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Acta Mechanica Sinica

, Volume 29, Issue 4, pp 567–574 | Cite as

Development of quadrilateral spline thin plate elements using the B-net method

  • Juan Chen
  • Chong-Jun LiEmail author
Research Paper

Abstract

The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh distortions. In a previouswork, we constructed an 8-node quadrilateral spline element L8 using the triangular area coordinates and the B-net method, which can be insensitive to mesh distortions and possess the second order completeness in the Cartesian coordinates. In this paper, a thin plate spline element is developed based on the spline element L8 and the refined technique. Numerical examples show that the present element indeed possesses higher accuracy than the DKQ element for distorted meshes.

Keywords

Spline finite element Refined quadrilateral element Discrete Kirchhoff plate element Triangular area coordinates B-net method 

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References

  1. 1.
    Batoz, L., Tahar, M.B.: Evaluation of a new quadrilateral thin plate bending element. Int. J. Numer. Meth. Engng. 18, 1655–1677 (1982)zbMATHCrossRefGoogle Scholar
  2. 2.
    Jeyachandrabose, C., Kirkhope, J., Meekisho, L.: An impoved discrete kirchhoff quadrilateral thin-plate bending element. Int. J. Numer. Meth. Engng. 24, 635–654 (1987)zbMATHCrossRefGoogle Scholar
  3. 3.
    Chen, W.J., Cheung, Y.K.: Refined quadrilateral discrete Kirchhoff thin plate bending element. Int. J. Numer. Meth. Engng. 40, 3937–3953 (1997)zbMATHCrossRefGoogle Scholar
  4. 4.
    Long, Y.Q., Bu, X.M., Long, Z.F., et al.: Generalized conforming plate bending element using point and line compatibility conditions. Compu. Struct. 54, 717–723 (1995)zbMATHCrossRefGoogle Scholar
  5. 5.
    Soh, A.K., Long, Z.F., Cen, S.: Development of a new quadrilateral thin plate element using area coordinates. Comput. Methods Appl. Mech. Engrg. 190, 979–987 (2000)zbMATHCrossRefGoogle Scholar
  6. 6.
    Chen, X.M., Cen, S., Long, Y.Q.: Two thin plate elements developed by assuming rotations and using quadrilateral area coordinates. Engineering Mechanics 22, 1–5 (2005)zbMATHGoogle Scholar
  7. 7.
    Long, Y.Q., Cen, S., Long, Z.F.: Advanced Finite Element Method in Structural Engineering. Springer-Verlag GmbH/Tsinghua University Press, Berlin, Heidelberg/Beijing (2009)zbMATHCrossRefGoogle Scholar
  8. 8.
    Farin, G.: Triangular Bernstein-Bézier patches. Computer Aided Geometric Design 3, 83–127 (1986)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Li, C.J., Wang, R.H.: A new 8-node quadrilateral spline finite element. J. Comput. Appl. Math. 195, 54–65 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Chen, J., Li, C.J., Chen, W.J.: A family of spline finite elements. Computers and Structures 88, 718–727 (2010)CrossRefGoogle Scholar
  11. 11.
    Chen, J., Li, C.J., Chen, W.J.: Construction of n-sided polygonal spline element using area coordinates and B-net method. Acta Mech. Sin. 26, 685–693 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Li, C.J., Chen, J., Chen, W.J.: A 3D hexahedral spline element. Computers and Structures 89, 2303–2308 (2011)CrossRefGoogle Scholar
  13. 13.
    Chen, J., Li, C.J., Chen, W.J.: A 3D pyramid spline element. Acta Mech. Sin. 27, 986–993 (2011)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Fraeijs, de Veubeke, B.: A conforming finite element for plate bending. Int. J. Solids Structure 4, 95–108 (1968)zbMATHCrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.School of Mathematics and Quantitative EconomicsDongbei University of Finance and EconomicsDalianChina
  2. 2.School of Mathematical SciencesDalian University of TechnologyDalianChina

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