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参数化水平集法在正交各向异性结构多目标拓扑优化中的应用

张建平 陈莉莉 左志坚 卢海山 刘庭显

张建平,陈莉莉,左志坚, 等. 参数化水平集法在正交各向异性结构多目标拓扑优化中的应用[J]. 机械科学与技术,2023,42(3):484-490 doi: 10.13433/j.cnki.1003-8728.20200592
引用本文: 张建平,陈莉莉,左志坚, 等. 参数化水平集法在正交各向异性结构多目标拓扑优化中的应用[J]. 机械科学与技术,2023,42(3):484-490 doi: 10.13433/j.cnki.1003-8728.20200592
ZHANG Jianping, CHEN Lili, ZUO Zhijian, LU Haishan, LIU Tingxian. Application of Parameterized Level Set Method to Multi-objective Topology Optimization of Orthotropic Structures[J]. Mechanical Science and Technology for Aerospace Engineering, 2023, 42(3): 484-490. doi: 10.13433/j.cnki.1003-8728.20200592
Citation: ZHANG Jianping, CHEN Lili, ZUO Zhijian, LU Haishan, LIU Tingxian. Application of Parameterized Level Set Method to Multi-objective Topology Optimization of Orthotropic Structures[J]. Mechanical Science and Technology for Aerospace Engineering, 2023, 42(3): 484-490. doi: 10.13433/j.cnki.1003-8728.20200592

参数化水平集法在正交各向异性结构多目标拓扑优化中的应用

doi: 10.13433/j.cnki.1003-8728.20200592
基金项目: 国家自然科学基金项目(51975503,51405415)、湖南省自然科学基金项目(2020JJ4582)及湖南省普通高校青年骨干教师培养经费(湘教通[2020]43号)
详细信息
    作者简介:

    张建平(1981−),教授,博士,研究方向为CAE理论与多学科结构优化,zhangjp@xtu.edu.cn

  • 中图分类号: TH122

Application of Parameterized Level Set Method to Multi-objective Topology Optimization of Orthotropic Structures

  • 摘要: 利用全局支撑径向基函数插值初始水平集函数,以水平集函数为设计变量,以结构柔度和散热弱度的加权函数为目标函数,基于参数化水平集法(Parameterized level set method,PLSM)建立了正交各向异性结构的热力耦合多目标拓扑优化模型。结合数值算例研究了权系数、材料方向角、泊松比因子和热导率因子对PLSM多目标最优拓扑结构和目标函数的影响,并给出了相关参数的合理取值范围;在3D打印实物的基础上完成了最优各向异性拓扑结构的性能分析,并与各向同性结构进行了对比讨论。结果表明,PLSM最优拓扑结构比变密度法的拓扑结构边界更光滑、清晰,不会出现中间密度和锯齿等现象;同时正交各向异性结构的温度场、位移场和应力场比各向同性结构均有较好地改善,加权目标函数、结构柔度和散热弱度分别降低了55%、3.18%和81.1%。
  • 图  1  全局坐标系和材料坐标系

    图  2  正交各向异性齿轮

    图  3  不同材料方向角下最优拓扑结构和加权目标函数值($w{\text{ = }}0.5$$Bt{\text{ = }}0.65$$Ht{\text{ = 0}}{\text{.5}}$

    图  4  不同泊松比因子下最优拓扑结构和加权目标函数值($w{\text{ = }}0.5$$Ht{\text{ = 0.5}}$$\theta {\text{ = }}{0}$

    图  5  不同热导率因子下最优拓扑结构和加权目标函数值($w{\text{ = }}0.5$$Bt{\text{ = }}0.65$$\theta {\text{ = }}{0 }$

    图  6  各向异性和各向同性齿轮的最优拓扑结构和3D模型

    图  7  各向异性齿轮最优拓扑结构的温度场、位移场和应力场($w{\text{ = }}0.5$$\theta {\text{ = }}{0 }$$Bt{\text{ = }}0.65$$Ht{\text{ = 0}}{\text{.1}}$

    图  8  各向同性齿轮最优拓扑结构的温度场、位移场和应力场($w{\text{ = }}0.5$$\theta {\text{ = }}{0 }$$Bt{\text{ = }}0.65$$Ht{\text{ = 0}}{\text{.1}}$

    表  1  权系数和正交各向异性参数的取值

    序号权系数$w $材料方向角θ/(°)泊松比因子Bt热导率因子Ht
    10、0.1、0.3、0.5、0.7、0.9、100.650.5
    20.50、15、30、45、60、750.650.5
    30.500.65、0.75、0.85、2、3、40.5
    40.500.650.10、0.25、0.50、2、4、10
    下载: 导出CSV

    表  2  不同权系数$w$下的最优拓扑结构 ($\theta {\text{ = }}{0 }$$Bt{\text{ = }}0.65$$Ht{\text{ = 0}}{\text{.5}}$

    $w{\text{ = }}0$$w{\text{ = }}0.1$$w{\text{ = }}0.3$$w{\text{ = }}0.5$$w{\text{ = }}0.7$$w{\text{ = }}0.9$$w{\text{ = 1}}$
    PLSM最优
    拓扑结构
    SIMP密度
    云图
    3D打印
    模型
    下载: 导出CSV

    表  3  权系数对齿轮加权目标函数、柔度和散热弱度的影响($\theta {\text{ = }}{0 }$$Bt{\text{ = }}0.65$$Ht{\text{ = 0}}{\text{.5}}$

    w0.10.30.50.70.9
    加权目标函数0.240.280.270.260.25
    柔度/Nm163.06156.59137.94131.65129.66
    散热弱度/W13.8214.0714.9516.5918.10
    下载: 导出CSV

    表  4  材料方向角对齿轮加权目标函数、柔度和散热弱度的影响 ($w{\text{ = }}0.5$$Bt{\text{ = }}0.65$$Ht{\text{ = 0}}{\text{.5}}$

    θ/(°)01530456075
    加权目标函数0.270.270.260.290.270.29
    柔度/Nm137.94138.22136.09143.56138.70144.57
    散热弱度/W14.9514.8415.0314.8114.7714.87
    下载: 导出CSV

    表  5  泊松比因子对齿轮加权目标函数、柔度和散热弱度的影响 ($w{\text{ = }}0.5$$Ht{\text{ = 0}}{\text{.5}}$$\theta {\text{ = }}{0 }$

    Bt0.650.750.85234
    加权目标函数0.270.280.300.430.500.60
    柔度/Nm137.94142.32145.78179.57199.80225.82
    散热弱度/W14.9515.0415.1716.4316.7917.29
    下载: 导出CSV

    表  6  热导率因子对齿轮加权目标函数、柔度和散热弱度的影响 ($w{\text{ = }}0.5$$Bt{\text{ = }}0.65$$\theta {\text{ = }}{0}$

    Ht0.100.250.502410
    加权目标函数0.180.220.270.430.510.62
    柔度/Nm144.77142.23137.94140.45144.68153.30
    散热弱度/W4.399.1514.9529.5134.8942.61
    下载: 导出CSV

    表  7  各向异性/各向同性齿轮的加权目标函数、柔度和散热弱度对比

    齿轮 加权目标函数柔度/Nm散热弱度/W
    各向异性0.18144.774.39
    各向同性0.40149.5223.23
    下载: 导出CSV
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  • 收稿日期:  2021-03-19
  • 刊出日期:  2023-03-25

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