• CN:11-2187/TH
  • ISSN:0577-6686

机械工程学报 ›› 2018, Vol. 54 ›› Issue (5): 210-219.doi: 10.3901/JME.2018.05.210

• 数字化设计与制造 • 上一篇    下一篇

多工况载荷下连续体结构柔顺度拓扑优化问题的新的求解方法

俞燎宏1,2,3, 荣见华1,3, 赵志军1,3, 陈一雄1,3, 李方义1,3   

  1. 1. 长沙理工大学汽车与机械工程学院 长沙 410114;
    2. 宜春学院物理科学与工程技术学院 宜春 336000;
    3. 工程车辆轻量化与可靠性技术湖南省高校重点实验室 长沙 410114
  • 收稿日期:2017-06-12 修回日期:2017-09-19 出版日期:2018-03-05 发布日期:2018-03-05
  • 通讯作者: 荣见华(通信作者),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动力学与优化设计。E-mail:rongjhua@aliyun.com
  • 作者简介:俞燎宏,男,1982年出生,博士研究生,讲师。主要研究方向为结构动力学与优化设计。E-mail:ylh310@163.com;赵志军,男,1982年出生,博士研究生。主要研究方向为结构动力学与优化设计。E-mail:18610964@qq.com;陈一雄,男,1992年出生,硕士研究生。主要研究方向为结构动力学与优化设计。E-mail:871547967@qq.com;李方义,男,1978年出生,博士,副教授,硕士研究生导师。主要研究方向为结构动力学与优化设计,可靠分析与设计。E-mail:lfy703@sina.com
  • 基金资助:
    国家自然科学基金(11372055,11772070)和工程车辆轻量化与可靠性技术湖南省高校重点实验室(长沙理工大学)开放基金(2013KFJJ03)资助项目。

A New Solving Method of the Compliance Topology Optimization Problem of Continuum Structures under Multiple Load Cases

YU Liaohong1,2,3, RONG Jianhua1,3, ZHAO Zhijun1,3, CHEN Yixiong1,3, LI Fangyi1,3   

  1. 1. School of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha 410114;
    2. School of Physical Science and Technology, Yichun University, Yichun 336000;
    3. Key Laboratory of Lightweight and Reliability Technology for Engineering Vehicle, College of Hunan Province, Changsha 410114
  • Received:2017-06-12 Revised:2017-09-19 Online:2018-03-05 Published:2018-03-05

摘要: 针对以多工况载荷下结构柔顺度最小为目标函数,结构体积为约束条件的优化问题,提出了一种新的拓扑优化求解方法。首先,参考限界公式法,通过一个限界变量将原多个目标函数转化为约束条件,引入一个新的该限界变量的二次函数作为目标函数。同时,结合变体积约束限技术,建立新的近似拓扑优化模型。然后,基于有理近似材料模型和移动渐进线方法,给出了目标函数和约束函数及其导数的显式近似式。利用光滑化对偶算法,构建了具有收敛性的多工况载荷下连续体结构的柔顺度拓扑优化算法。给出的算例结果表明,与现有方法比,该方法可获得更优解或可高效地获得相同的优化解。且所提方法可稳健地获得清晰0/1分布的优化结构拓扑。

关键词: 对偶算法, 多目标优化, 多载荷工况, 结构柔顺度, 结构拓扑优化

Abstract: Most of engineering structures work under multiple load cases, and topology compliance minimization under multiple load cases are of important engineering value. A new compliance topology optimization method of continuum structures under multiple load cases with a volume constraint is proposed. Firstly, being referred to the bound formulation method, original multiple objective functions dealing with structural compliance under multiple load cases are transferred to multiple constraints by using a bound variable, and a novel quadratic function of the bound variable is treated as a new objective function. At the same time, being integrated with a varied volume limit scheme, a novel and equivalent approximate topology model is constructed. Then, convex and separable quadratic approximate functions for the volume and structural compliance under multiple load cases, are formed, based on the rational approximation for material properties (RAMP) and the method of moving asymptotes (MMA). The approximate optimization model is solved by adopting a smooth dual algorithm, and a new compliance topology optimization procedure, possessing convergence, is proposed. It is concluded from given examples that the proposed method is higher efficient for generating a same optimal topology, or may obtain a more optimal topology than the existed methods; and an optimal topology with clear 0/1 distribution, may robustly be obtained by the proposed method.

Key words: dual algorithm, multiple load cases, multiple objective optimization, structural compliance, structural topology optimization

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