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一种密度约束的拓扑优化方法

闫晓磊 谢露 陈佳文 花海燕 黄晓东

闫晓磊, 谢露, 陈佳文, 花海燕, 黄晓东. 一种密度约束的拓扑优化方法[J]. 机械科学与技术, 2021, 40(3): 350-355. doi: 10.13433/j.cnki.1003-8728.20200077
引用本文: 闫晓磊, 谢露, 陈佳文, 花海燕, 黄晓东. 一种密度约束的拓扑优化方法[J]. 机械科学与技术, 2021, 40(3): 350-355. doi: 10.13433/j.cnki.1003-8728.20200077
YAN Xiaolei, XIE Lu, CHEN Jiawen, HUA Haiyan, HUANG Xiaodong. A Density-constrained Topological Optimization Method[J]. Mechanical Science and Technology for Aerospace Engineering, 2021, 40(3): 350-355. doi: 10.13433/j.cnki.1003-8728.20200077
Citation: YAN Xiaolei, XIE Lu, CHEN Jiawen, HUA Haiyan, HUANG Xiaodong. A Density-constrained Topological Optimization Method[J]. Mechanical Science and Technology for Aerospace Engineering, 2021, 40(3): 350-355. doi: 10.13433/j.cnki.1003-8728.20200077

一种密度约束的拓扑优化方法

doi: 10.13433/j.cnki.1003-8728.20200077
基金项目: 

国家自然科学基金项目 51905100

福建省高校杰出青年科研人才培育计划 GY-Z160148

福建省客车及特种车辆研发协同创新中心项目 2016BJC012

闽江学者科研基金项目 GY-Z17015

详细信息
    作者简介:

    闫晓磊(1981-), 教授, 博士, 研究方向为结构创新设计与轻量化, yanxiaolei@fjut.edu.cn

  • 中图分类号: TH12

A Density-constrained Topological Optimization Method

  • 摘要: 拓扑优化方法是改善结构性能、实现结构创新设计的有效手段。本文采用浮动映射技术,提出了一种密度约束的拓扑优化(Density-constrained topology optimization, DCTO)方法。该方法不同于SIMP方法,采用线性无惩罚材料插值模型,通过准则优化,首先找到结构的最优“厚度”(材料相对密度)分布,然后通过浮动映射函数不断对材料相对密度施加约束,使其逐渐趋于0/1分布。所提出拓扑优化方法的材料相对密度直接代表了材料在结构中的“厚度”分布,其求解原理与SIMP方法有着本质区别。数值算例表明,该方法得到的拓扑结构边界更清晰、光滑,且可避免材料插值模型选取问题。
  • 图  1  DCTO方法流程

    图  2  悬臂梁设计域

    图  3  悬臂梁目标柔度C的收敛曲线

    图  4  Heaviside浮动映射函数β值的迭代图

    图  5  DCTO法优化的悬臂梁拓扑(Vf*=0.4)

    图  6  不同方法的目标柔度C的收敛曲线

    图  7  形心受集中质量的两端固支梁设计域

    图  8  不同方法目标固有频率ω的收敛曲线

    图  9  三维支座设计域

    表  1  不同方法的悬臂梁柔度优化结果对比(Vf*=0.4)

    优化方法及目标函数 优化拓扑图(深色)及其相对密度等高线图(浅色)
    SIMP (C=230.03 N·mm)
    BESO (C=202.21 N·mm)
    文本DCTO (C=199.12 N·mm)
    下载: 导出CSV

    表  2  不同方法的固支梁固有频率优化结果对比

    优化方法及目标函数 优化拓扑图(深色)及其相对密度等高线图(浅色)
    SIMP ω=783.3 rad/s
    BESO ω=825.1 rad/s
    文本DCTO ω=834.3 rad/s
    下载: 导出CSV

    表  3  DCTO方法的三维支座拓扑优化结果

    体积约束及目标柔度C 优化拓扑图(深色)及相对密度等高线图(浅色)
    Vf*=0.2
    C=196.16 N·mm
    Vf*=0.1
    C=250.50 N·mm
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-11-06
  • 刊出日期:  2021-03-01

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