A 17-Node Quadrilateral Spline Finite Element Using the Triangular Area Coordinates

CHEN Juan; LI Chong-jun; CHEN Wan-ji

doi:10.3879/j.issn.1000-0887.2010.01.013

Volume 31 Issue 1

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CHEN Juan, LI Chong-jun, CHEN Wan-ji. A 17-Node Quadrilateral Spline Finite Element Using the Triangular Area Coordinates[J]. Applied Mathematics and Mechanics, 2010, 31(1): 117-126. doi: 10.3879/j.issn.1000-0887.2010.01.013

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A 17-Node Quadrilateral Spline Finite Element Using the Triangular Area Coordinates

doi: 10.3879/j.issn.1000-0887.2010.01.013

1.
School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, P. R. China;
State Key Laboratory for Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116024, P. R. China;

Received Date: 2009-07-20
Rev Recd Date: 2009-12-04
Publish Date: 2010-01-15

Abstract

Abstract

A 17-node quadrilateral element had been developed using the bivariate quartic spline interpolation basis and the triangular area coordinates, which could exactly model the quartic field. Some appropriate examples are employed to illustrate that the element possesses high precision and is insensitive to mesh distortions.
- 17-node quadrilateral element,
- bivariate spline in terpolation basis,
- triangular area coordinates,
- B-netmethod,
- fourth-order completeness

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References(11)

References

[1]	Zienkiewicz O C，Taylor R L. The Finite Element Method[M]. 5th ed. Singapore: Elsevier Pte Itd，2005.
[2]	Lee N S，Bathe K J. Effects of element distortion on the performance of isoparametric elements[J]. Int J Numer Methods Engrg，1993，36(20): 3553-3576. doi: 10.1002/nme.1620362009
[3]	Long Y Q,Li J X,Long Z F,et al.Area coordinates used in quadrilateral element[J]. Commun Numer Methods Engrg，1999，15(8): 533-545. doi: 10.1002/(SICI)1099-0887(199908)15:8<533::AID-CNM265>3.0.CO;2-D
[4]	Cen S，Chen X M，Fu X R. Quadrilateral membrane element family formulated by the quadrilateral area coordinate method[J]. Comput Methods Appl Mech Engrg，2007，196(41/44): 4337-4353. doi: 10.1016/j.cma.2007.05.004
[5]	李勇东，陈万吉. 精化不协调平面八节点元[J]. 计算力学学报，1997，14(3): 276-285.
[6]	Li C J，Wang R H. A new 8-node quadrilateral spline finite element[J]. J Comput Appl Math，2006，195(1/2): 54-65. doi: 10.1016/j.cam.2005.07.017
[7]	Rathod H T，Kilari S. General complete Lagrange family for the cube in finite element interpolations[J]. Comput Methods Appl Mech Engrg，2000，181(1/3): 295-344. doi: 10.1016/S0045-7825(99)00080-8
[8]	Ho S P，Yeh Y L. The use of 2D enriched elements with bubble functions for finite element ￣analysis[J]. Computers and Structures，2006，84(29/30): 2081-2091. doi: 10.1016/j.compstruc.2006.04.008
[9]	Wang R H. The structural characterization and interpolation for multivariate splines[J]. Acta Math Sinica，1975，18(2): 91-106.
[10]	Wang R H. Multivariate Spline Functions and Their Applications[M]. Beijing，New York，Dordrecht，Boston，London: Science Press，Kluwer Academic Publishers，2001.
[11]	Farin G. Triangular Bernstein-Bézier patches[J]. Computer Aided Geometric Design，1986，3(2): 83-127. doi: 10.1016/0167-8396(86)90016-6