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采用花朵授粉算法的等几何边界元形状优化

高翔 王林军 刘洋 陈保家 付君健

高翔,王林军,刘洋,等. 采用花朵授粉算法的等几何边界元形状优化[J]. 北京航空航天大学学报,2023,49(5):1148-1155 doi: 10.13700/j.bh.1001-5965.2021.0383
引用本文: 高翔,王林军,刘洋,等. 采用花朵授粉算法的等几何边界元形状优化[J]. 北京航空航天大学学报,2023,49(5):1148-1155 doi: 10.13700/j.bh.1001-5965.2021.0383
GAO X,WANG L J,LIU Y,et al. Shape optimization of isogeometric boundary element method using flower pollination algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(5):1148-1155 (in Chinese) doi: 10.13700/j.bh.1001-5965.2021.0383
Citation: GAO X,WANG L J,LIU Y,et al. Shape optimization of isogeometric boundary element method using flower pollination algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(5):1148-1155 (in Chinese) doi: 10.13700/j.bh.1001-5965.2021.0383

采用花朵授粉算法的等几何边界元形状优化

doi: 10.13700/j.bh.1001-5965.2021.0383
基金项目: 国家自然科学基金(51975324)
详细信息
    通讯作者:

    E-mail:ljwang2006@126.com

  • 中图分类号: TH122

Shape optimization of isogeometric boundary element method using flower pollination algorithm

Funds: National Natural Science Foundation of China (51975324)
More Information
  • 摘要:

    为了避免离散整个结构,以及减少几何模型与离散模型之间的误差,提出一种改进的花朵授粉算法优化等几何边界元模型的形状优化算法。采用的边界元法仅需离散结构边界,简化了离散过程,且加入的等几何分析可提高计算精度。以最小化位移或应力为目标函数,以结构面积等于指定面积为约束条件,采用增广乘子法将约束优化模型转化为无约束优化模型;通过等几何边界元法对结构的受力情况进行分析;采用精英反向学习策略及大规模分布估计算法(LSEDA)改进花朵授粉算法,通过花朵授粉算法优化控制点的坐标值,并通过非均匀有理 B 样条(NURBS)基函数构建结构的边界,输出最优结构的形状。Ackley函数的测试结果表明:改进的花朵授粉算法14步收敛,而原始花朵授粉算法136步收敛,且所得最小值为8.881 8×10−16,小于0.001 4,改进的花朵授粉算法寻优能力更强。形状优化的计算结果表明:所提算法可有效求解二维等几何边界元形状优化问题。

     

  • 图 1  对数坐标系下的Gauss-Lévy混合模型

    Figure 1.  Gauss-Lévy mixed model in logarithmic coordinate

    图 2  改进的花朵授粉算法流程

    Figure 2.  Flow chart of improved flower pollination algorithm

    图 3  两种花朵授粉算法的对比

    Figure 3.  Comparation of two kinds of flower pollination algorithms

    图 4  本文算法流程

    Figure 4.  Flowchart of the proposed algorithm

    图 5  位移最小化

    Figure 5.  Minimization of displacement

    图 6  应力最小化

    Figure 6.  Minimization of stress

    表  1  位移算例的控制点及节点向量

    Table  1.   Control points and knot vectors for displacement example

    参数数值
    ${\boldsymbol{P}}$[0, 0; 10, 0; 20, 0; 20, 5; 20, 10; 20, 15; 20, 20;
    10, 20; 0, 20; 0, 15; 0, 10; 0, 5; 0, 0]
    ${\boldsymbol{\varXi } }$
    [0, 0, 0, 1/6, 1/6, 2/6, 2/6, 3/6, 3/6, 4/6, 4/6, 5/6, 5/6, 1, 1, 1]
    下载: 导出CSV

    表  2  应力算力的控制点及节点向量

    Table  2.   Control points and knot vectors for stress example

    参数数值
    ${\boldsymbol{P}}$[0, 0; 10, 0; 20, 0; 20, 5; 20, 10; 20, 15; 20, 20;
    10, 20; 0, 20; 0, 15; 0, 10; 0, 5; 0, 0]
    ${\boldsymbol{\varXi } }$
    [0, 0, 0, 1/8, 1/8, 2/8, 3/8, 4/8, 4/8, 5/8, 5/8, 6/8, 7/8, 1, 1, 1]
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-07-08
  • 录用日期:  2021-08-29
  • 网络出版日期:  2021-09-14
  • 整期出版日期:  2023-05-31

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