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变厚度连续纤维增强复合材料铺层设计优化方法

杜晨 彭雄奇

杜晨,彭雄奇. 变厚度连续纤维增强复合材料铺层设计优化方法 [J]. 应用数学和力学,2022,43(12):1313-1323 doi: 10.21656/1000-0887.420410
引用本文: 杜晨,彭雄奇. 变厚度连续纤维增强复合材料铺层设计优化方法 [J]. 应用数学和力学,2022,43(12):1313-1323 doi: 10.21656/1000-0887.420410
DU Chen, PENG Xiongqi. Lamination Design Optimization for Continuous Fiber Reinforced Composites of Variable Thicknesses[J]. Applied Mathematics and Mechanics, 2022, 43(12): 1313-1323. doi: 10.21656/1000-0887.420410
Citation: DU Chen, PENG Xiongqi. Lamination Design Optimization for Continuous Fiber Reinforced Composites of Variable Thicknesses[J]. Applied Mathematics and Mechanics, 2022, 43(12): 1313-1323. doi: 10.21656/1000-0887.420410

变厚度连续纤维增强复合材料铺层设计优化方法

doi: 10.21656/1000-0887.420410
基金项目: 国家自然科学基金(U20A20288;11972225)
详细信息
    作者简介:

    杜晨(1999—),男,硕士生(E-mail:ChenDu@sjtu.edu.cn

    彭雄奇(1970—),男,教授,博士,博士生导师(通讯作者. E-mail:xqpeng@sjtu.edu.cn

  • 中图分类号: TB332; O39

Lamination Design Optimization for Continuous Fiber Reinforced Composites of Variable Thicknesses

  • 摘要:

    由于具备高的比强度、比刚度,利用连续纤维增强复合材料代替传统金属材料以实现结构轻量化正受到设计者们的广泛关注。然而,结构的复杂性给复合材料的铺层设计与优化带来了很大的挑战。针对航空用复合材料铺层设计约束多的问题,通过逐步构建设计变量准确表达结构的铺层信息。基于经典遗传算法框架,结合各设计变量特点,定义了铺层优化算法中的遗传算子,通过引入“修复”策略保证了每一代解都能满足设计约束,分布在可行域区间内。最后利用精英保留策略提高了算法的局部寻优能力,可以降低复杂复合材料结构铺层设计的计算成本。通过解决经典benchmark问题并与已有优化结果的比较,验证了前述铺层优化算法的全局、局部寻优能力,为工程实际中的复合材料铺层设计优化提供了理论支撑。

  • 图  1  连续厚度变化层合板

    注 为了解释图中的颜色,读者可以参考本文的电子网页版本,后同。

    Figure  1.  Continuous thickness varying laminates

    图  2  铺层顺序变量生成步骤

    Figure  2.  The generation steps of stacking sequence variables

    图  3  SinsSlam得到铺层角度信息

    Figure  3.  The ply angle information obtained from Sins and Slam

    图  4  双点交叉过程

    Figure  4.  The process of 2-point chiasma

    图  5  OX过程

    Figure  5.  The process of OX

    图  6  单点交叉过程

    Figure  6.  The process of single-point chiasma

    图  7  单点变异过程

    Figure  7.  The process of single-point mutation

    图  8  反转变异过程

    Figure  8.  The process of swap mutation

    图  9  用于变量Slam的修复策略[11]

    Figure  9.  The repair strategy for Slam variable[11]

    图  10  铺层优化流程

    Figure  10.  The layering optimization process

    图  11  经典benchmark问题算例[5]

    Figure  11.  Classic examples of benchmark problems[5]

    图  12  4种可选铺层角度下最小重量-进化代数收敛曲线

    Figure  12.  Minimum weight-generation convergence curves under 4 alternative ply angles

    图  13  12种可选铺层角度下最小重量-进化代数收敛曲线

    Figure  13.  Minimum weight-generation convergence curves under 12 alternative ply angles

    表  1  优化算法参数取值

    Table  1.   Optimization algorithm parameter values

    parametervalue
    populationsize S100
    number of generations G1000, 2 000
    probability of chiasma Pc/%0.9
    probability of mutation Pm/%0.1
    elite reserved individual I2
    number of competition selections c2
    下载: 导出CSV

    表  2  四种可选铺层角度下最优解变量取值

    Table  2.   Variable value of the optimal solution under 4 alternative ply angles

    variablevariable value
    Nstr[35 29 23 19 17 23 19 25 39 36 31 29 23 19 26 32 19 23]
    final Nstr[34 29 21 19 16 22 19 25 39 36 31 29 22 19 26 32 19 23]
    Slam[−45° 0° −45° 90° 45° 90° −45° −45° 0° −45° −45° 90° 45° 0° 45° 0° 0° 45° 0° 0° 45° 90° 45° 0°]
    Sins[0 1 2 2 0 1 6 1 5 1 0 0 8 4 1 4 0 1 1 1 7 0 9 1 3 1 0 7 5 6 0 3]
    下载: 导出CSV

    表  3  与SST方法最优解的比较

    Table  3.   Comparison with the optimal solution of the SST method

    panelthis paper solutionSST
    number of plies Npliemargin η/%number of plies Npliemargin η/%
    134(0)2.73417.2
    229(−1)0.63015.9
    321(−1)1.42236.4
    419( + 1)9.61813.3
    516(−2)10.31859.3
    622(0)4.42222.6
    719( + 1)6.2189.8
    825(−1)2.82631.9
    939( + 1)0.6386.9
    1036(−2)0.63825.6
    1131( + 1)5.73010.0
    1229(−1)0.13027.1
    1322(0)9.32228.3
    1419( + 1)16.31820.2
    1526(0)11.92627.8
    1632( + 2)3.2306.8
    1719( + 1)7.71811.3
    1823( + 1)8.02211.2
    number of total plies Ntotal461460
    weight W/kg28.829 128.85
    下载: 导出CSV

    表  4  12种可选铺层角度下最优解变量取值

    Table  4.   Variable values of the optimal solution under 12 alternative ply angles

    variablevariable value
    Nstr[34 29 21 19 16 22 19 25 40 36 31 31 22 19 27 32 19 23]
    final Nstr[34 29 21 19 16 22 19 25 39 36 31 29 22 19 26 31 19 23]
    Slam[90° −45° −30° 0° −30° 0° −45° −30° −60° −45° 90° 45° 30° 45° 60° 30° 60° 30° 45° 0° 30° 0° −30° 0°]
    Sins[0 9 1 3 1 1 0 1 0 7 1 6 0 2 0 8 1 7 6 0 1 5 0 1 2 3 5 0 4 1 4 1]
    下载: 导出CSV

    表  5  与SST方法最优解的比较

    Table  5.   Comparison with the optimal solution of the SST method

    panelthis paper solutionSST
    number of plies Npliemargin η/%number of plies Npliemargin η/%
    134(0)5.83417.2
    229(− 1)2.93015.9
    321(− 1)1.42236.4
    419( + 1)9.41813.3
    516(− 2)8.61859.3
    622(0)4.62222.6
    719( + 1)6.0189.8
    825(− 1)2.82631.9
    939( + 1)4.6386.9
    1036(− 2)3.13825.6
    1131( + 1)10.53010.0
    1229(− 1)2.43027.1
    1322(0)9.52228.3
    1419( + 1)16.11820.2
    1526(0)11.72627.8
    1631( + 1)4.6306.8
    1719( + 1)7.51811.3
    1823( + 1)7.72211.2
    number of total plies Ntotal460460
    weight W/kg28.782 628.85
    下载: 导出CSV
  • [1] 朱迪, 姚远, 彭雄奇. 碳纤维汽车底盘后纵臂CAE设计的优化算法[J]. 应用数学和力学, 2018, 39(8): 925-934

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    [11] FEDON N, WEAVER P M, PIRRERA A, et al. A repair algorithm for composite laminates to satisfy lay-up design guidelines[J]. Composite Structures, 2021, 259: 113448. doi: 10.1016/j.compstruct.2020.113448
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出版历程
  • 收稿日期:  2021-12-28
  • 修回日期:  2022-12-01
  • 网络出版日期:  2022-12-08
  • 刊出日期:  2022-12-01

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