EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

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): 1-17 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): 1-17 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): 1-17 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): 1-17 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:

    彭林欣, 教授, 主要研究方向: 无网格方法. E-mail: penglx@gxu.edu.cn

  • 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 9 th)

    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 6 th)

    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

    序号本文解x (m)挠度 (mm)理论解x (m)挠度 (mm)相对误差 (%)
    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

    序号肋条位置 x中点挠度 (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

    Nox1 (m)x2 (m)中点挠度 (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肋条位置θ/(rad)基频/(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

    Noθ1/(rad)θ2/(rad)基频/(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
  • [1] Yi K, Choi KK, Kim NH, et al. Continuum-based design sensitivity analysis and optimization of nonlinear shell structures using meshfree method. International Journal for Numerical Methods in Engineering, 2010, 68(2): 231-266
    [2] 彭细荣, 隋允康. 考虑破损-安全的连续体结构拓扑优化ICM方法. 力学学报, 2018, 50(3): 11 (Peng Xirong, Sui Yunkang. A damage-safe continuum structure topology optimization ICM method. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 11 (in Chinese) doi: 10.6052/0459-1879-17-366
    [3] 陈炉云, 张裕芳. 基于遗传算法的复合材料结构-声辐射优化研究. 复合材料学报, 2012, 029(3): 203-207 (Chen Luyun, Zhang Yufang. Research on structure-acoustic radiation optimization of composite materials based on genetic algorithm. Acta Materiae Compositae Sinica, 2012, 029(3): 203-207 (in Chinese) doi: 10.13801/j.cnki.fhclxb.2012.03.033
    [4] 李林远, 彭林欣. 基于无网格及混合遗传算法的矩形加肋板肋条布置优化. 应用力学学报, 2018, 35(6): 7 (Li Linyuan, Peng Linxin. Optimization of rib layout of rectangular ribbed slab based on meshless and hybrid genetic algorithm. Chinese Journal of Applied Mechanics, 2018, 35(6): 7 (in Chinese)
    [5] Wodesenbet E, Kidane S, Pang SS. Optimization for buckling loads of grid stiffened composite panels. Composite Structures, 2003, 60(2): 159-169 doi: 10.1016/S0263-8223(02)00315-X
    [6] 李琳, 石峰, 项松等. 基于遗传算法和复合二次径向基函数的复合材料层合板自由振动分析. 工程数学学报, 2022(039-002)

    Li Lin, Shi Feng, Xiang Song, et al. Free vibration analysis of composite laminates based on genetic algorithm and compound quadratic radial basis function. Chinese Journal of Engineering Mathematics, 2022(039-002) (in Chinese))
    [7] 王选, 刘宏亮, 龙凯等. 基于改进的双向渐进结构优化法的应力约束拓扑优化. 力学学报, 2018

    Wang Xuan, Liu Hongliang, Long Kai, et al. Stress constrained topology optimization based on improved bidirectional progressive structural optimization method. Chinese Journal of Theoretical and Applied Mechanics, 2018 (in Chinese))
    [8] 米大海, 杨睿, 周亮等. 以频率为目标的加筋平板结构优化设计研究. 机械强度, 2013, 35(2): 4 (Mi Dahai, Yang Rui, Zhou Liang, et al. Research on optimization design of stiffened plate structure with frequency as target. Journal of Mechanical Strength, 2013, 35(2): 4 (in Chinese) doi: 10.16579/j.issn.1001.9669.2013.02.002
    [9] Afonso S, Sienz J, Belblidia F. Structural optimization strategies for simple and integrally stiffened plates and shells. Engineering Computations, 2005, 22(4): 429-452 doi: 10.1108/02644400510598769
    [10] 王博, 郝鹏, 田阔. 加筋薄壳结构分析与优化设计研究进展. 计算力学学报, 2019, 36(1): 12 (Wang Bo, Hao Peng, Tian Kuo. Research progress on the analysis and optimization design of stiffened thin shell structures. Chinese Journal of Computational Mechanics, 2019, 36(1): 12 (in Chinese)
    [11] 文立中. 偏压作用下钢木组合柱非线性分析及截面优化设计. 中南林业科技大学, 2021

    Wen Lizhong. Nonlinear analysis and section optimization design of steel-wood composite column under eccentric pressure. Central South University of Forestry and Technology, 2021 (in Chinese))
    [12] 周俊文, 刘界鹏. 基于多种群遗传算法的钢框架结构优化设计. 土木与环境工程学报, 1-11(2022-09-16)(Zhou Junwen, Liu Jiepeng. Optimal design of steel frame structure based on multiple population genetic algorithm. Journal of Civil and Environmental Engineering, 1-11(2022-09-16) (in Chinese))
    [13] 王栋, 李正浩. 薄板结构加筋布局优化设计方法研究. 计算力学学报, 2018, 35(2): 6 (Wang Dong, Li Zhenghao. Research on optimization design method of reinforcement layout of thin plate structure. Chinese Journal of Computational Mechanics, 2018, 35(2): 6 (in Chinese)
    [14] Csonka B, Kozák I, Soares C, et al. Shape optimization of axisymmetric shells using a higher order shear deformation theory. Structural Optimization, 1995, 9(2): 117-127 doi: 10.1007/BF01758828
    [15] T, Belytschko, Y, et al. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering, 1994.
    [16] 张雄, 宋康祖, 陆明万. 无网格法研究进展及其应用. 中国计算力学大会. 2001: 730-742

    Zhang Xiong, Song Kangzu, Lu Mingwan. Research progress and application of meshless method. China Computational Mechanics Conference, 2001: 730-742 (in Chinese))
    [17] 邓立克, 王东东, 王家睿等. 薄板分析的线性基梯度光滑伽辽金无网格法. 力学学报, 2019, 51(3): 690-702 (Deng Like, Wang Dongdong, Wang Jiarui, et al. A gradient smoothing Galerkin meshfree method for thin plate analysis with linear basis function. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 690-702 (in Chinese) doi: 10.6052/0459-1879-19-004
    [18] 覃霞, 刘珊珊, 吴宇等. 平行四边形加肋板自由振动分析的无网格法. 工程力学, 2019, 36(3): 24-32,39 (Qin Xia, Liu Shanshan, Wu Yu, et al. The meshless method for free vibration analysis of parallelogram ribbed plates. Engineering Mechanics, 2019, 36(3): 24-32,39 (in Chinese)
    [19] 张雄, 刘岩, 马上. 无网格法的理论及应用. 力学进展, 2009(1): 36 (Zhang Xiong, Liu Yan, Ma shang. Theory and application of meshless method. Advances in Mechanics, 2009(1): 36 (in Chinese) doi: 10.6052/1000-0992-2009-1-J2008-010
    [20] 张建平, 刘庭显, 龚曙光等. 基于无网格法的热力耦合周期性结构多目标拓扑优化. 机械工程学报, 2022, 58(14): 223-232 (Zhang Jianping, Liu Tingxian, Gong Shuguang, et al. Multi-objective topology optimization of thermomechanical coupled periodic structures based on meshless method. Journal of Mechanical Engineering, 2022, 58(14): 223-232 (in Chinese)
    [21] 彭林欣. 矩形加肋板线性弯曲分析的移动最小二乘无网格法. 计算力学学报, 2012, 29(02): 210-216 (Peng Linxin. Moving least squares meshless method for linear bending analysis of rectangular ribbed plates. Chinese Journal of Computational Mechanics, 2012, 29(02): 210-216 (in Chinese) doi: 10.7511/jslx201202011
    [22] 宋超, 彭慧凯, 王东东. 薄板壳屈曲分析的埃尔米特无网格法. 中国计算力学大会2014暨第三届钱令希计算力学奖颁奖大会论文集. 2014

    Song Chao, Peng Huikai, Wang Dongdong. Hermitian meshless method for buckling analysis of thin shells. Proceedings of the China Computational Mechanics Conference 2014 and the 3 rd Qian Lingxi Computational Mechanics Award Conference, 2014 (in Chinese)
    [23] 张驰, 校金友, 张硕. 用无网格法分析功能梯度材料圆板的自由振动. 科学技术与工程, 2014(13): 6 (Zhang Chi, Xiao Jinyou, Zhang Shuo. Analysis of free vibration of circular plates with functionally gradient materials by meshless method. Science Technology and Engineering, 2014(13): 6 (in Chinese)
    [24] 杨柳, 彭建设. 解平行四边形板弯曲问题的GD法. 成都大学学报:自然科学版, 2014, 33(3): 4 (Yang Liu, Peng Jianshe. GD method for solving parallelogram plate bending problem. Journal of Chengdu University (Natural Science Edition), 2014, 33(3): 4 (in Chinese)
    [25] 马文涛. 二维弹性力学问题的光滑无网格伽辽金法. 力学学报, 2018, 50(5): 1115-1124 (Ma Wentao. A smoothed meshfree Galerkin method for 2 D elasticity problem. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(5): 1115-1124 (in Chinese) doi: 10.6052/0459-1879-18-135
    [26] 方电新, 李卧东, 王元汉等. 用无网格法计算平板弯曲问题. 岩土力学, 2001, 22(3): 3 (Fang Lixin, Li Wodong, Wang Yuanhan, et al. Calculation of plate bending problems using the meshless method. Rock and Soil Mechanics, 2001, 22(3): 3 (in Chinese) doi: 10.3969/j.issn.1000-7598.2001.03.026
    [27] 曾军才, 王久法, 姚望等. 正交各向异性矩形板的自由振动特性分析. 振动与冲击, 2015, 34(24): 123-127 (Zeng Juncai, Wang Jiufa, Yao Wang, et al. Analysis of free vibration characteristics of orthotropic rectangular plates. Journal of Vibration and Shock, 2015, 34(24): 123-127 (in Chinese) doi: 10.13465/j.cnki.jvs.2015.24.021
    [28] Zhou L, Zheng WX. Vibration of skew plates by the MLS-Ritz method. International Journal of Mechanical Sciences, 2008, 50(7): 1133-1141 doi: 10.1016/j.ijmecsci.2008.05.002
    [29] Reddy JN. Theory and Analysis of Elastic Plates and Shells. 2006
    [30] 彭林欣. 加肋板自由振动的移动最小二乘无单元分析. 振动与冲击, 2011, 30(6): 67-73 (Peng Linxin. Moving least squares element-free analysis of free vibration of ribbed plates. Journal of Vibration and Shock, 2011, 30(6): 67-73 (in Chinese) doi: 10.3969/j.issn.1000-3835.2011.06.015
    [31] Chen JS, Pan CH, Wu CT, et al. Reproducing Kernel particle methods for large deformation analysis of non-linear structures. Computer Methods in Applied Mechanics and Engineering, 1996, 139(01): 195-227
    [32] Peng LX, Kitipornchai S, Liew KM. Free vibration analysis of folded plate structures by the FSDT meshfree method. Computational Mechanics, 2007, 39(6): 799-814 doi: 10.1007/s00466-006-0070-9
    [33] 彭林欣. 折板结构非线性弯曲分析的移动最小二乘无网格法. 工程力学, 2011, 28(12): 126-132 (Peng Linxin. Moving least squares meshless method for nonlinear bending analysis of folded plate structures. Engineering Mechanics, 2011, 28(12): 126-132 (in Chinese)
    [34] 彭林欣, 谌亚菁, 覃霞等. 弹性地基圆形加肋板静力弯曲及弯曲自由振动分析的无网格法. 振动与冲击, 2022, 41(07): 11-22 + 30. 2022.07. 002

    Peng Linxin, Cen Yajin, Qin Xia, et al. Meshless method for static bending and bending free vibration analysis of circular ribbed plates in elastic foundation. Journal of Vibration and Shock, 2022, 41(07): 11-22 + 30. 2022.07. 002 (in Chinese)
    [35] Qin X, Shen Y, Chen W, et al. Bending and free vibration analyses of circular stiffened plates using the FSDT mesh-free method. International Journal of Mechanical Sciences, 2021(3): 106498
    [36] Goldberg DE. Genetic algorithms in search, optimization, and machine learning. Ethnographic Praxis in Industry Conference Proceedings, 1988, 9(2)
  • 加载中
图(18) / 表(5)
计量
  • 文章访问数:  70
  • HTML全文浏览量:  10
  • PDF下载量:  17
  • 被引次数: 0
出版历程
  • 网络出版日期:  2022-11-16

目录

    /

    返回文章
    返回