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金字塔点阵单元力学性能多目标优化

张坤 李建 卢福聪

张坤,李建,卢福聪. 金字塔点阵单元力学性能多目标优化[J]. 机械科学与技术,2024,43(5):882-890 doi: 10.13433/j.cnki.1003-8728.20220249
引用本文: 张坤,李建,卢福聪. 金字塔点阵单元力学性能多目标优化[J]. 机械科学与技术,2024,43(5):882-890 doi: 10.13433/j.cnki.1003-8728.20220249
ZHANG Kun, LI Jian, LU Fucong. Multi-objective Optimization of Mechanical Performance of Pyramid Lattice Element[J]. Mechanical Science and Technology for Aerospace Engineering, 2024, 43(5): 882-890. doi: 10.13433/j.cnki.1003-8728.20220249
Citation: ZHANG Kun, LI Jian, LU Fucong. Multi-objective Optimization of Mechanical Performance of Pyramid Lattice Element[J]. Mechanical Science and Technology for Aerospace Engineering, 2024, 43(5): 882-890. doi: 10.13433/j.cnki.1003-8728.20220249

金字塔点阵单元力学性能多目标优化

doi: 10.13433/j.cnki.1003-8728.20220249
基金项目: 国家自然科学基金项目(12002093)、广西自然基金项目(2018GXNSFBA281199)及中物院总体工程研究所科技专项(2020KJZ02)
详细信息
    作者简介:

    张坤,硕士研究生,15290420180@163.com

    通讯作者:

    卢福聪,讲师,硕士生导师, fuconglu@gxu.edu.cn

  • 中图分类号: O342

Multi-objective Optimization of Mechanical Performance of Pyramid Lattice Element

  • 摘要: 本文以金字塔点阵单元的平压与剪切比极限承载力作为优化目标,基于遗传算法(GA)和响应面法(RSM)对结构参数进行多目标优化,并对优化结果进行有限元和试验验证。研究结果表明:基于遗传算法预测的优化结构与一般结构相比,其平压与剪切比极限承载力预测结果分别提高了30.1%和91.6%;在优化结果验证方面,通过有限元分析得到的优化结构平压和剪切比极限承载力分别提高了39.7%和90.5%;通过试验获得最优结构的平压比极限承载力较一般结构提高了44%。有限元分析和试验均验证了本文优化方法的有效性,可将其推广应用于点阵结构的优化设计。
  • 图  1  点阵单元几何模型

    Figure  1.  Geometric model of lattice element

    图  2  点阵单元平压加载示意图

    Figure  2.  Schematic diagram of uniaxial compression of lattice element

    图  3  点阵单元剪切加载示意图

    Figure  3.  Schematic diagram of lattice element shear loading

    图  4  3D打印材料的应力-应变曲线

    Figure  4.  Stress-strain curve of 3D printed materials

    图  5  点阵单元平压极限比承载力图

    Figure  5.  Ultimate specific bearing capacity of lattice element under uniaxial compression

    图  6  点阵单元剪切极限比承载力图

    Figure  6.  Ultimate specific bearing capacity of lattice element under shear loading

    图  7  一般结构与优化结构的平压加载图

    Figure  7.  The uniaxial compression of conventional structure and optimal structure

    图  8  试验的一般结构与优化结构平压比荷载-位移曲线

    Figure  8.  Conventional structure and optimal structure uniaxial compression specific load-displacement curve of the experiment

    图  9  模拟的一般结构与优化结构平压比荷载-位移曲线

    Figure  9.  Simulated uniaxial compression specific load-displacement curves of conventional structure and optimal structure

    表  1  样本点与模拟值

    Table  1.   Sample points and simulated values

    样本点 θ/(°) d/mm Fc/M Fs/M 样本点 θ/(°) d/mm Fc/M Fs/M
    1 40.00 0.48 0.26 0.19 23 57.14 0.39 0.54 0.27
    2 40.61 0.39 0.13 0.10 24 57.76 0.48 1.33 0.46
    3 41.22 0.31 0.07 0.05 25 58.98 0.31 0.34 0.14
    4 41.84 0.45 0.26 0.18 26 59.59 0.45 1.27 0.42
    5 43.06 0.34 0.12 0.07 27 60.20 0.34 0.54 0.20
    6 43.67 0.37 0.16 0.11 28 60.82 0.37 0.76 0.27
    7 44.29 0.47 0.39 0.23 29 61.43 0.40 1.02 0.35
    8 44.90 0.50 0.50 0.28 30 62.04 0.49 1.88 0.54
    9 45.51 0.39 0.23 0.14 31 62.65 0.43 1.39 0.42
    10 46.70 0.43 0.37 0.21 32 63.27 0.32 0.54 0.19
    11 47.30 0.34 0.17 0.10 33 63.88 0.46 1.84 0.50
    12 47.96 0.46 0.52 0.27 34 64.49 0.35 0.82 0.26
    13 48.57 0.37 0.26 0.15 35 65.10 0.38 1.15 0.35
    14 49.80 0.41 0.42 0.22 36 65.71 0.41 1.55 0.42
    15 50.41 0.32 0.17 0.10 37 66.33 0.50 2.54 0.63
    16 51.02 0.43 0.53 0.26 38 66.94 0.30 0.59 0.17
    17 51.63 0.35 0.30 0.15 39 67.50 0.44 2.09 0.51
    18 52.24 0.46 0.75 0.33 40 68.16 0.33 0.95 0.26
    19 52.86 0.38 0.42 0.21 41 69.39 0.36 1.34 0.33
    20 53.47 0.49 1.01 0.40 42 70.00 0.40 1.95 0.45
    21 54.08 0.41 0.59 0.27 43 57.14 0.39 0.54 0.27
    22 54.69 0.30 0.20 0.09 44 57.76 0.48 1.33 0.46
    下载: 导出CSV

    表  2  抽样点的模拟值与预测值

    Table  2.   Simulated and predicted values of sampling points

    样本点 θ/(°) d/mm M/g Fc/M Fs/M
    模拟值/(N·g−1 预测值/(N·g−1 误差/% 模拟值/(N·g−1 预测值/(N·g−1 误差/%
    1 55.31 0.44 19.71 0.84 0.860 2.3 0.34 0.336 1.1
    2 46.12 0.32 28.36 0.13 0.125 3.8 0.07 0.068 2.9
    3 58.37 0.42 16.38 0.93 0.950 2.1 0.34 0.345 1.4
    4 68.78 0.47 10.32 2.64 2.590 1.9 0.59 0.610 3.4
    5 42.40 0.42 38.58 0.21 0.200 4.5 0.15 0.154 2.6
    下载: 导出CSV

    表  3  优化结构与一般结构的预测值比较

    Table  3.   Comparison of predicted values between optimal structure and conventional structure

    结构类型 θ/(°) d/mm $\dfrac{F_{\mathrm{c}}}{M} $/(N·g−1 $\dfrac{F_{\mathrm{s}}}{M} $/(N·g−1
    一般结构 69.53 0.32 1.03 0.24
    优化结构 55.96 0.499 1.34 0.46
    下载: 导出CSV
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  • 收稿日期:  2021-12-30
  • 刊出日期:  2024-05-31

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