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互逆规划的拓宽和深化及其在结构拓扑优化的应用

铁军 隋允康 彭细荣

铁军, 隋允康, 彭细荣. 互逆规划的拓宽和深化及其在结构拓扑优化的应用[J]. 力学学报, 2020, 52(6): 1822-1837. doi: 10.6052/0459-1879-20-188
引用本文: 铁军, 隋允康, 彭细荣. 互逆规划的拓宽和深化及其在结构拓扑优化的应用[J]. 力学学报, 2020, 52(6): 1822-1837. doi: 10.6052/0459-1879-20-188
Tie Jun, Sui Yunkang, Peng Xirong. WIDENING AND DEEPENING OF RECIPROCAL PROGRAMMING AND ITS APPLICATION TO STRUCTURAL TOPOLOGY OPTIMIZATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(6): 1822-1837. doi: 10.6052/0459-1879-20-188
Citation: Tie Jun, Sui Yunkang, Peng Xirong. WIDENING AND DEEPENING OF RECIPROCAL PROGRAMMING AND ITS APPLICATION TO STRUCTURAL TOPOLOGY OPTIMIZATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(6): 1822-1837. doi: 10.6052/0459-1879-20-188

互逆规划的拓宽和深化及其在结构拓扑优化的应用

doi: 10.6052/0459-1879-20-188
基金项目: 1) 国家自然科学基金资助项目(11672103)
详细信息
    作者简介:

    4) 彭细荣,教授,主要研究方向:结构多学科优化. E-mail: pxr568@163.com
    3) 隋允康,教授,主要研究方向:结构多学科优化. E-mail: ysui@bjut.edu.cn;
    2) 铁军,副教授,主要研究方向:运筹学与控制论,结构多学科优化. E-mail: tielaoshi@sina.com;

    通讯作者:

    铁军

    隋允康

    铁军,隋允康,彭细荣

  • 中图分类号: O343.1

WIDENING AND DEEPENING OF RECIPROCAL PROGRAMMING AND ITS APPLICATION TO STRUCTURAL TOPOLOGY OPTIMIZATION

  • 摘要: 本文的工作涉及数学与力学两方面,数学方面:(1) 将数学规划论中新提出的互逆规划,从 s-m 型 (或称为 m-s 型) 发展出 s-s 型和 m-m 型互逆规划 (其中 s 意为单目标,m 意为多目标),从而使互逆规划的定义完备成为 3 种;(2) 从 KKT 条件审视互逆规划的两方面,得到了互逆规划双方求解涉及拟同构和拟同解的 3 个定理,并且予以证明,提供了在求解中对于互逆规划双方在求解中相互借鉴的理论基础;(3) 对一对互逆规划双方皆合理的情况和某一方不合理的情况,皆给出了求解策略和具体解法. 力学方面:(1) 给出结构优化设计模型合理与否的诠释;(2) 在互逆规划对结构拓扑优化的应用中,提出了不合理结构拓扑优化模型的求解策略;(3) 给出了借助 MVCC 模型 (多个柔顺度约束下的体积最小化) 解决 MCVC 模型 (对于给定体积下的多个柔顺度的最小化) 的途径,其中的建模基于 ICM (独立连续映射) 方法. 用 Matlab 编程给出了数值算例. 其中两个数学问题图示了互逆规划的双方关系;其中,结构拓扑优化问题是众多结构拓扑优化中的两个个案;数值结果均支持了本文提出的互逆规划理论.

     

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  • 被引次数: 0
出版历程
  • 收稿日期:  2020-06-03
  • 刊出日期:  2020-12-10

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