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用第三类四边形面积坐标构造一个四结点四边形膜元 被引量：2

A FOUR-NODE QUADRILATERAL MEMBRANE ELEMENT FORMULATED BY THE THIRD VERSION OF THE QUADRILATERAL AREA COORDINATE METHOD
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摘要 四边形第一类和第二类面积坐标(QAC-Ⅰ和QAC-Ⅱ)分别被提出以后,又提出了第三类面积坐标(QAC-Ⅲ),它不仅保留了QAC-Ⅰ和QAC-Ⅱ的主要优点,而且具有其他一些优异特性。该文应用第三类四边形面积坐标(QAC-Ⅲ),构造出一个含内参的四结点四边形膜元,记为QACⅢ-Q6元。这个新单元有以下优点:1)与Wilson的Q6元相比,新单元具有计算精度高,对网格畸变不敏感的优点;2)与基于QAC-Ⅰ和基于QAC-Ⅱ的Q6元相比,新单元不仅具有同样优异的单元性能,而且其推导方法更为简明,其形函数更为简洁。 With the first version and second version of quadrilateral area coordinate method （QAC-Ⅰ and QAC-Ⅱ） developed, the third version of quadrilateral area coordinate method （QAC-Ⅲ） is proposed, which, except for retaining main advantages of QAC-Ⅰ and QAC-Ⅱ, owns some other distinguishing features. In this paper, QAC-Ⅲ is used to formulate a new 4-node membrane element with internal parameters, denoted as element QACIII-Q6. This new element exhibits the following advantages： 1） compared with Wilson＇s element Q6, this new element possesses high accuracy and is insensitive to mesh distortion. 2） this new element has comparable performance to the Q6 elements formulated by QAC-Ⅰ and QAC-Ⅱ, moreover, the procedure in formulation is simple, and the expression for the shape function matrix is concise.
作者 王丽 龙志飞 龙驭球
机构地区 中国矿业大学(北京)力学与建筑工程学院 清华大学土木工程系
出处 《工程力学》 EI CSCD 北大核心 2009年第8期1-5,共5页 Engineering Mechanics
关键词 有限元 四边形膜元 第三类面积坐标 位移函数 网格畸变 finite element quadrilateral membrane element the third version of area coordinate displacement function mesh distortio
分类号 O241.82 [理学—计算数学]
  • 相关文献

参考文献9

  • 1龙驭球,龙志飞,王丽.四边形单元第三类面积坐标系统[J].工程力学,2009,26(2):1-4. 被引量：5
  • 2Long Yuqiu, Li Juxian, Long Zhifei, Cen Song. Area coordinates used in quadrilateral elements [J]. Communications in Numerical Methods in Engineering, 1999, 15(8): 533-545.
  • 3Chen X M, Cen S, Fu X R, Long Y Q. A new quadrilateral area coordinate method (QAC-Ⅱ) for developing quadrilateral finite element models [J]. International Journal for Numerical Methods in Engineering, 2008, 73(13): 1911-1941.
  • 4Wilson E L, Taylor R L, Doherty W P, Ghabussi T. Incompatible displacement models[C]// Fenven S T. Numerical and Computer Methods in Structural Mechanics. New York: Academic Press, 1973: 43 - 57.
  • 5Taylor R L, Beresford P J, Wilson E L. A non-conforming element for stress analysis [J]. International Journal for Numerical Methods in Engineering, 1976(10): 1211-1219.
  • 6Chen X M, Cen S, Long Y Q, Yao Z H. Membrane elements insensitive to distortion using the quadrilateral area coordinate method [J]. Computers and Structures, 2004, 82(1): 35-54.
  • 7Wu C C, Huang M G, Pian T H. Consistency condition and convergence criteria of incompatible elements: general formulation of incompatible functions and its application [J]. Computers & Structures, 1987, 27: 639- 644.
  • 8陈万吉 唐立民.等参拟协调元[J].大连工学院学报,1981,20(1):63-74.
  • 9Piltner R, Taylor R L. A systematic constructions of B-bar functions for linear and nonlinear mixed-enhanced finite elements for plane elasticity problems [J]. International Journal for Numerical Methods Engineering, 1997, 44: 615-639.

二级参考文献9

  • 1Long Yuqiu, Li Juxian, Long Zhifei. Area coordinates used in quadrilateral elements [J]. Communications in Numerical Methods in Engineering, 1999, 15(8): 533-545.
  • 2Chen X M, Cen S, Fu X R, Long Y Q. A new quadrilateral area coordinate method (QAC-II) for developing quadrilateral finite element models [J]. International Journal for Numerical Methods in Engineering, 2008, 73(13): 1911 - 1941.
  • 3Long Z F, Li J X, Cen S, Long Y Q. Some basic formulae for area coordinates used in quadrilateral elements [J]. Communications in Numerical Methods in Engineering, 1999, 15(12): 841-852.
  • 4Chen X M, Cen S, Long Y Q, Yao Z H. Membrane elements insensitive to distortion using the quadrilateral area coordinate method [J]. Computers and Structures, 2004, 82(1): 35-54.
  • 5Cen S, Du Y, Chen X M, Fu X R. The analytical element stiffness matrix of a recent 4-node membrane dement formulated by the quadrilateral area coordinate method [J]. Communications in Numerical Methods in Engineering, 2007, 23(12): 1095-1110.
  • 6Soh A K, Long Y Q, Cen S. Development of eight-node quadrilateral membrane elements using the area coordinates method [J]. Computational Mechanics, 2000, 25(4): 376-384.
  • 7Cen S, Long Y Q, Yao Z H, Chiew S P. Application of the quadrilateral area coordinate method: A new element for Mindlin-Reissner plate [J]. International Journal for Numerical Methods in Engineering, 2006, 66(1): 1 -45.
  • 8Song Cen,Xiangrong Fu,Yuqiu Long,Hongguang Li,Zhenhan Yao.Application of the quadrilateral area coordinate method:a new element for laminated composite plate bending problems[J].Acta Mechanica Sinica,2007,23(5):561-575. 被引量：6
  • 9龙驭球,李聚轩,龙志飞,岑松.四边形单元面积坐标理论[J].工程力学,1997,14(3):1-11. 被引量：29

共引文献15

同被引文献15

  • 1Long Yuqiu, Li Juxian, Long Zhifci. Area coordinates used in quadrilateral elements [J]. Communications in Numerical Methods in Engineering, 1999, 15(8): 533- 545.
  • 2Chen X M, Cen S, Fu X R, Long Y Q. A new quadrilateral area coordinate method (QAC-II ) for developing quadrilateral finite element models [J]. International Journal for Numerical Methods in Engineering, 2008, 73(13): 1911- 1941.
  • 3Lee N S, Bathe K J. Effects of element distortion on the performance of isoparametric elements [J]. International Journal for Numerical Methods in Engineering, 1993, 36: 3553 -3576.
  • 4Soh A K, Long Y Q, Ceil S. Development of eight-nodo quadrilateral membrane elements using the area coordinates method [J]. Computational Mechanics, 2000, 25(4): 376-384.
  • 5岑松,龙志飞,张春生.两个采用面积坐标的四边形八结点膜元[J].第7届全国结构工程学术会议论文集(Ⅰ),石家庄,1998,I(增刊):237-241.
  • 6Wilson E L, Taylor R L, Doherty W P, Ghabussi T. Incompatible displacement models [C]. Fenven ST. Numerical and Computer Methods in Structural Mechanics, Academic Press: New York, 1973: 43-57.
  • 7Long Yuqiu, Li Juxian, Long Zhifei. Area coordinated used in quadrilateral elements [J]. Communications in Numerical Methods in Engineering, 1999, 15(8): 533-545.
  • 8Chen X M, Cen S, Fu X R, Long Y Q. A new quadrilateral area coordinate method (QACM-II) for developing quadrilateral finite element models [J]. International Journal for Numerical Methods in Engineering, 2008, 73(13): 1911 - 1941.
  • 9Felippa C A, Bergan P G. Triangular bending FE based on energy-orthogonal free formulation [J]. Computer Methods in Applied Mechanics and Engineering, 1987, 61: 129-160.
  • 10Batoz J L, Tahar M B. Evaluation of a new quadrilateral thin plate bending elements [J]. International Journal for Numerical Methods in Engineering, 1982, 18: 1655- 1677.

引证文献2

二级引证文献5

工程力学
2009年 第8期

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