Nonconforming Stabilized Combined Finite Element Method for the Reissner-Mindlin Plate
-
摘要: 基于Reissner-Mindlin板的组合变分格式,提出了一种非协调稳定化组合有限元方法.若有限元空间满足能量协调条件,该方法收敛,并有误差估计.作为应用,讨论了3种有限元空间,并和MITC4和DKQ方法比较.数值结果表明该方法对网格畸变不敏感,若选取适当的参数,在粗网格上就有高精度.
-
关键词:
- Reissner-Mindlin板 /
- 能量协调条件 /
- 组合杂交元 /
- 非协调有限元
Abstract: Based on the combination of two variational principles, a nonoonfornung stabilized futile element method was presented for the Reissner-Mindlin plates. -
[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
点击查看大图
计量
- 文章访问数: 2697
- HTML全文浏览量: 80
- PDF下载量: 881
- 被引次数: 0