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基于非线性分析的加肋板肋条位置无网格优化

彭林欣 李知闲 项嘉诚 覃霞

彭林欣, 李知闲, 项嘉诚, 覃霞. 基于非线性分析的加肋板肋条位置无网格优化. 力学学报, 2022, 54(12): 3366-3382 doi: 10.6052/0459-1879-22-433
引用本文: 彭林欣, 李知闲, 项嘉诚, 覃霞. 基于非线性分析的加肋板肋条位置无网格优化. 力学学报, 2022, 54(12): 3366-3382 doi: 10.6052/0459-1879-22-433
Peng Linxin, Li Zhixian, Xiang Jiacheng, Qin Xia. The optimization of ribs position based on stiffened plates meshless model with nonlinearity. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3366-3382 doi: 10.6052/0459-1879-22-433
Citation: Peng Linxin, Li Zhixian, Xiang Jiacheng, Qin Xia. The optimization of ribs position based on stiffened plates meshless model with nonlinearity. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3366-3382 doi: 10.6052/0459-1879-22-433

基于非线性分析的加肋板肋条位置无网格优化

doi: 10.6052/0459-1879-22-433
基金项目: 国家自然科学基金(12162004), 国家重点研发计划(2019YFC1511103)和广西重点研发计划(桂科 AB22036007)资助项目
详细信息
    作者简介:

    覃霞, 博士, 主要研究方向: 无网格方法. E-mail: sarah0901@yeah.net

  • 中图分类号: TU339

THE OPTIMIZATION OF RIBS POSITION BASED ON STIFFENED PLATES MESHLESS MODEL WITH NONLINEARITY

  • 摘要: 在加肋板无网格模型中, 肋条的位置对各种工况下加肋板受力性能的影响至关重要. 文章基于一阶剪切变形和移动最小二乘法理论提出一种考虑非线性影响的加肋板无网格模型, 并利用遗传算法优化肋条位置. 首先, 采用离散节点分别对平板和肋条进行离散, 得到加肋板的无网格离散模型; 其次, 通过冯·卡门大挠度理论得到非矩形板几何非线性问题的弯曲控制方程; 再次, 通过哈密顿原理得到加肋非矩形板自由振动问题的控制方程; 最后引入遗传算法, 以肋条的位置为设计变量、非矩形加肋板中心点挠度最小或自振频率最大为目标函数, 对肋条位置进行优化. 在考虑了几何非线性影响的肋条位置优化过程中, 肋条位置改变时只需重新计算位移转换矩阵, 避免了网格重构. 本文以全局荷载下单肋条菱形板为例与理论解进行对比, 进行有效性验证. 再以板的中点挠度最小和自振频率最大为优化目标, 对局部荷载作用下不同形状、不同肋条布置方式的加肋板进行优化, 分析方法的收敛性及稳定性.

     

  • 图  1  加肋圆板的无网格模型

    Figure  1.  The meshless model of the circular stiffened plate

    图  2  加肋圆板

    Figure  2.  The circular stiffened plate

    图  3  圆形影响域

    Figure  3.  Circular domain of influence

    图  4  位移协调示意图

    Figure  4.  Indication of displacement coordination

    图  5  离散节点加密

    Figure  5.  The encryption of discrete nodes

    图  6  受面外均布力和集中力P作用的加肋圆板

    Figure  6.  A circular stiffened plate subject to an out-plane force and concentrated force P

    图  7  受均布荷载作用的单肋菱形板

    Figure  7.  Single stiffener stiffened plate subjected to uniformly distributed load

    图  8  均布荷载作用下本文解与理论解的对比

    Figure  8.  Comparison of the presented solution and the theoretical solution

    图  9  均布荷载作用下单肋条优化迭代过程的种群分布(第9次计算结果)

    Figure  9.  Population distribution of single rib optimization iterative process under uniform load (the 9th result)

    图  10  均布荷载作用下单肋条优化迭代过程的种群分布(第6次计算结果)

    Figure  10.  Population distribution of single rib optimization iterative process under uniform load (the 6th result)

    图  11  局部荷载下单肋条菱形板

    Figure  11.  Single-stiffened skew plate under local load

    图  12  局部荷载作用下单肋条优化迭代过程的种群分布

    Figure  12.  Population distribution of single rib optimization iterative process under local load

    图  13  局部荷载下双肋条菱形板

    Figure  13.  Double-stiffened skew plate under local load

    图  14  局部荷载作用下双肋条优化迭代过程的种群分布

    Figure  14.  Population distribution of double-rib optimization iterative process under local load

    图  15  双肋条加肋圆板

    Figure  15.  Circular stiffened plate with two stiffeners

    图  16  加肋圆板单肋条优化迭代过程的种群分布

    Figure  16.  Population distribution of single rib optimization iterative process of circular stiffened plate

    图  17  双肋条加肋圆板

    Figure  17.  Circular stiffened plate with two stiffeners

    图  18  加肋半圆板肋条优化迭代过程的种群分布

    Figure  18.  Population distribution of double-rib optimization iterative process of semicircular stiffened plate

    表  1  均布荷载下加肋菱形板肋条位置10次优化结果

    Table  1.   Results of rib position optimization of the skew stiffened plate under uniformly distributed load

    No.Present
    results x/m
    Deflection/
    mm
    Theoretical
    results x/m
    Deflection/
    mm
    Relative errors/
    %
    10.7578779.553060.759.356541.0502
    20.7463119.448570.759.35654−0.4918
    30.7528459.427530.759.356540.3794
    40.7673129.826570.759.356542.3083
    50.7475229.418370.759.35654−0.3304
    60.52401312.178420.759.3565430.1333
    70.7516369.472910.759.356540.6219
    80.7647679.725000.759.356541.9690
    90.7546649.397350.759.356540.2181
    100.7440439.505170.759.35654−0.7943
    下载: 导出CSV

    表  2  局部布荷载下双肋条位置优化结果

    Table  2.   Results of rib position optimization under local load

    No.rib position xmodpoint deflection/mm
    10.6315705.11805
    20.6701695.51728
    30.6695695.51653
    40.6469805.52643
    50.7524115.53346
    60.6651605.51104
    70.6940065.12778
    80.6501855.52243
    90.6674215.51386
    100.6629065.05741
    下载: 导出CSV

    表  3  局部布荷载下双肋条位置优化结果

    Table  3.   Results of double ribs position optimization under local load

    No.x1/mx2/mMidpoint deflection/mm
    10.661520.655215.99517
    20.753920.749566.06845
    30.651610.602615.99052
    40.660890.442676.45433
    50.691290.756876.10183
    60.650120.621335.97900
    70.759850.690626.10205
    80.755410.552567.05198
    90.651950.688626.10291
    100.708220.749126.11253
    下载: 导出CSV

    表  4  加肋圆板单肋条位置优化结果

    Table  4.   Results of rib position optimization of circular stiffened plate

    No.Rib position θBase frequency/Hz
    11.5289867.30954
    21.5403167.43255
    31.5490667.52759
    41.5570467.61421
    51.2563265.27400
    61.4148966.07094
    70.9394461.49203
    81.5263167.28055
    91.4314966.25119
    101.4197666.12386
    下载: 导出CSV

    表  5  加肋半圆板条位置优化结果

    Table  5.   Results of double ribs position optimization of semicircular stiffened plate

    No.θ1/radθ2/radBase frequency/Hz
    10.456010.4411846.0592
    20.571870.5623742.4454
    30.438370.4380046.5886
    40.383770.3713248.1074
    50.347070.3337448.1441
    60.318320.3103047.9313
    70.276960.2680946.6987
    80.368180.3734248.1778
    90.391790.4040048.0054
    100.330780.3196148.0986
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-09-17
  • 录用日期:  2022-11-16
  • 网络出版日期:  2022-11-19
  • 刊出日期:  2022-12-15

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