轴向荷载下功能梯度材料圆柱壳的动力屈曲

周佳华 杨强 韩志军 路国运

周佳华, 杨强, 韩志军, 路国运. 轴向荷载下功能梯度材料圆柱壳的动力屈曲[J]. 高压物理学报, 2018, 32(5): 054102. doi: 10.11858/gywlxb.20180502
引用本文: 周佳华, 杨强, 韩志军, 路国运. 轴向荷载下功能梯度材料圆柱壳的动力屈曲[J]. 高压物理学报, 2018, 32(5): 054102. doi: 10.11858/gywlxb.20180502
ZHOU Jiahua, YANG Qiang, HAN Zhijun, LU Guoyun. Dynamic Buckling of Functionally Graded Cylindrical Shells under Axial Loading[J]. Chinese Journal of High Pressure Physics, 2018, 32(5): 054102. doi: 10.11858/gywlxb.20180502
Citation: ZHOU Jiahua, YANG Qiang, HAN Zhijun, LU Guoyun. Dynamic Buckling of Functionally Graded Cylindrical Shells under Axial Loading[J]. Chinese Journal of High Pressure Physics, 2018, 32(5): 054102. doi: 10.11858/gywlxb.20180502

轴向荷载下功能梯度材料圆柱壳的动力屈曲

doi: 10.11858/gywlxb.20180502
基金项目: 

国家自然科学基金 11372209

详细信息
    作者简介:

    周佳华(1992—), 女, 硕士研究生, 主要从事非线性动力屈曲研究. E-mail: 18234133316@163.com

    通讯作者:

    杨强(1962—), 男, 博士, 副教授, 主要从事非线性动力屈曲研究. E-mail: yangqiang62@126.com

  • 中图分类号: O343

Dynamic Buckling of Functionally Graded Cylindrical Shells under Axial Loading

  • 摘要: 基于Donnell壳体理论和经典板壳理论,利用Hamilton变分原理得到轴向荷载作用下材料属性呈幂律分布的功能梯度材料圆柱壳的动力屈曲控制方程。根据圆柱壳周向连续性设出径向位移的函数表达,利用分离变量法求解得到功能梯度材料圆柱壳在轴向荷载作用下的动力屈曲临界荷载的解析表达式和屈曲解。利用MATLAB软件编程计算,讨论了径厚比、梯度指数、环向模态数、轴向模态数等对功能梯度材料圆柱壳动力屈曲临界荷载的影响。结果表明:圆柱壳的临界荷载随临界长度的增加而减小;冲击端为夹支的临界荷载比冲击端为简支的临界荷载大,说明约束条件对临界荷载有较大影响;圆柱壳的临界荷载随着模态数的增加而增大,说明临界荷载越大,高阶模态越易被激发;屈曲模态图随着模态数的增加而复杂化。

     

  • 图  圆柱壳坐标系统

    Figure  1.  Cylindrical shell coordinates

    图  材料沿壁厚分布

    Figure  2.  Distribution of material along wall thickness

    图  不同材料组成下临界荷载与临界长度的关系

    Figure  3.  Critical load vs.critical length under different material composition conditions

    图  冲击端为夹支时不同径厚比下临界荷载与临界长度的关系

    Figure  4.  Critical load vs.critical length under clamped edge and different diameter-thickness ratios conditions

    图  冲击端为简支时不同径厚比下临界荷载与临界长度的关系

    Figure  5.  Critical load vs.critical length under simple support and different diameter-thickness ratios conditions

    图  冲击端为夹支时不同梯度指数下临界荷载与临界长度的关系

    Figure  6.  Critical load vs.critical length under clamped edge and different gradient indexes conditions

    图  冲击端为简支时不同梯度指数下临界荷载与临界长度的关系

    Figure  7.  Critical load vs.critical length under simple support and different gradient indexes conditions

    图  冲击端为夹支时不同环向模态数下临界荷载与临界长度的关系

    Figure  8.  Critical load vs.critical length under clamped edge and different circumferential modal number conditions

    图  冲击端为简支时不同环向模态数下临界荷载与临界长度的关系

    Figure  9.  Critical load vs.critical length under simple support and different circumferential modal number conditions

    图  10  冲击端为夹支时不同轴向模态数下临界荷载与临界长度的关系

    Figure  10.  Critical load vs.critical length under clamped edge and different axial modal number conditions

    图  11  冲击端为简支时不同轴向模态数下临界荷载与临界长度的关系

    Figure  11.  Critical load vs.critical length under simple support and different axial modal number conditions

    图  12  不同环向屈曲模态图(n=1;m=1, 2, 3, 4, 5, 6)

    Figure  12.  Different circumferential buckling modes (n=1;m=1, 2, 3, 4, 5, 6)

    图  13  不同轴向屈曲模态图(m=2;n=1, 2, 3, 4, 5, 6)

    Figure  13.  Different axial buckling modes (m=2;n=1, 2, 3, 4, 5, 6)

    表  1  材料参数

    Table  1.   Material parameters

    Material E/GPa ρ/(g·cm-3) μ
    Ceramic 385 3.96 0.230
    Ti 109 4.54 0.410
    Fe 155 7.86 0.291
    Cu 119 8.96 0.326
    下载: 导出CSV
  • [1] KOIZUMI M. The concept of FGM//ZHAI P C, JIANG C R, ZHANG Q J, et al. Ceramic Transactions: Functionally Gradient Materials. Westerville, OH: The American Ceramic Society, 1993, 34: 3-10.
    [2] LOY C T, LAM K Y, REDDY J N.Vibration of functionally graded cylindrical shells[J].International Journal of Mechanical Sciences, 1999, 41(3):309-324. doi: 10.1016/S0020-7403(98)00054-X
    [3] SURESH S, MORTENSEN A.Fundamentals of functionally graded materials[M].The Institute of Materials, 1998:18.
    [4] ELLINAS C P, CROLL J G A.Elastic-plastic buckling design of cylindrical shells subject to combined axial compression and pressure loading[J].International Journal of Solids and Structures, 1986, 22(9):1007-1017. doi: 10.1016/0020-7683(86)90033-8
    [5] VAZIRI A, ESTEKANCHI H E.Buckling of cracked cylindrical thin shells under combined internal pressure and axial compression[J].Thin-Walled Structures, 2006, 44(2):141-151. doi: 10.1016/j.tws.2006.02.004
    [6] LATIFI M, FARHATNIA F, KADKHODAEI M.Buckling analysis of rectangular functionally graded plates under various edge conditions using Fourier series expansion[J].European Journal of Mechanics-A/Solids, 2013, 41(11):16-27. http://linkinghub.elsevier.com/retrieve/pii/S0997753813000107
    [7] MANTARI J L, MONGE J C.Buckling, free vibration and bending analysis of functionally graded sandwich plates based on an optimized hyperbolic unified formulation[J].International Journal of Mechanical Sciences, 2016, 119:170-186. doi: 10.1016/j.ijmecsci.2016.10.015
    [8] LI S R, BATRA R C.Buckling of axially compressed thin cylindrical shells with functionally graded middle layer[J].Thin-Walled Structures, 2006, 44(10):1039-1047. doi: 10.1016/j.tws.2006.10.006
    [9] BENI T Y, MEHRALIAN F, ZEIGHAMPOUR H.The modified couple stress functionally graded cylindrical thin shell formulation[J].Mechanics of Advanced Materials and Structures, 2016, 23(7):791-801. doi: 10.1080/15376494.2015.1029167
    [10] KARGARNOVIN M H, HASHEMI M.Buckling analysis of multilayered functionally graded composite cylindrical shells//Applied Mechanics and Materials.Trans Tech Publications, 2012, 108:74-79. http://adsabs.harvard.edu/abs/2011AMM...108...74K
    [11] SOFIYEV A, DENIZ A, MECITOGLU Z, et al.Buckling of shear deformable functionally graded orthotropic cylindrical shells under a lateral pressure[J].Acta Physica Polonica A, 2015, 127(4):907-909. doi: 10.12693/APhysPolA.127.907
    [12] KHAZAEINEJAD P, NAJAFIZADEH M M, JENABI J, et al.On the buckling of functionally graded cylindrical shells under combined external pressure and axial compression[J].Journal of Pressure Vessel Technology, 2010, 132(6):064501. doi: 10.1115/1.4001659
    [13] KHALILI S M R, MALEKZADEH K, DAVAR A.Dynamic response of functionally graded circular cylindrical shells//Advanced Materials Research.Trans Tech Publications, 2008, 47:608-611. http://www.scientific.net/AMR.47-50.608
    [14] ALASHTI R A, AHMADI S A.Buckling analysis of functionally graded thick cylindrical shells with variable thickness using DQM[J].Arabian Journal for Science and Engineering, 2014, 39(11):8121-8133. doi: 10.1007/s13369-014-1356-4
    [15] 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.
    [16] 孟豪, 韩志军, 路国运.复合材料圆柱壳非轴对称动力屈曲[J].振动与冲击, 2017, 36(11):27-30. http://d.old.wanfangdata.com.cn/Periodical/zdycj201711005

    MENG H, HAN Z J, LU G Y.Non-axisymmetric dynamic buckling of composite cylindrical shells[J].Journal of Vibration and Shock, 2017, 36(11):27-30. http://d.old.wanfangdata.com.cn/Periodical/zdycj201711005
    [17] WANG J Q, HAN Z J, LU G Y.Dynamic buckling of elastic cylindrical shells under axial step load[J].Applied Mechanics & Materials, 2015, 751:182-188. http://www.scientific.net/AMM.751.182
    [18] 韩志军.直杆的撞击屈曲及其应力波效应的实验和理论研究.太原:太原理工大学, 2005.
    [19] YU X H, HAN Z J, KANG Z Y, et al. Computer simulation of cylindrical shell penetrated by rigid projectile//Applied Mechanics and Materials. Trans Tech Publications, 2012, 152: 594-598.
    [20] 李楠, 韩志军, 路国运.基于里兹法研究复合材料层合板的动力屈曲问题[J].振动与冲击, 2016, 35(10):180-184. http://d.old.wanfangdata.com.cn/Periodical/zdycj201610029

    LI N, HAN Z J, LU G Y.Dynamic buckling analysis of laminated composite plates by using Ritz method[J].Journal of Vibration and Shock, 2016, 35(10):180-184. http://d.old.wanfangdata.com.cn/Periodical/zdycj201610029
  • 加载中
图(13) / 表(1)
计量
  • 文章访问数:  7162
  • HTML全文浏览量:  3246
  • PDF下载量:  179
出版历程
  • 收稿日期:  2018-01-08
  • 修回日期:  2018-05-22

目录

    /

    返回文章
    返回