Volume 45 Issue 9
Sep.  2024
Turn off MathJax
Article Contents
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

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

doi: 10.21656/1000-0887.440283
  • Received Date: 2023-09-20
  • Rev Recd Date: 2024-05-27
  • Publish Date: 2024-09-01
  • The multiweb box structures in the wings are paid special attention in aircrafts' structural design. The multiweb box is mainly composed of skins and stiffeners. The skins are approximately divided into many rectangular panels by stiffeners. During the service of an aircraft, the wing majorly bears bending, torsion, and bending-torsion coupling loads, etc., so the panels in box structures are susceptible to instability. In traditional buckling analysis of composite panels, the boundary conditions were typically simplified as either clamped or simply supported boundaries, with significant deviations from experimental results. On the other hand, comprehensive simulations with the finite element method are generally inefficient. Aimed at the above issues, a rapid buckling analysis method combining the unit cell model with the differential quadrature method for composite panels was proposed. Firstly, the unit cell model was established to calculate the stiffness coefficients of elastic boundaries of rectangular panels. The governing equations were then solved with the differential quadrature method to obtain the buckling loads on the panels. Finally, the buckling loads on composite panels in different types of box structures were calculated and compared to the results obtained with the finite element method to verify the accuracy of the presented buckling analysis method.
  • (Contributed by LI Rui, M.AMM Editorial Board)
  • loading
  • [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

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(16)  / Tables(12)

    Article Metrics

    Article views (121) PDF downloads(30) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return