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

基于弹性边界的多墙式盒段结构复合材料壁板屈曲分析方法

赵北 熊斯浚 陈亮 王成波 李锐

赵北, 熊斯浚, 陈亮, 王成波, 李锐. 基于弹性边界的多墙式盒段结构复合材料壁板屈曲分析方法[J]. 应用数学和力学, 2024, 45(9): 1182-1199. doi: 10.21656/1000-0887.440283
引用本文: 赵北, 熊斯浚, 陈亮, 王成波, 李锐. 基于弹性边界的多墙式盒段结构复合材料壁板屈曲分析方法[J]. 应用数学和力学, 2024, 45(9): 1182-1199. doi: 10.21656/1000-0887.440283
ZHAO Bei, XIONG Sijun, CHEN Liang, WANG Chengbo, LI Rui. A Buckling Analysis Method for Composite Panels in Multiweb Box Structures Based on Elastic Boundaries[J]. Applied Mathematics and Mechanics, 2024, 45(9): 1182-1199. doi: 10.21656/1000-0887.440283
Citation: ZHAO Bei, XIONG Sijun, CHEN Liang, WANG Chengbo, LI Rui. A Buckling Analysis Method for Composite Panels in Multiweb Box Structures Based on Elastic Boundaries[J]. Applied Mathematics and Mechanics, 2024, 45(9): 1182-1199. doi: 10.21656/1000-0887.440283

基于弹性边界的多墙式盒段结构复合材料壁板屈曲分析方法

doi: 10.21656/1000-0887.440283
(我刊编委李锐来稿)
基金项目: 

国家自然科学基金 12372067

国家自然科学基金 12022209

详细信息
    作者简介:

    赵北(1998—),男,助理工程师(E-mail: zhaobei1998@163.com)

    熊斯浚(1994—),男,工程师(E-mail: xiongsijun@mail.dlut.edu.cn)

    陈亮(1977—),男,研究员(E-mail: liangchen110035@163.com)

    王成波(1977—),男,正高级工程师(E-mail: chengbowang110035@163.com)

    通讯作者:

    李锐(1985—),男,教授,博士,博士生导师(通讯作者. E-mail: ruili@dlut.edu.cn)

  • 中图分类号: O343.9

A Buckling Analysis Method for Composite Panels in Multiweb Box Structures Based on Elastic Boundaries

(Contributed by LI Rui, M.AMM Editorial Board)
  • 摘要: 机翼中的多墙式盒段结构是飞机结构设计的重点关注区域之一. 盒段结构主要由蒙皮以及支撑件组合而成,其中蒙皮被支撑件近似分隔为多个矩形壁板. 在飞机服役过程中,机翼主要承受弯曲、扭转或者弯扭耦合载荷等作用,导致盒段结构中矩形壁板容易产生失稳. 在传统复合材料壁板屈曲分析中,往往将边界简化为固支或简支,所得结果与试验差距较大,而采用有限元方法进行全面模拟往往效率较低. 针对上述问题,该文提出了一种结合单胞模型以及微分求积法的复合材料壁板快速屈曲分析方法. 首先,建立了单胞模型计算矩形壁板的弹性边界刚度系数;然后,通过微分求积法求解控制方程,获得了壁板的屈曲载荷;最后,计算了不同类型盒段结构中复合材料壁板的屈曲载荷,并与有限元结果进行对比,验证了该文屈曲分析方法的准确性.
    1)  (我刊编委李锐来稿)
  • 图  1  微分求积法的收敛性分析

    Figure  1.  Convergence study of the differential quadrature method

    图  2  弹性边界示意图

    Figure  2.  Schematic of elastic boundaries

    图  3  复合材料层合板屈曲载荷与边界条件的关系

    Figure  3.  Buckling loads on composite laminates vs. the boundary conditions

    图  4  单胞模型

    Figure  4.  The unit cell model

    图  5  边界与弯矩载荷

    Figure  5.  Boundaries and bending moment loads

    图  6  层合板各单层z坐标

    Figure  6.  Z-coordinates of each layer of the laminate

    图  7  基于弹性边界的多墙式盒段结构复合材料壁板屈曲分析流程

    Figure  7.  Process of buckling analysis on composite panels for multiweb box structures based on elastic boundaries

    图  8  1号盒段模型

    Figure  8.  Box model 1

    图  9  1号盒段模型

    Figure  9.  Box model 1

    图  10  求解矩形壁板弹性边界刚度系数的单胞模型

    Figure  10.  The unit cell model for calculating the stiffness coefficients of elastic boundaries of the rectangular panel

    图  11  2号盒段模型

    Figure  11.  Box model 2

    图  12  3号盒段模型

    Figure  12.  Box model 3

    图  13  4号盒段模型

    Figure  13.  Box model 4

    图  14  弯剪工况下四种类型盒段结构复合材料壁板在不同边界条件下的屈曲载荷

    Figure  14.  Buckling loads on composite panels in 4 types of box structures with different boundary conditions under bending and shearing

    图  15  单轴压工况

    Figure  15.  The uniaxial compression condition

    图  16  单轴压工况下四种盒段结构复合材料壁板在不同边界条件下的屈曲载荷

    Figure  16.  Buckling loads on composite panels in 4 box structures with different boundary conditions under uniaxial compression

    表  1  常用节点分布公式

    Table  1.   Commonly used formulas of node distribution

    number formula
    1 $x_i=2 \frac{i-1}{N}-1, x_1=-1, x_{N+1}=1$
    2 $x_i=\frac{1}{2}-\frac{1}{2} \cos \left[\frac{(i-1) \pi}{N}\right]$
    3 $x_i=\frac{1}{2}+\frac{1}{2} \cos \left[\frac{(N+1-i) \pi}{N}\right]$
    4 $x_i=\cos \left[\frac{(N+1-i) \pi}{N}\right]$
    5 $x_i=-\frac{1}{2} \cos \left[\frac{(i-1) \pi}{N}\right]$
    下载: 导出CSV

    表  2  正交各向异性单层板无量纲屈曲载荷Ncr的收敛性分析

    Table  2.   Dimensionless buckling loads on the orthotropic single-layer plate

    N dimensionless buckling load Ncr
    clamped boundary simply supported boundary
    5 11.175 4.479 2
    6 12.321 4.498 9
    7 12.428 4.500 0
    8 12.487 4.500 0
    9 12.403 4.500 0
    10 12.448 4.500 0
    20 12.449 4.500 0
    50 12.449 4.500 0
    下载: 导出CSV

    表  3  弹性边界下正交各向异性单层板的无量纲屈曲载荷Ncr

    Table  3.   Dimensionless buckling loads Ncr on the orthotropic single-layer plate under elastic boundaries

    η R ref. [27] present
    0.5 0.1 6.436 1 6.436 1
    0.3 7.537 4 7.537 4
    0.5 9.073 5 9.073 5
    0.7 11.147 11.147
    1 0.1 4.827 1 4.827 1
    0.3 5.654 8 5.654 8
    0.5 6.820 4 6.820 4
    0.7 8.511 6 8.511 6
    2 0.1 3.218 1 3.218 1
    0.3 3.769 9 3.769 9
    0.5 4.548 4 4.548 4
    0.7 5.688 3 5.688 3
    下载: 导出CSV

    表  4  T300/976的材料参数

    Table  4.   Material parameters of T300/976

    material parameter E11/MPa E22/MPa G12/MPa G13/MPa G23/MPa υ12
    value 156 500 13 000 6 960 6 960 3 450 0.23
    下载: 导出CSV

    表  5  单轴压工况下复合材料层合板的无量纲屈曲载荷Ncr

    Table  5.   Dimensionless buckling loads Ncr on composite laminates under uniaxial compression

    R Ncr error ε/%
    FEM present
    0.000 01 22.110 22.288 0.80
    0.1 22.802 22.987 0.81
    0.2 23.599 23.792 0.82
    0.3 24.530 24.729 0.81
    0.4 25.632 25.836 0.79
    0.5 26.964 27.170 0.76
    0.6 28.616 28.821 0.72
    0.7 30.756 30.959 0.66
    0.8 33.743 33.945 0.60
    0.9 38.428 38.645 0.56
    0.999 99 47.122 47.422 0.64
    下载: 导出CSV

    表  6  双轴压工况下复合材料层合板的无量纲屈曲载荷Ncr

    Table  6.   Dimensionless buckling loads Ncr on composite laminates under biaxial compression

    R Ncr error ε/%
    FEM present
    0.000 01 9.942 7 9.970 2 0.28
    0.1 10.457 10.491 0.33
    0.2 11.071 11.113 0.38
    0.3 11.816 11.867 0.43
    0.4 12.650 12.744 0.74
    0.5 13.642 13.743 0.74
    0.6 14.932 15.039 0.71
    0.7 16.690 16.804 0.68
    0.8 19.259 19.380 0.63
    0.9 23.406 23.532 0.54
    0.999 99 30.298 30.423 0.41
    下载: 导出CSV

    表  7  不同边界下复合材料层合板的屈曲载荷

    Table  7.   Buckling loads on composite laminates under different boundary conditions

    simply supported boundary Ncr/N clamped boundary Ncr/N elastic boundary Ncr/N
    R=0.3 R=0.4 R=0.5 R=0.6 R=0.7
    61.42 130.68 71.96 76.88 82.85 89.91 96.12
    下载: 导出CSV

    表  8  不同边界下模型1壁板的屈曲载荷

    Table  8.   Buckling loads on the panel in box model 1 under different boundary conditions

    FEM boundary conditions
    simply supported boundary clamped boundary elastic boundary
    the buckling load Ncr/N 8 763 3 261 11 776 8 723
    error ε/% - -62.79 34.38 -0.46
    下载: 导出CSV

    表  9  不同边界下模型2壁板的屈曲载荷

    Table  9.   Buckling loads on the panel in box model 2 under different boundary conditions

    FEM boundary conditions
    simply supported boundary clamped boundary elastic boundary
    the buckling load Ncr/N 3 854 1 975 4 685 3 950
    error ε/% - -48.75 21.55 2.50
    下载: 导出CSV

    表  10  不同边界下模型3壁板的屈曲载荷

    Table  10.   Buckling loads on the panel in box model 3 under different boundary conditions

    FEM boundary condition
    simply supported boundary clamped boundary elastic boundary
    the buckling load Ncr/N 1 477 740 1 724 1 492
    error ε/% - -49.87 16.70 1.03
    下载: 导出CSV

    表  11  不同边界下模型4壁板的屈曲载荷

    Table  11.   Buckling loads on the panel in box model 4 under different boundary conditions

    FEM boundary condition
    simply supported boundary clamped boundary elastic boundary
    the buckling load Ncr/N 2 663 1 160 3 203 2 764
    error ε/% - -56.43 20.28 3.82
    下载: 导出CSV

    表  12  单轴压工况下四种盒段模型中矩形壁板在不同边界下的屈曲载荷

    Table  12.   Buckling loads on rectangular panels in 4 box models with different boundary conditions under uniaxial compression

    box models FEM Ncr/N elastic boundary Ncr/N error ε/% simply supported boundary Ncr/N error ε/% clamped boundary Ncr/N error ε/%
    model 1 55 545 51 690 -6.94 21 166 -61.89 67 471 21.47
    model 2 36 460 35 986 -1.30 17 994 -50.65 42 783 17.34
    model 3 24 664 24 396 -1.09 12 929 -47.58 27 861 12.96
    model 4 64 470 69 312 7.51 34 543 -46.42 81 996 27.18
    下载: 导出CSV
  • [1] 党乐, 郑洁, 杜凯, 等. 复合材料多墙盒段弯扭耦合下的屈曲和后屈曲[J]. 力学季刊, 2022, 43(2): 271-280.

    DANG Le, ZHENG Jie, DU Kai, et al. Buckling and post buckling of composite multi-wall box section under bending-torsion coupled loads[J]. Chinese Quarterly of Mechanics, 2022, 43(2): 271-280. (in Chinese)
    [2] 钱伟长. 奇异摄动理论及其在力学中的应用[M]. 北京: 科学出版社, 1981.

    CHIEN Weizang. Singular Perturbation Theory and Its Applications in Mechanics[M]. Beijing: Science Press, 1981. (in Chinese)
    [3] STEEN E. Application of the perturbation method to plate buckling problems[R]. 1998.
    [4] 付为刚, 廖喆, 熊焕杰, 等. 含对边自由边界矩形板屈曲失稳的有限差分法求解[J]. 陕西科技大学学报, 2022, 40(4): 134-141.

    FU Weigang, LIAO Zhe, XIONG Huanjie, et al. Finite difference method for the solution of buckling instability for rectangular plates with opposite free boundary edges[J]. Journal of Shaanxi University of Science & Technology, 2022, 40(4): 134-141. (in Chinese)
    [5] ALTINTAŞ G, BAǦCI M. Determination of the steady-state response of viscoelastically supported rectangular orthotropic mass loaded plates by an energy-based finite difference method[J]. Journal of Vibration and Control, 2005, 11(12): 1535-1552. doi: 10.1177/1077546305061037
    [6] NAJARZADEH L, MOVAHEDIAN B, AZHARI M. Free vibration and buckling analysis of thin plates subjected to high gradients stresses using the combination of finite strip and boundary element methods[J]. Thin-Walled Structures, 2018, 123 : 36-47. doi: 10.1016/j.tws.2017.11.015
    [7] HEUER R, IRSCHIK H. A boundary element method for eigenvalue problems of polygonal membranes and plates[J]. Acta Mechanica, 1987, 66(1/4): 9-20.
    [8] RODRIGUES J D, ROQUE C M C, FERREIRA A J M. An improved meshless method for the static and vibration analysis of plates[J]. Mechanics Based Design of Structures and Machines, 2013, 41(1): 21-39. doi: 10.1080/15397734.2012.680348
    [9] HOSSEINI S, RAHIMI G, ANANI Y. A meshless collocation method based on radial basis functions for free and forced vibration analysis of functionally graded plates using FSDT[J]. Engineering Analysis With Boundary Elements, 2021, 125 : 168-177. doi: 10.1016/j.enganabound.2020.12.016
    [10] 王伟, 姚林泉, 伊士超. 分析复合材料层合板弯曲和振动的一种有效无网格方法[J]. 应用数学和力学, 2015, 36(12): 1274-1284. doi: 10.3879/j.issn.1000-0887.2015.12.006

    WANG Wei, YAO Linquan, YIN Shichao. An effective meshfree method for bending and vibration analyses of laminated composite plates[J]. Applied Mathematics and Mechanics, 2015, 36(12): 1274-1284. (in Chinese) doi: 10.3879/j.issn.1000-0887.2015.12.006
    [11] 彭林欣, 张鉴飞, 陈卫. 基于3D连续壳理论和无网格法的任意壳受迫振动分析[J]. 固体力学学报, 2024, 45(2): 238-252.

    PENG Linxin, ZHANG Jianfei, CHEN Wei. Forced vibration analysis of arbitrary shells based on 3D continuous shell theory and meshless method[J]. Chinese Journal of Solid Mechanics, 2024, 45(2): 238-252. (in Chinese)
    [12] ZAMANIFAR H, SARRAMI-FOROUSHANI S, AZHARI M. Static and dynamic analysis of corrugated-core sandwich plates using finite strip method[J]. Engineering Structures, 2019, 183 : 30-51. doi: 10.1016/j.engstruct.2018.12.102
    [13] SHEIKH H A, MUSHOPADYAY M. Forced vibration of plates with elastically restrained edges by the spline finite strip method[J]. JSME International Journal (Series C): Dynamics Control Robotics Design and Manufacturing, 1993, 36(3): 301-306. doi: 10.1299/jsmec1993.36.301
    [14] YUAN W, DAWE D J. Free vibration and stability analysis of stiffened sandwich plates[J]. Composite Structures, 2004, 63(1): 123-137. doi: 10.1016/S0263-8223(03)00139-9
    [15] BATHE K J. Finite Element Method[M]. Wiley, 2008: 1-12.
    [16] WANG X, HUANG J. Elastoplastic buckling analyses of rectangular plates under biaxial loadings by the differential qudrature method[J]. Thin-Walled Structures, 2009, 47(1): 14-20. doi: 10.1016/j.tws.2008.04.006
    [17] LI P, YING W. Differential quadrature method for vibration analysis of prestressed beams[J]. E 3 S Web of Conferences, 2021, 237 : 03029. doi: 10.1051/e3sconf/202123703029
    [18] UDAYAKUMAR B, GOPAL N. Analysis of layered panels with mixed edge boundary conditions using state space differential quadrature method[J]. Composite Structures, 2021, 274 : 114355. doi: 10.1016/j.compstruct.2021.114355
    [19] MOHAMMADIMEHR M, MEHDI M, AFSHARI B, et al. Bending, buckling and vibration analyses of MSGT microcomposite circular-annular sandwich plate under hydro-thermo-magneto-mechanical loadings using DQM[J]. International Journal of Smart and Nano Materials, 2018, 9(4): 233-260. doi: 10.1080/19475411.2017.1377312
    [20] 陈明飞, 刘坤鹏, 靳国永, 等. 面内功能梯度三角形板等几何面内振动分析[J]. 应用数学和力学, 2020, 41(2): 156-170.

    CHEN Mingfei, LIU Kunpeng, JIN Guoyong, et al. Isogeometric in-plane vibration analysis of functionally graded triangular plates[J]. Applied Mathematics and Mechanics, 2020, 41(2): 156-170. (in Chinese)
    [21] LAURA P A A, DURAN R. A note on forced vibrations of a clamped rectangular plate[J]. Journal of Sound and Vibration, 1975, 42(1): 129-135. doi: 10.1016/0022-460X(75)90307-7
    [22] BELLMAN R, CASTI J. Differential quadrature and long-term integration[J]. Journal of Mathematical Analysis and Applications, 1971, 34(2): 235-238. doi: 10.1016/0022-247X(71)90110-7
    [23] 王永亮. 微分求积法和微分求积单元法: 原理与应用[D]. 南京: 南京航空航天大学, 2002.

    WANG Yongliang. Differential quadrature method and differential quadrature element method: theory and application[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2002. (in Chinese)
    [24] 张太莲. 微分求积法在一类时间分数阶微分方程中的应用[D]. 广州: 华南理工大学, 2015.

    ZHANG Tailian. The application and generalization of a differential quadrature algorithm for time-fractional telegraph equation[D]. Guangzhou: South China University of Technology, 2015. (in Chinese)
    [25] REDDY J N. Mechanics of Laminated Composite Plates and Shells[M]. Boca Raton: CRC Press, 2004.
    [26] ZHANG S, XU L. Bending of rectangular orthotropic thin plates with rotationally restrained edges: a finite integral transform solution[J]. Applied Mathematical Modelling, 2017, 46 : 48-62. doi: 10.1016/j.apm.2017.01.053
    [27] ZHANG J, ZHAO Q, ULLAH S, et al. An accurate computational method for buckling of orthotropic composite plate with non-classical boundary restraints[J]. International Journal of Structural Stability and Dynamics, 2023, 23(7): 2350080. doi: 10.1142/S0219455423500803
    [28] 鹿澳沣. 基于Puck准则的航空用复合材料失效分析及实验研究[D]. 南京: 南京航空航天大学, 2019.

    LU Aofeng. The failure analysis and experimental research of aviation composites based on Puck criterion[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2019. (in Chinese)
    [29] 沈观林, 胡更开, 刘彬. 复合材料力学[M]. 2版. 北京: 清华大学出版社, 2013.

    SHEN Guanlin, HU Gengkai, LIU Bin. Mechanics of Composite Materials[M]. 2nd ed. Beijing: Tsinghua University Press, 2013. (in Chinese)
  • 加载中
图(16) / 表(12)
计量
  • 文章访问数:  106
  • HTML全文浏览量:  34
  • PDF下载量:  29
  • 被引次数: 0
出版历程
  • 收稿日期:  2023-09-20
  • 修回日期:  2024-05-27
  • 刊出日期:  2024-09-01

目录

    /

    返回文章
    返回