Advertisement

Generalized Conforming Thin Plate Element II—Line-Point and SemiLoof Conforming Schemes

  • Zhi-Fei Long
  • Song Cen

Abstract

Five groups of construction schemes for the generalized conforming thin plate elements are proposed in Sect. 5.4. This chapter discusses the first three groups: (1) line conform ing scheme (Sect. 6.1); (2) line-point conforming scheme (Sects. 6.2 and 6.3) and super-basis line-point conforming scheme (Sect. 6.4); and (3) super-basis point conforming scheme (Sect. 6.5) and SemiLoof conforming scheme (Sect. 6.6). Formulations of 13 triangular, rectangular and quadrilateral generaliz ed conforming thin plate elements, which are constructed by the above schemes, are introduced in detail. The elements formulated in Sects. 6.1 to 6.3 belong to the equal-basis elements, in which the number m of the unknown coefficients or basis functions in an interpolation formula for the element deflection field equals to the number n of DOFs. And, the elements formulated in Sects. 6.4 to 6.6 belong to the super-basis elements, in which m>n. Numerical examples show that these models exhibit excellent performance in the analysis of thin plates. This denotes that the difficulty of C1 continuity problem can be solved completely.

Keywords

thin plate element generalized conforming line-point conforming SemiLoof conforming 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Bazeley GP, Cheung YK, Irons BM, Zienkiewicz OC (1965) Triangular elements in bending-conforming and nonconforming solution. In: Proceedings of the Conference on Matrix Methods in Structural Mechanics. Air Force Institute of Technology, Ohio: Wright-Patterson A. F. Base pp 547–576Google Scholar
  2. [2]
    Batoz JL, Bathe KJ, Ho LW (1980) A study of three-node triangular plate bending elements. International Journal for Numerical Methods in Engineering 15: 1771–1812CrossRefzbMATHGoogle Scholar
  3. [3]
    Stricklin JA, Haisler WE, Tisdale PR, Gunderson R (1969) A rapidly converging triangular plate element. AIAA Journal 7: 180–181CrossRefzbMATHGoogle Scholar
  4. [4]
    Allman DJ (1971) Triangular finite element plate bending with constant and linearly varying bending moments. In: BF de Veubeke (ed) High Speed Computing of Elastic Structures. Liege Belgium, pp 105–136Google Scholar
  5. [5]
    Clough RW, Tocher JL (1965) Finite element stiffness matrices for analysis of plate bending. In: Proceedings of the Conference on Matrix Methods in Structural Mechanics. Air Force Institute of Technology, Ohio: Wright-Patterson A. F. Base, pp 515–545Google Scholar
  6. [6]
    Melosh RJ (1963) Basis for derivation of matrices for the direct stiffness method. AIAA Journal 1(7): 1631–1637CrossRefGoogle Scholar
  7. [7]
    Tocher JL, Kapur KK (1965) Comment on “basis of derivation of matrices for direct stiffness method”. AIAA Journal 3(6): 1215–1216CrossRefGoogle Scholar
  8. [8]
    Kapur KK, Hartz BJ (1966) Stability of thin plates using the finite element method. In: Proceedings of American Socity of Civil Engineering, pp 177–195Google Scholar
  9. [9]
    Xu Y Long ZF (1995) A simple generalized conforming rectangular plate bending element. In: Proceedings of the Fourth National Conference on Structural Engineering, pp 315–319 (in Chinese)Google Scholar
  10. [10]
    Long ZF (1993) Generalized conforming triangular elements for plate bending. Communications in Numerical Methods in Engineering 9: 53–65CrossRefGoogle Scholar
  11. [11]
    Fricker AJ (1985) An improved three-node triangular element for plate bending. International Journal for Numerical Methods in Engineering 21: 105–114CrossRefzbMATHGoogle Scholar
  12. [12]
    Jeyachandrabose C, Kirkhope J (1986) Construction of new efficient three-node triangular thin plate bending elements. Computers & Structures 23(5): 587–603CrossRefzbMATHGoogle Scholar
  13. [13]
    Long YQ, Bu XM, Long ZF, Xu Y (1995) Generalized conforming plate bending elements using point and line compatibility conditions. Computers & Structures 54(4): 717–723CrossRefzbMATHGoogle Scholar
  14. [14]
    Felippa CA, Bergan PG (1987) Triangular bending FE based on energy-orthogonal free formulation. Computer Methods in Applied Mechanics and Engineering 61: 129–160CrossRefzbMATHGoogle Scholar
  15. [15]
    Razzaque A (1973) Program for triangular bending element with derivative smoothing. International Journal for Numerical Methods in Engineering 6: 333–343CrossRefGoogle Scholar
  16. [16]
    Zienkiewicz OC, Lefebyre D (1988) A robust triangular plate bending element of the Reissner-Mindlin type. International Journal for Numerical Methods in Engineering 26: 1169–1184CrossRefzbMATHGoogle Scholar
  17. [17]
    Long YQ, Bu XM (1990) A family of efficient elements for thin plate bending. Journal of Tsinghua University 30(5): 9–15 (in Chinese)Google Scholar
  18. [18]
    Long ZF (1991) Low-order and high-precision triangular elements for plate bending. In: Cheung, Lee & Leung (eds) Computational Mechanics. Rotterdam: Balkema, pp 1793–1797Google Scholar
  19. [19]
    Specht B (1988) Modified shape functions for the three-node plate bending element passing the patch test. International Journal for Numerical Methods in Engineering 26: 705–715CrossRefzbMATHGoogle Scholar
  20. [20]
    Irons BM (1976) The SemiLoof shell element. In: Gallagher RH, Ashwell DG (eds) Finite Element for Thin and Curved Member. Wiley, pp 197–222Google Scholar
  21. [21]
    Long ZF (1992) Two generalized conforming plate elements based on SemiLoof constraints. Computers & Structures 9(1): 53–65Google Scholar
  22. [22]
    Long ZF (1993) Generalized conforming quadrilateral plate element by using SemiLoof constraints. Communications in Numerical Methods in Engineering 9: 417–426CrossRefzbMATHGoogle Scholar
  23. [23]
    Long ZF (1992) Triangular and rectangular plate elements based on generalized compatibility conditions. Computational Mechanics 10(3/4): 281–288CrossRefzbMATHGoogle Scholar

Copyright information

© Tsinghua University Press, Beijing and Springer-Verlag GmbH Berlin Heidelberg 2009

Authors and Affiliations

  • Zhi-Fei Long
    • 1
  • Song Cen
    • 2
  1. 1.School of Mechanics & Civil EngineeringChina University of Mining & TechnologyBeijingChina
  2. 2.Department of Engineering Mechanics, School of AerospaceTsinghua UniversityBeijingChina

Personalised recommendations