面向复杂设计域的三维薄壁-填充结构静动态多目标拓扑优化方法

doi:10.3901/JME.2025.23.193

机械工程学报 ›› 2025, Vol. 61 ›› Issue (23): 193-202.doi: 10.3901/JME.2025.23.193

• 数字化设计与制造 • 上一篇

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面向复杂设计域的三维薄壁-填充结构静动态多目标拓扑优化方法

李思奇, 刘康, 陈一铭, 蔡嘉乐, 白影春

北京理工大学电动车辆国家工程研究中心北京 100081

收稿日期:2024-12-16 修回日期:2025-04-10 发布日期:2026-01-22
作者简介:李思奇,男,1992 年出生,博士研究生。主要研究方向为多材料和薄壁填充结构拓扑结构优化。E-mail:lisiqi@bit.edu.cn
刘康,男,1997 年出生,硕士研究生。主要研究方向为汽车轻量化拓扑优化设计方法及应用。E-mail:3120200356@bit.edu.cn
陈一铭,男,2002 年出生,硕士研究生。主要研究方向为汽车结构拓扑优化设计方法及应用。E-mail:3220240415@bit.edu.cn
蔡嘉乐,男,1999 年出生,硕士研究生。主要研究方向为结构拓扑优化算法及其应用。E-mail:3220210221@bit.edu.cn
白影春(通信作者),男,1987 年出生,博士,副教授,博士研究生导师。主要研究方向为新能源汽车与高端装备结构优化设计理论及应用。E-mail:baiyc@bit.edu.cn
基金资助:
国家自然科学基金资助项目(51805032)

Static and Dynamic Muti-objective Topology Optimization of 3D Thin-walled Infill Structures Towards to Complex Design Domains

LI Siqi, LIU Kang, CHEN Yiming, CAI Jiale, BAI Yingchun

National Engineering Research Center of Electric Vehicles, Beijing Institute of Technology, Beijing 100081

Received:2024-12-16 Revised:2025-04-10 Published:2026-01-22

摘要/Abstract

摘要： 提出了一种面向复杂设计域的薄壁-填充结构静动态多目标拓扑优化方法，以实现面向三维复杂几何设计域、设计域-非设计域一体化及结构静动态性能的薄壁填充结构拓扑构型的自动获取。基于三角框重叠算法和漫水填充算法实现复杂设计域的表征，结合两步滤波法进行薄壁-填充构型特征描述，建立以结构柔度和特征频率为目标、以体积分数为约束的静动态多目标拓扑优化模型。为提高设计效率，分别采用灵活广义极小残量法(Flexible generalized minimal residual,FGMRES)和Krylov-Schur方法进行静力学控制方程和模态频率特征值方程的并行求解。在拓扑优化中，通过模态追踪策略(Modalassurance criterion,MAC)获取模态阶次，并通过移动渐近线法(Method of moving asymptotes,MMA)对优化问题进行高效求解。研究了夹紧梁在复杂设计域内多目标拓扑优化设计，验证了算法的有效性，并将其应用于悬架控制臂的设计，减重达21.24%，证明该算法在结构设计中的潜在应用价值。

关键词: 薄壁-填充结构, 复杂设计域, 拓扑优化, 静动态多目标优化, 并行计算

Abstract: In this paper, a hydrostatic and dynamic multi-objective topology optimization method for thin-walled infill structures for complex design domains is proposed, which realizes the automatic acquisition of topological configurations of thin-walled infill structures for three-dimensional complex geometric design domains, design domain-non-design domain integration, and considering the static and dynamic performance of structures. A static and dynamic multi-objective topology optimization model with structural compliance and eigenfrequency as the goal and volume fraction as the constraint is established, based on the triangle box overlap algorithm and the diffuse water filling algorithm to realize the characterization of complex design domains, combined with the two-step filtering method to describe the characteristics of thin-walled infill configuration. In order to improve the design efficiency, the Generalized minimal residual (GMRES) method and the Krylov-Schur method are used to solve the static governing equations and modal frequency eigenvalue equations in parallel, respectively. In topology optimization, the modal order is obtained by the Mode tracking strategy (MAC), and the optimization problem is efficiently solved by the Moving asymptote method (MMA). In order to verify the effectiveness of the algorithm, the multi-objective topology optimization design of a two-dimensional clamp beam with a complex design domain is studied, and the algorithm is applied to the design of the suspension control arm structure, which reduced the structural mass by 21.24%, and proved the potential application value of the algorithm in structural design.

Key words: shell-infill structures, complex design domain, topology optimization, static and dynamic multi-objective optimization, parallel computing

中图分类号:

TG156

李思奇, 刘康, 陈一铭, 蔡嘉乐, 白影春. 面向复杂设计域的三维薄壁-填充结构静动态多目标拓扑优化方法[J]. 机械工程学报, 2025, 61(23): 193-202.

LI Siqi, LIU Kang, CHEN Yiming, CAI Jiale, BAI Yingchun. Static and Dynamic Muti-objective Topology Optimization of 3D Thin-walled Infill Structures Towards to Complex Design Domains[J]. Journal of Mechanical Engineering, 2025, 61(23): 193-202.

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面向复杂设计域的三维薄壁-填充结构静动态多目标拓扑优化方法

Static and Dynamic Muti-objective Topology Optimization of 3D Thin-walled Infill Structures Towards to Complex Design Domains

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