FENG Min-fu, YANG Yan, ZHOU Tian-xiao. Nonconforming Stabilized Combined Finite Element Method for the Reissner-Mindlin Plate[J]. Applied Mathematics and Mechanics, 2009, 30(2): 192-202.
Citation: FENG Min-fu, YANG Yan, ZHOU Tian-xiao. Nonconforming Stabilized Combined Finite Element Method for the Reissner-Mindlin Plate[J]. Applied Mathematics and Mechanics, 2009, 30(2): 192-202.

Nonconforming Stabilized Combined Finite Element Method for the Reissner-Mindlin Plate

  • Received Date: 2007-12-24
  • Rev Recd Date: 2008-12-09
  • Publish Date: 2009-02-15
  • Based on the combination of two variational principles, a nonoonfornung stabilized futile element method was presented for the Reissner-Mindlin plates.
  • loading
  • [1]
    Brezzi F.Numerical approximation of Mindlin-Reissner plates[J].Math Comput,1986,47(175):151-158. doi: 10.1090/S0025-5718-1986-0842127-7
    [2]
    Duran R,Lieberman E.On mixed finite element methods for the Reissner-Mindlin plate model[J].Math Comput,1992,58(198):561-573.
    [3]
    ZHOU Tian-xiao. The partial projection method in the finite element discretization of the Reissner-Mindlin plate model[J].J Comput Math,1995,13(2):172-191.
    [4]
    Chinosi C. Remarks on some mixed finite element schemes for Reissner-Mindlin plate model[J].Calcolo,2002,39(2):87-108. doi: 10.1007/s100920200006
    [5]
    Lovadina C. A low-order nonconforming finite element for Reissner-Mindlin plates[J].SIAM J Numer Anal,2005,42(6):2688-2705. doi: 10.1137/040603474
    [6]
    Chinosi C,Lovadina C,Marini L D.Nonconforming locking-free finite elements for Reissner-Mindlin plates[J].Comput Methods Appl Mech Engng,2006,195(25/28):3448-3460. doi: 10.1016/j.cma.2005.06.025
    [7]
    MING Ping-bing,SHI Zhong-ci. Two nonconforming quadrilateral elements for the Reissner-Mindlin plate[J].Mathematical Models and Methods in Applied Science,2005,15(10):1503-1517. doi: 10.1142/S0218202505000868
    [8]
    LUO Kun,ZHOU Tian-xiao.An accurate quadrilateral plate element based on energy optimization[J].Commum Numer Meth Engng,2005,21(9):487-498. doi: 10.1002/cnm.761
    [9]
    CHEN Shao-chun,SHI Dong-yang. General error estimates of nonconforming plate elements[J].Mathematica Numerica Sinica,2000,22(1):295-300.
    [10]
    HU Jun,SHI Zhong-ci. Two lower order nonconforming rectangular elements for the Reissner-Mindlin plate[J].Math Comput,2007,76(260):1771-1786. doi: 10.1090/S0025-5718-07-01952-7
    [11]
    龙驭球,赵俊卿.厚板薄板通用的广义协调元[J].工程力学,1988,5(1):1-8.
    [12]
    龙志飞,岑松.有限元法新论[M].北京:中国水利水电出版社,2001.
    [13]
    CEN Song,LONG Yu-qiu,YAO Zhen-han,et al.Application of the quadrilateral area co-ordinate method: a new element for Mindlin-Reissner plate[J].Interernat J Numer Methods Engrg,2006,66(1):1-45. doi: 10.1002/nme.1533
    [14]
    FENG Min-fu,YANG Rong-kui,XIONG Hua-xin. Stabilized finite element methods for the Reissner-Mindlin plate[J].J Numer Math,1999,8(2):125-132.
    [15]
    Taylor R L,Simo J C,Zienkiewicz O C,et al. The patch test—a condition for assessing FEM convergence[J].Internat J Numer Methods Engrg,1986,22(1):39-62. doi: 10.1002/nme.1620220105
    [16]
    WU Chang-chun,BIAN Xue-huang.Nonconforming Numerical Analysis and Combined Hybird Finite Element Methods[M].Beijing:Science Press,1997.
    [17]
    SHI Zhong-ci. A convergence condition for the quadrilateral Wilson element[J].Numer Math,1984,44(3):349-361. doi: 10.1007/BF01405567
    [18]
    ZHANG Zhi-min,ZHANG Shang-you. Derivative superconvergence of rectangular finite elements for the reissner--mindlin plate[J].Comput Methods Appl Mech Eng,1995,134(1):1-16 .
    [19]
    Bathe K J,Dvorkin E. A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation[J].Internat J Numer Methods Engrg,1985,21(2):367-383. doi: 10.1002/nme.1620210213
    [20]
    Batoz J L,Bentahar M. Evaluation of a new quadrilateral thin plate bending element[J].Internat J Numer Methods Engrg,1982,18(11):1655-1677. doi: 10.1002/nme.1620181106
    [21]
    Brezzi F,Fortin M. Mixed and Hybrid Finite Method[M].New York:Springer-Verlag,1991.
    [22]
    ZHOU Tian-xiao. Stabilized hybrid finite element methods based on the combination of saddle point principles of elasticity problems[J].Math Comput,2003,72(244):1655-1673. doi: 10.1090/S0025-5718-03-01473-X
  • 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

    Article Metrics

    Article views (2676) PDF downloads(880) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return