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基于遗传算法的CFRP层合板单搭胶接结构的多目标优化

胡春幸 侯玉亮 铁瑛 李成 田可可

胡春幸, 侯玉亮, 铁瑛, 等. 基于遗传算法的CFRP层合板单搭胶接结构的多目标优化[J]. 复合材料学报, 2020, 37(0): 1-12
引用本文: 胡春幸, 侯玉亮, 铁瑛, 等. 基于遗传算法的CFRP层合板单搭胶接结构的多目标优化[J]. 复合材料学报, 2020, 37(0): 1-12
Chunxing HU, Yuliang HOU, Ying TIE, Cheng LI, Keke TIAN. Multi-objective optimization of adhesively bonded single-lap joints of CFRP laminates based on genetic algorithm[J]. Acta Materiae Compositae Sinica.
Citation: Chunxing HU, Yuliang HOU, Ying TIE, Cheng LI, Keke TIAN. Multi-objective optimization of adhesively bonded single-lap joints of CFRP laminates based on genetic algorithm[J]. Acta Materiae Compositae Sinica.

基于遗传算法的CFRP层合板单搭胶接结构的多目标优化

基金项目: 国家自然科学基金民航联合基金重点项目(U1833116);国家博士后科学基金面上资助项目(2018M642775);河南省等学校重点科研项目(20A46000)
详细信息
    通讯作者:

    李成,博士,教授,博士生导师,研究方向为复合材料损伤分析和复合材料损伤检查 E-mail:chengli@zzu.edu.cn

  • 中图分类号: TB332

Multi-objective optimization of adhesively bonded single-lap joints of CFRP laminates based on genetic algorithm

  • 摘要: 基于遗传算法对碳纤维增强树脂复合材料(CFRP)层合板单搭胶接结构进行了多目标优化,以提高其结构性能。首先,通过三维Hashin准则和三角形内聚力模型建立三维有限元模型来预测CFRP层内损伤过程、层间失效和胶层损伤过程,并通过试验验证其有效性。其次,利用拉丁超立方抽样(LHS)方法和二次多项式响应面法(RSM),基于搭接长度、胶层厚度和被胶接件宽度等胶接参数建立以拉伸强度和剪切强度为目标函数的多目标优化代理模型。最后,基于遗传算法(GA)对拉伸强度和剪切强度代理模型进行优化,得出一组Pareto解集,并基于理想解排序方法(TOPSIS)对Pareto非劣解集进行折中处理,得到最好的胶接参数设计方案。结果表明:CFRP层合板单搭胶接结构的数值模拟结果与试验结果相比具有很高的吻合度,验证了有限元方法的可靠性;CFRP层合板单搭胶接结构的拉伸强度和剪切强度与搭接长度、胶层厚度和被胶接件宽度具有显著的关联性;二次响应面代理模型结果与数值模拟结果相比误差均小于2.3%;与常规的单搭胶接结构方案进行对比,搭接拉伸强度和剪切强度分别提高了2.65%和17.24%。
  • 图  1  碳纤维增强树脂复合材料(CFRP)层合板单搭胶接结构试件示意图与WDW-300型万能拉伸试验机

    Figure  1.  Adhesively bonded single-lap joint of carbon fiber reinforced polymer(CFRP) laminate specimen sketch and WDW-300 universal tensile test machine

    图  2  Cohesive单元的双线性本构模型

    Figure  2.  Bilinear constitutive model of cohesive element

    图  3  CFRP层合板单搭接结构有限元模型

    Figure  3.  Finite element model of CFRP laminate single lap structure

    图  4  不同搭接长度的CFRP层合板单搭胶接结构的极限失效载荷

    Figure  4.  Ultimate failure loads of adhesively bonded single-lap joints of CFRP laminates with different lap lengths

    图  5  搭接长度为15 mm的CFRP层合板单搭胶接结构的载荷-位移曲线

    Figure  5.  Load-displacement curves of single lap bonded structures of CFRP laminates with lap length of 15 mm

    图  6  搭接长度对CFRP层合板单搭胶接结构拉伸强度和剪切强度的影响

    Figure  6.  Effects of lap length on tensile strength and shear strength of adhesively bonded single-lap joints of CFRP laminates

    图  7  不同搭接长度CFRP层合板单搭胶接结构的失效模式

    Figure  7.  Failure modes of adhesively bonded single-lap joints of CFRP laminates with different lap lengths

    图  8  不同搭接长度单搭胶接结构的胶层自身剪切失效(a)及层合板层间分层失效(b)

    Figure  8.  Adhesive shear failure(a) and delamination of laminates(b) of adhesively bonded single-lap joints with different lap lengths

    图  9  不同搭接宽度的CFRP层合板单搭胶接结构的极限失效载荷变化曲线

    Figure  9.  Ultimate failure load curves of adhesively bonded single-lap joints of CFRP laminates with different lap widths

    图  10  搭接宽度对CFRP层合板单搭胶接结构拉伸强度和剪切强度的影响

    Figure  10.  Effects of lap width on tensile strength and shear strength of adhesively bonded single-lap joints of CFRP laminates

    图  11  不同搭接宽度CFRP层合板单搭胶接结构的失效模式

    Figure  11.  Failure modes of adhesively bonded single-lap joints of CFRP laminates with different lap widths

    图  12  不同搭接宽度单搭胶接结构的胶层自身剪切失效(a)及层合板层间分层失效(b)

    Figure  12.  Adhesive shear failure(a) and delamination of laminates(b) of adhesively bonded single-lap joints with different lap widths

    图  13  不同情况下失效载荷F的三维分布和等值线分布

    Figure  13.  Three-dimensional distribution and contour distribution of failure load F under different conditions

    图  14  Pareto前沿

    Figure  14.  Pareto front

    表  1  T300/7901碳纤维/环氧树脂复合材料层合板力学参数[23-24]

    Table  1.   Mechanical properties of T300/7901 carbon fiber/epoxy resin composite laminate

    PropertyValue
    Young’s modulus E11/MPa 125000
    Young’s modulus E22,E33/MPa 11300
    Shear modulus G12,G13/MPa 5430
    Shear modulus G23/MPa 3980
    Poisson’s ratio v12,v13 0.3
    Poisson’s ratio v23 0.42
    Longitudinal tensile strength Xt/MPa 2000
    Longitudinal compressive strength Xc/MPa 1100
    Transverse tensile strength Yt/MPa 80
    Transverse compressive strength Yc/MPa 280
    Shear strength S/MPa 120
    Interface stiffness Knn, Kss, Ktt/(N.mm−3) 105
    Maximum normal traction $t_{\rm{n}}^0$/MPa 50
    Maximum shear traction $t_{\rm{s}}^0$, $t_{\rm{t}}^0$/MPa 90
    Toughness in tension $G_{\rm{n}}^{\rm{C}}$/(kJ.m−2) 0.52
    Toughness in shear $G_{\rm{s}}^{\rm{C}}$, $G_{\rm{t}}^{\rm{C}}$/(kJ.m−2) 0.92
    下载: 导出CSV

    表  2  LJM-170胶膜的力学参数[25]

    Table  2.   Mechanical properties of adhesive film LJM-170

    PropertyValue
    Young’s modulus E/MPa 2200
    Shear modulus G/MPa 815
    Tensile strength $t_{\rm{n}}^0$/MPa 31.9
    Shear strength $\tau _{\rm{s}}^0$, $\tau _{\rm{t}}^0$/MPa 21.2
    Toughness in tension $G_{\rm{n}}^{\rm{C}}$/(kJ.m-2) 0.48
    Toughness in shear $G_{\rm{s}}^{\rm{C}}$, $G_{\rm{t}}^{\rm{C}}$/(kJ.m-2) 1.83
    下载: 导出CSV

    表  3  样本点与对应的模拟结果

    Table  3.   Samples and corresponding simulation results

    Sample numberL/mmT/mmW/mmF/Nσ/MPaτ/MPa
    1 16.82 0.081 27.97 10734 106.61 22.82
    2 10.80 0.128 23.98 7876 91.230 30.41
    3 18.99 0.134 29.71 11605 108.50 20.57
    4 11.89 0.105 20.01 6868 95.340 28.87
    5 18.16 0.123 25.71 9930 107.28 21.27
    6 20.23 0.095 18.93 7523 110.39 19.64
    7 14.24 0.143 28.76 10511 101.52 25.67
    8 11.63 0.109 26.84 9181 95.010 29.41
    9 15.43 0.158 19.00 7007 102.44 23.90
    10 15.15 0.120 23.97 8911 103.26 24.54
    11 17.55 0.151 21.83 8290 105.49 21.64
    12 12.69 0.092 22.94 8125 98.390 27.91
    Notes:L—Lap the length; T—Adhesive thickness; W—Width of the bonded parts; F—Ultimate failure load; σ—Tension strength; τ—Shear strength.
    下载: 导出CSV

    表  4  检验样本的τσ估计值与模拟值对比

    Table  4.   Comparison between the estimated and simulated values of τ and σ for the test samples

    Sample numberL/mmT/mmW/mmτ/MPaσ/MPa
    Estimated valueAnalog valueRelative error/%Estimated valueAnalog valueRelative error/%
    1 10.91 0.112 25.33 30.43 30.33 0.33 92.360 91.920 0.477
    2 18.92 0.146 21.62 20.44 20.45 0.049 107.28 107.47 0.177
    3 17.26 0.113 29.04 22.33 22.23 0.45 107.22 106.58 0.600
    4 14.60 0.090 24.95 25.38 25.37 0.039 102.82 102.93 0.166
    5 13.30 0.130 18.62 26.77 27.38 2.23 98.900 101.15 2.220
    下载: 导出CSV

    表  5  优化方案排序结果

    Table  5.   Ranking result of the optimization schemes

    Sample numberParameter valueTarget valueStandardized indicatorsEuclide-an distance from positive
    ideal solution
    Euclide-an distance from negative
    ideal solution
    Relative
    proximity
    Result
    L/
    mm
    T/
    mm
    W/
    mm
    σ/
    kN
    τ/
    MPa
    στ
    1 14.51 0.082 10.57 108.21 25.99 0.3099 0.3312 0.0160 0.0484 0.7516 3
    2 15.48 0.08 12.74 108.91 24.69 0.3119 0.3146 0.0261 0.0320 0.5508 6
    3 16.05 0.08 10 112.11 24.28 0.3211 0.3094 0.0281 0.0294 0.5113 7
    4 14.14 0.083 10 107.72 26.47 0.3085 0.3373 0.0162 0.0545 0.7709 2
    5 16.16 0.08 10 112.33 24.15 0.3217 0.3078 0.0297 0.0283 0.4879 9
    6 15.84 0.084 11.73 110.14 24.34 0.3154 0.3102 0.0287 0.0283 0.4965 8
    7 14.62 0.08 10 109.42 25.91 0.3134 0.3302 0.0133 0.0477 0.782 1
    8 15.74 0.081 10 111.51 24.62 0.3193 0.3138 0.0241 0.0328 0.5764 5
    9 17.91 0.08 12.02 113.37 22.19 0.3247 0.2828 0.0545 0.0162 0.2291 10
    10 15.19 0.08 10 110.35 25.24 0.3160 0.3217 0.0179 0.0396 0.6887 4
    下载: 导出CSV
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