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互逆规划理论及其用于建立结构拓扑优化的合理模型

隋允康 彭细荣 叶红玲 铁军

隋允康, 彭细荣, 叶红玲, 铁军. 互逆规划理论及其用于建立结构拓扑优化的合理模型[J]. 力学学报, 2019, 51(6): 1940-1948. doi: 10.6052/0459-1879-19-259
引用本文: 隋允康, 彭细荣, 叶红玲, 铁军. 互逆规划理论及其用于建立结构拓扑优化的合理模型[J]. 力学学报, 2019, 51(6): 1940-1948. doi: 10.6052/0459-1879-19-259
Sui Yunkang, Peng Xirong, Ye Hongling, Tie Jun. RECIPROCAL PROGRAMMING THEORY AND ITS APPLICATION TO ESTABLISH A REASONABLE MODEL OF STRUCTURAL TOPOLOGY OPTIMIZATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6): 1940-1948. doi: 10.6052/0459-1879-19-259
Citation: Sui Yunkang, Peng Xirong, Ye Hongling, Tie Jun. RECIPROCAL PROGRAMMING THEORY AND ITS APPLICATION TO ESTABLISH A REASONABLE MODEL OF STRUCTURAL TOPOLOGY OPTIMIZATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6): 1940-1948. doi: 10.6052/0459-1879-19-259

互逆规划理论及其用于建立结构拓扑优化的合理模型

doi: 10.6052/0459-1879-19-259
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:

    2) 隋允康,教授,主要研究方向:结构优化. E-mail:ysui@bjut.edu.cn

    通讯作者:

    彭细荣

  • 中图分类号: O343.1

RECIPROCAL PROGRAMMING THEORY AND ITS APPLICATION TO ESTABLISH A REASONABLE MODEL OF STRUCTURAL TOPOLOGY OPTIMIZATION

  • 摘要: 在数学规划的领域里定义了互逆规划——各自目标函数与约束条件位置相互交换的一对规划. 接着指出,尽管互逆规划与对 偶规划在表面上似乎类似,但是二者存在 5 点不同:(1) 是否为同一个问题的不同;(2) 存在``对偶间隙''与否的不同;(3) 设计变量数目的不同;(4) 是否单目标与多目标问题的不同;(5) 问题合理与否的不同. 然后,基于互逆规划的定义,用以审视结 构拓扑优化模型,给出如下结果:(1) 从这个角度洞悉,在结构优化中,确实有不合理的模型一直被沿用着;(2) 找到了修正不 合理模型使之合理化的方法;(3) 对于给定体积下的柔顺度最小化 (MCVC) 模型,指出了其不合理的原因;(4) MCVC 模型实际是互 逆规划的 m 方,由此建立起其对应的 s 方, 即给出了多个柔顺度约束的体积最小化 (MVCC) 模型;(5)给出了MVCC模型中的结构 柔顺度约束的物理解释和算法,论证了 ICM (independent continuous and mapping) 方法以往关于全局化应力约束的概念和方法;(6)数值算例表明了 MCVC 与 MVCC 模型作为互逆规划的差异,且印证了 MVCC 模型的合理性.MCVC 模型在不同体积约束及多工况下不同的权系数时,得到最优拓扑不同;但 MVCC 模型在多工况柔顺度约束下可得到唯一的最优拓扑.

     

  • 1 隋允康 . 建模$\cdot $变换$\cdot $优化: 结构综合方法新进展. 大连: 大连理工大学出版社, 1996
    1 ( Sui Yunkang. Modeling, Transformation and Optimization -- New Development of Structural Synthesis Method. Dalian: Dalian University of Technology Press, 1996 (in Chinese))
    2 隋允康, 叶红玲 . 连续体结构拓扑优化的ICM方法. 北京: 科学出版社, 2013
    2 ( Sui Yunkang, Ye Hongling. Continuum Topology Optimization ICM Method. Beijing: Science Press, 2013 (in Chinese))
    3 Sui YK, Peng XR . Modeling, Solving and application for topology optimization of continuum structures, ICM Method Based on Step Function. Elsevier, 2018
    4 Fleury C. Structural weight optimization by dual methods of convex programming. International Journal for Numerical Methods in Engineering, 1979,14(2):1761-1783
    5 Fleury C. Primal and dual methods in structural optimization. Journal of the Structural Division, 1980,106(5):1117-1133
    6 Fleury C, Braibant V. Structural optimization: A new dual method using mixed variables. International Journal for Numerical Methods in Engineering, 1986,23(3):409-428
    7 钱令希, 钟万勰, 程耿东 等. 工程结构优化设计的一个新途径——序列二次规划SQP. 计算结构力学及其应用, 1984,1(1):7-20
    7 ( Qian Lingxi, Zhong Wanxie, Cheng Gendong, et al. An approach to structural optimization --- sequential quadratic programming, SQP. Computational Structural Mechanics and Applications, 1984,1(1):7-20 (in Chinese))
    8 Fleury C. CONLIN: An efficient dual optimizer based on convex approximation concepts. Structural Optimization, 1989,1(2):81-89
    9 Svanberg K. The method of moving asymptotes---a new method for structural optimization. International Journal for Numerical Methods in Engineering, 1987,24(2):359-373
    10 Beekers M, Fleury C. A primal-dual approach in truss topology optimization. Computers & Structures, 1997,64(1-4):77-88
    11 Hoppe RHW, Linsenmann C, Petrova SI. Primal-dual newton methods in structural optimization. Comput Visual Sci, 2006,9(2):71-87
    12 Bubeck S. Convex optimization: Algorithms and complexity. Foundations and Trends in Machine Learning, 2015,8(3-4):231-357
    13 隋允康, 阳志光 . 应用两点有理逼近改进的牛顿法和对偶法. 大连理工大学学报, 1994,34(1):1-9
    13 ( Sui Yunkang, Yang Zhiguang, Modified Newton's method and dual method through rational approximation at two expanded points. Journal of Dalian University of Technology, 1994,34(1):1-9 (in Chinese))
    14 隋允康, 邢誉峰, 张桂明 . 基于两点累积信息的原/倒变量展开的对偶优化方法. 力学学报, 1994,26(6):699-710
    14 ( Sui Yunkang, Xing Yifeng, Zhang Guiming, The dual optimization method by original/reciprocal variables' expansion based on cumulative information at two points. Acta Mechanica Sinica, 1994,26(6):699-710 (in Chinese))
    15 Bendsoe MP, Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 1988,71(2):197-224
    16 Rozvany G. A critical review of established methods of structural topology optimization. Structural and Multidisciplinary Optimization, 2009,37(3):217-237
    17 Sigmund O, Maute K. Topology optimization approaches. Structural and Multidisciplinary Optimization, 2013,48(6):1031-1055
    18 蔡守宇, 张卫红, 高彤 等. 基于固定网格和拓扑导数的结构拓扑优化自适应泡泡法. 力学学报, 2019,51(4):1235-1244
    18 ( Cai Shouyu, Zhang Weihong, Gao Tong, et al. Adaptive bubble method using fixed mesh and topological derivative for structural topology optimization. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(4):1235-1244 (in Chinese))
    19 Mlejnek HP. Some aspects of the genesis of structures. Structural Optimization, 1992,5(1-2):64-69
    20 Norato J, Bends?e M, Haber R, et al. A topological derivative method for topology optimization. Structural and Multidisciplinary Optimization, 2007,33(4-5):375-386
    21 Xie YM, Steven GP. A simple evolutionary procedure for structural optimization. Comput Struct, 1993,49(5):885-896
    22 Osher S, Sethian J. Fronts propagating with curvature dependent speed-algorithms based on hamilton-jacobi formulations. J Comput Phys, 1988,79(1):12-49
    23 Bourdin B, Chambolle A. Design-dependent loads in topology optimization. ESAIM: Control, Optimisation and Calculus of Variations, 2003,9(8):19-48
    24 Zhang WS, Li D, Yuan J. A new three-dimensional topology optimization method based on moving morphable components (MMCs). Computational Mechanics, 2017,59(4):647-665
    25 Yi GL, Sui YK. Different effects of economic and structural performance indicators on model construction of structural topology optimization. Acta Mechanica Sinia, 2015,9:1-12
    26 彭细荣, 隋允康 . 对连续体结构拓扑优化合理模型的再探讨. 固体力学学报, 2016,37(1):1-11
    26 ( Peng Xirong, Sui Yunkang, A further discussion on rational topology optimization models for continuum structures. Chinese Journal of Solid Mechanics, 2016,37(1):1-11 (in Chinese))
    27 隋允康, 叶红玲, 彭细荣 . 应力约束全局化策略下的连续体结构拓扑优化. 力学学报, 2006,38(3):364-370
    27 ( Sui Yunkang, Ye Hongling, Peng Xirong, Topological optimization of continuum structure under the strategy of globalization of stress constraints. Chinese Journal of Theoretical and Applied Mechanics, 2006,38(3):364-370 (in Chinese))
    28 隋允康, 彭细荣, 叶红玲 . 应力约束全局化处理的连续体结构ICM拓扑优化方法. 工程力学, 2006,23(7):1-7
    28 ( Sui Yunkang, Peng Xirong, Ye Hongling, Topology optimization of continuum structure with globalization of stress constraints by ICM method. Engineering Mechanics, 2006,23(7):1-7 (in Chinese))
    29 隋允康, 彭细荣 . 求解一类可分离凸规划的对偶显式模型DP-EM方法. 力学学报, 2017,49(5):1135-1144
    29 ( Sui Yunkang, Peng Xirong, A dual explicit model based DP-EM method for solving a class of separable convex programming. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(5):1135-1144 (in Chinese))
    30 Sui YK, Peng XR. Explicit model of dual programming and solving method for a class of separable convex programming problems. Engineering Optimization, 2019,51(7-9):1604-1625
    31 Andreassen E, Clausen A, Lazarov BS, et al. Efficient topology optimization in MATLAB using 88 lines of code. Structural Multidisciplinary Optimization, 2011,43(1):1-16
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出版历程
  • 收稿日期:  2019-09-12
  • 刊出日期:  2019-11-18

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