基于连续体拓扑优化的拉/压结构设计方法

doi:10.3901/JME.2025.09.449

机械工程学报 ›› 2025, Vol. 61 ›› Issue (9): 449-460.doi: 10.3901/JME.2025.09.449

• 数字化设计与制造 • 上一篇

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基于连续体拓扑优化的拉/压结构设计方法

蔡金虎¹, 荣见华¹, 丁慧冰¹, 赵磊², 张明军¹, 赵志军³

1. 长沙理工大学汽车与机械工程学院长沙 410114;
2. 长沙理工大学土木工程学院长沙 410114;
3. 长沙学院土木工程系长沙 410076

收稿日期:2024-05-26 修回日期:2024-12-12 发布日期:2025-06-12
通讯作者: 荣见华,男,1963年出生,博士,教授,博士研究生导师。主要研究方向为结构拓扑优化,轻质材料与结构拓扑一体化设计。E-mail:rongjhua@aliyun.com E-mail:rongjhua@aliyun.com
作者简介:蔡金虎,男,1992年出生,博士。主要研究方向为结构拓扑优化。E-mail:caijinhu@csust.edu.cn
基金资助:
国家自然科学基金(12172065,12102066)、湖南省自然科学基金(2024JJ6045,2022JJ40465,2022JJ30610)和中国建筑第五工程局有限公司合作研究(2019RG088)资助项目。

Topology Optimization of Strut and Tie Structures with Multiple Tensile/compressive Asymmetry Materials

CAI Jinhu¹, RONG Jianhua¹, DING Huibing¹, ZHAO Lei², ZHANG Mingjun¹, ZHAO Zhijun³

1. School of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha, 410114;
2. School of Civil Engineering, Changsha University of Science and Technology, Changsha 410114;
3. Department of Civil Engineering, Changsha Institute, Changsha, 410076

Received:2024-05-26 Revised:2024-12-12 Published:2025-06-12

摘要/Abstract

摘要： 由具有不同拉伸和压缩性能材料组成的复合材料结构在实际工程中应用广泛，然而针对这类材料所组成的拉/压结构拓扑优化设计的研究很少，亟需深入研究。提出了一种基于纯受拉、纯受压、正交异性材料和空属性材料的四相材料模型的拉/压结构拓扑优化方法，该方法采用混合应力单元离散设计域，建立了一种基于主应力值与拉/压容限的单元拉/压状态判断准则，可以更准确地识别单元的拉/压状态，以实现基于单元应力状态的材料分布。针对多工况载荷设计，构建了基于拉/压应变能差异容差限的多工况载荷下的单元拉/压状态判断方法。采用四相材料模型进行拉/压结构设计，可以获得性能更优的设计结果。通过算例验证了所提方法设计拉/压结构的有效性，以及各参数、载荷边界及多工况条件对设计结果的影响。

关键词: 拓扑优化, 拉/压非对称材料, 主应力, 多材料结构, 混合应力单元

Abstract: Composite materials composed of materials with different tensile and compressive properties are widely used in practical engineering, however, there are few studies on the topology optimization design of tensile/compressive structures composed of such materials, and in-depth research is urgently needed. A topology optimization method for tension/compression structures based on a four phase material model consisting of pure tension, pure compression, orthotropic materials, and void property materials. is proposed. The method adopts a hybrid stress element discrete design domain and establishes a criterion for determining the tension/compression state of elements based on principal stress values and tension/compression tolerances. This can more accurately identify the tension/compression state of elements and achieve material distribution based on element stress states. For the design of multiple load cases, a method for determining the element tensile/compressive state under multiple load cases based on the tolerance limit of tensile/compressive strain energy difference is constructed. The use of four phase materials models for tensile/compressive structural design can achieve better performance design results. The effectiveness of proposed method is verified through several numerical examples, as well as the influence of various parameters, boundary conditions, and multiple load conditions on the design results.

Key words: topology optimization, tension/compression asymmetric material, principal stress, composite structures, hybrid stress element

中图分类号:

TG156

蔡金虎, 荣见华, 丁慧冰, 赵磊, 张明军, 赵志军. 基于连续体拓扑优化的拉/压结构设计方法[J]. 机械工程学报, 2025, 61(9): 449-460.

CAI Jinhu, RONG Jianhua, DING Huibing, ZHAO Lei, ZHANG Mingjun, ZHAO Zhijun. Topology Optimization of Strut and Tie Structures with Multiple Tensile/compressive Asymmetry Materials[J]. Journal of Mechanical Engineering, 2025, 61(9): 449-460.

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基于连续体拓扑优化的拉/压结构设计方法

Topology Optimization of Strut and Tie Structures with Multiple Tensile/compressive Asymmetry Materials

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