducive to obtaining high-performance node designs. The filter radius and mesh density mainly affect the design quality of optimized nodes. The smaller the filter radius, the finer the node design, and the finer the mesh density, the smoother the node design. Conclusions The optimized design obtained by the method here not only possesses an innovative configuration but also meets the casting requirements. This work provides a useful reference for the optimized design of cast-steel nodes with castability consideration.

Key words: Topology optimization; Cross-plate nodes; Castability; Cast-steel nodes; Spatial structure