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基于响应面法的纤维金属层合板抗弹性能优化设计

孔祥韶 杨豹 周沪 郑成 刘芳 吴卫国

孔祥韶, 杨豹, 周沪, 郑成, 刘芳, 吴卫国. 基于响应面法的纤维金属层合板抗弹性能优化设计[J]. 爆炸与冲击, 2022, 42(4): 043301. doi: 10.11883/bzycj-2021-0146
引用本文: 孔祥韶, 杨豹, 周沪, 郑成, 刘芳, 吴卫国. 基于响应面法的纤维金属层合板抗弹性能优化设计[J]. 爆炸与冲击, 2022, 42(4): 043301. doi: 10.11883/bzycj-2021-0146
KONG Xiangshao, YANG Bao, ZHOU Hu, ZHENG Cheng, LIU Fang, WU Weiguo. Optimal design of ballistic performance of fiber-metal laminates based on the response surface method[J]. Explosion And Shock Waves, 2022, 42(4): 043301. doi: 10.11883/bzycj-2021-0146
Citation: KONG Xiangshao, YANG Bao, ZHOU Hu, ZHENG Cheng, LIU Fang, WU Weiguo. Optimal design of ballistic performance of fiber-metal laminates based on the response surface method[J]. Explosion And Shock Waves, 2022, 42(4): 043301. doi: 10.11883/bzycj-2021-0146

基于响应面法的纤维金属层合板抗弹性能优化设计

doi: 10.11883/bzycj-2021-0146
基金项目: 国家自然科学基金(52171318);装备预研教育部联合基金青年人才项目(6141A02033108)
详细信息
    作者简介:

    孔祥韶(1983- ),男,博士,教授,kongxs@whut.edu.cn

    通讯作者:

    刘 芳(1984- ),女,博士,副教授,fang_liu@whut.edu.cn

  • 中图分类号: O342; TB333

Optimal design of ballistic performance of fiber-metal laminates based on the response surface method

  • 摘要: 纤维金属层合板因其复合材料的各向异性和层合结构特征而具有较好的可设计性,开展金属纤维层合板的优化设计研究对其力学性能的增强和轻量化具有重要意义。为提高纤维金属层合板的抗弹性能,基于响应面分析法对纤维金属层合板的铺层方向和铺层厚度进行了优化设计。采用Box-Behnken方法进行方案设计,以纤维金属层合板各铺层相对厚度比为设计变量,以结构的比吸能为设计目标,根据设计的方案进行参数化建模获取样本点,在对设计样本进行方差分析和参数估计的基础上,建立了结构比吸能的响应面模型并验证了其精确度。采用遗传算法对响应面方程进行寻优分析,通过显式动力学计算程序ABAQUS/Explicit验证优化效果。最终,在最优的铺层方案下,层合板的质量减小了11.70%,能量吸收增加了19.40%,抗弹性能显著提升。
  • 图  1  A3G23层合板铺层方案示意图

    Figure  1.  Schematic diagram of A3G23 laminate layup scheme

    图  2  优化前的层合板模型

    Figure  2.  The original laminate model

    图  3  纤维金属层合板高速冲击实验布置

    Figure  3.  Layout diagram of high-speed impact experiment for fiber metal laminates

    图  4  弹体剩余速度与入射速度的关系曲线

    Figure  4.  Change of projectile residual velocity with its incident velocity

    图  5  实验与数值模拟的纤维金属层合板横截面破坏形貌

    Figure  5.  Experimental and numerical failure morphologies of fiber-metal laminates (a cross-sectioned view)

    图  6  实验与数值模拟的纤维金属层合板背面破坏形貌

    Figure  6.  Experimental and numerical failure morphologies of fiber-metal laminates (a top view)

    图  7  不同铺层方向下弹体动能-时间变化曲线

    Figure  7.  Kinetic energy-time curves of projectile under different layup directions

    图  8  不同铺层方案下层合板的吸能效果

    Figure  8.  Energy absorption effects of the lower laminatesunder different layer schemes

    图  9  响应面优化设计流程

    Figure  9.  Response surface optimization design process

    图  10  ${\alpha _1}$${\alpha _4}$交互作用对比吸能影响的响应面和等高线

    Figure  10.  Response surfaces and contour lines of interaction between $ {\alpha _1} $ and $ {\alpha _4} $ on specific energy absorption

    图  11  ${\alpha _3}$${\alpha _4}$交互作用对比吸能影响的响应面和等高线

    Figure  11.  Response surfaces and contour lines of interaction between $ {\alpha _3} $ and $ {\alpha _4} $ on specific energy absorption

    图  12  遗传算法寻优过程

    Figure  12.  Genetic algorithm optimization process

    图  13  优化后层合板模型

    Figure  13.  Optimized laminate model

    图  14  层合板最终变形模式(背面板)

    Figure  14.  Final deformation mode of laminates (back plate)

    图  15  层合板最终变形模式(前面板)

    Figure  15.  Final deformation mode of laminates (front plate)

    图  16  弹体侵彻层合板过程

    Figure  16.  Process of a projectile penetrating laminated plates

    图  17  优化前后层合板吸能效果

    Figure  17.  Energy absorption effect of original and optimized laminates

    表  1  热塑性纤维增强材料的弹性参数

    Table  1.   Elastic parameters of thermoplastic fiber reinforced materials

    ρ/(kg∙m−3E1/GPaE2/GPaE3/GPaμ12μ13μ23G12/GPaG13/GPaG23/GPa
    1 80013134.80.10.30.31.721.691.69
    下载: 导出CSV

    表  2  热塑性纤维增强材料的强度参数

    Table  2.   Strength parameters of thermoplastic fiber reinforced materials

    XT/MPaXC/MPaYT/MPaYC/MPaS12/MPaS13/MPaS23/MPa
    300200300200120120120
    下载: 导出CSV

    表  3  网格收敛性分析

    Table  3.   Analysis of grid convergence

    网格尺寸/mm网格数量吸能/J相对偏差/%
    2.0 43 90890.7234.70
    1.0171 40869.42 3.07
    0.5680 00067.350
    下载: 导出CSV

    表  4  Cohesive单元的材料参数[16]

    Table  4.   Material parameters of the cohesive element[16]

    ρc/(kg∙m−3)En/GPaEs/GPaEt/GPa$s_{\rm{n} }^{(0)}$/MPa$s_{\rm{s} }^{(0)}$/MPa$s_{\rm{t} }^{(0)}$/MPa$G_{\rm{n} }^{(0)}$/(J∙m−2)$G_{\rm{s} }^{(0)}$/(J∙m−2)$G_{\rm{t} }^{(0)}$/(J∙m−2)
    9002.050.720.7270100100300700700
    下载: 导出CSV

    表  5  弹体剩余速度实验结果与数值模拟结果对比

    Table  5.   Comparison of projectile residual velocities between experimental and numerical results

    实验工况实验初速/(m·s−1)实验剩余速度/(m·s−1)模拟剩余速度/(m·s−1)剩余速度相对误差/%
    3Al(6-O)/2G-1143109107.9–1.0
    3Al(6-O)/2G-2172125127.6 2.1
    3Al(6-O)/2G-3195150151.1 0.7
    3Al(6-O)/2G-4214181172.1–4.9
    3Al(6-O)/2G-5252216211.5–2.1
    下载: 导出CSV

    表  6  纤维金属层合板铺层方案

    Table  6.   Layer schemes of fiber metal laminates

    铺层方案铺层方向铺层方案铺层方向
    1Al/45°/90°/0°/Al/0°/90°/45°/Al7Al/90°/0°/–45°/Al/–45°/0°/90°/Al
    2Al/45°/90°/–45°/Al/–45°/90°/45°/Al8Al/90°/45°/0°/Al/0°/45°/90°/Al
    3Al/45°/0°/90°/Al/90°/0°/45°/Al9Al/90°/45°/–45°/Al/–45°/45°/90°/Al
    4Al/45°/0°/–45°/Al/–45°/0°/45°/Al10Al/90°/–45°/0°/Al/0°/–45°/90°/Al
    5Al/45°/–45°/0°/Al/0°/–45°/45°/Al11Al/0°/45°/–45°/Al/–45°/45°/0°/Al
    6Al/45°/–45°/90°/Al/90°/–45°/45°/Al12Al/0°/90°/–45°/Al/–45°/90°/0°/Al
    下载: 导出CSV

    表  7  设计因子水平

    Table  7.   Design factor levels

    设计因子低水平高水平
    $ {\alpha _1} $0.0290.200
    $ {\alpha _2} $0.0290.200
    $ {\alpha _3} $0.0290.200
    $ {\alpha _4} $0.2000.457
    下载: 导出CSV

    表  8  BBD实验设计

    Table  8.   Experimental schemes designed by the BBD method

    实验方案$ {\alpha _1} $$ {\alpha _2} $$ {\alpha _3} $$ {\alpha _4} $$Q/({\rm{J}} \cdot {\rm{kg}^{ - 1} })$${Q_{\rm{{pre}}} }/({\rm{J} } \cdot {\rm{kg}^{ - 1} })$
    1–100–1982.58983.58
    200–11820.35815.75
    3100–11 032.251 041.37
    40000799.74799.74
    50–10–1979.84965.03
    6–1001675.37671.43
    7–1100836.94847.07
    81–100846.44859.65
    900–1–11 135.931 143.95
    10–1010780.02754.93
    1110–101 015.361 002.85
    120–1–10914.80912.54
    13–1–100730.39746.48
    140101808.02808.85
    151100960.88960.23
    161010881.44868.10
    170000799.74799.74
    18001–1913.77937.77
    190000799.74799.74
    2001–10976.15985.71
    210011741.05752.42
    221001835.80839.97
    23–10–10887.89889.69
    24010–11 092.941 065.62
    250–101716.09708.26
    260–110754.74750.36
    270110870.92878.37
    下载: 导出CSV

    表  9  方差分析和参数估计

    Table  9.   Analysis of variance and parameter estimation

    方差来源平方和自由度均方FP
    模型366 000.001133 247.56156.55< 0.000 1
    $ {\alpha _1} $38 416.01138 416.01180.89< 0.000 1
    $ {\alpha _2} $30 354.44130 354.44142.93< 0.000 1
    $ {\alpha _3} $54 478.75154 478.75256.52< 0.000 1
    $ {\alpha _4} $198 000.001198 000.00931.36< 0.000 1
    $ {\alpha _1} \times {\alpha _4} $3 066.7813 066.7814.440.001 4
    $ {\alpha _2} \times {\alpha _3} $751.721751.723.540.077 2
    $ {\alpha _3} \times {\alpha _4} $5 101.7414 179.8924.020.000 1
    $ {\alpha _1} \times {\alpha _1} $4 179.8915 170.5919.680.000 4
    $ {\alpha _2} \times {\alpha _2} $5 170.59118 752.3624.350.000 1
    $ {\alpha _3} \times {\alpha _3} $18 752.36122 551.0888.30< 0.000 1
    $ {\alpha _4} \times {\alpha _4} $22 551.0813 066.78106.19< 0.000 1
    残差3 610.3917212.38
    总和370 000.0028
    $ {R^2} $0.99
    $R_{\rm{{adj}}}^2$0.98
    下载: 导出CSV

    表  10  遗传算法优化结果

    Table  10.   Genetic algorithm optimization results

    实验方案$ {\alpha _1} $$ {\alpha _2} $$ {\alpha _3} $$ {\alpha _4} $$Q/({\rm{{J}}} \cdot {\rm{kg}^{ - 1} })$
    优化0.1830.1980.0410.2171186.0
    下载: 导出CSV

    表  11  优化前后层合板主要参数

    Table  11.   The main parameters of original and optimized laminates

    层合板方案$ {t_1}/{\text{mm}} $$ {t_2}/{\text{mm}} $$ {t_3}/{\text{mm}} $$ {t_4}/{\text{mm}} $$t_{0}/{\text{mm} }$$m/{\text{g} }$$Q/({\rm{{J}}} \cdot {\rm{kg}^{ - 1} })$
    原方案0.500.500.501.003.5078.70882.12
    优化后0.640.690.140.763.0069.501192.66
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-04-20
  • 录用日期:  2022-03-28
  • 修回日期:  2022-01-14
  • 网络出版日期:  2022-04-07
  • 刊出日期:  2022-05-09

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