力学学报 ›› 2016, Vol. 48 ›› Issue (4): 984-993.doi: 10.6052/0459-1879-15-441

• 生物、工程及交叉力学 • 上一篇    下一篇

面向连续体拓扑优化的多样性设计求解方法

王博1, 周演1, 周鸣2   

  1. 1. 大连理工大学工业装备结构分析国家重点实验室, 工程力学系, 大连 116023;
    2. 上海电气风电设备有限公司, 上海 200241
  • 收稿日期:2015-12-10 修回日期:2015-03-21 出版日期:2016-07-15 发布日期:2016-07-28
  • 通讯作者: 王博,教授,主要研究方向:结构与多学科优化、结构拓扑优化、航天先进材料与结构设计.E-mail:wangbo@dlut.edu.cn E-mail:wangbo@dlut.edu.cn
  • 基金资助:

    “973”计划(2014CB049000) 和国家自然科学基金(11372062, 11402049) 资助项目.

MULTIPLE DESIGNS APPROACH FOR CONTINUUM TOPOLOGY OPTIMIZATION

Wang Bo1, Zhou Yan1, Zhou Yiming2   

  1. 1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China;
    2. Shanghai Electric Wind Power Equipment Co. Ltd., Shanghai 200241, China
  • Received:2015-12-10 Revised:2015-03-21 Online:2016-07-15 Published:2016-07-28

摘要:

拓扑优化可以在概念设计阶段为工业产品结构的概念设计提供新颖的设计思路. 传统的连续体结构拓扑优化方法通常只能获得一个优化的拓扑构型,但在实际工程应用中,这个构型在后续设计阶段可能会由于分析模型逐步细化、设计要求的进一步明确而无法满足改变后的设计目标和约束. 针对此问题,提出了多样性设计求解方法(multiple designs approach,MDA),使得能够在优化过程中获得若干个多样性设计,以此减少在可能在设计初期由于信息不完整所带来的风险. 给出MDA 基本的优化列式,将目标函数定义为多个设计构型的目标性能加权之和,并通过加入对多样性度量的约束条件,在优化过程中驱动各个设计产生几何构型上差异. 给出了一种具体的多样性度量方法,并对其物理意义和特征进行描述和讨论. 以基于变密度法的最小柔顺性问题作为优化算例,给出了具体的优化列式及敏度推导. 在算例中,研究了目标函数和约束中不同参数对结果的影响,并对目标函数之外的其他潜在结构性能进行了讨论和比较. 结果表明,通过MDA 能够有效地给出一批多样性设计构型,为后续的精细化设计提供多种设计方案和思路.

关键词:

结构优化|拓扑优化|多样性设计|概念设计

Abstract:

Topology optimization can provide creative conceptual designs for structure of industry product in the preliminary design stage. However, the traditional topology optimization approaches focus on searching for one optimal solution which may be invalid due to the refinements of models or the additional design requirements. This paper presents the multiple designs approach (MDA) to get two or more diverse topology designs simultaneously in conceptual design, which can reduce the risk of lacking full knowledge of the designs by providing multiple designs. This paper gives general optimization model formulations for MDA in which weighting function is used as the objective function to evaluate the performances of multiple solutions and diversity measure is used as constraint to make difference between configurations. A kind of diversity measure is presented in the paper and its physical significance and features are also discussed at the same time. This paper solves two compliance minimization problems based on variable density method as examples and gives detailed optimization model formulations and sensitivity analysis. The parameters of objective function and constraints in MDA and latent performances of different solutions are also discussed in the examples. The results show that MDA could propose multiple diverse designs for detailed design stage.

Key words:

structural optimization|topology optimization|multiple design optimization|conceptual design

中图分类号: 

  • O302