Structural Engineering and Mechanics

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An accurate and efficient shell element with improved reduced integration rules

  • Zhong, Z.H. (College of Mechanical and Automotive Engineering, Hunan University) ;
  • Tan, M.J. (School of Mechanical and Production Engineering, Nanyang Technological University) ;
  • Li, G.Y. (School of Mechanical and Production Engineering, Nanyang Technological University)
  • Published : 1999.12.25
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Abstract

An accurate and efficient shell element is presented. The stiffness of the shell element is decomposed into two parts with one part corresponding to stretching and bending deformation and the other part corresponding to shear deformation of the shell. Both parts of the stiffness are calculated with reduced integration rules, thereby improving computational efficiency. Shear strains are averaged on the reference surface such that neither locking phenomena nor any zero energy mode can occur. The satisfactory behaviour of the element is demonstrated in several numerical examples.

Keywords

References

  1. Belytschko, T., Tsay, C.S. and Liu, W.K. (1981), A stabilization matrix for the bilinear mindlin plate element" , Computer Methods in Applied Mechanics and Engineering, 29, 313-327. https://doi.org/10.1016/0045-7825(81)90048-7
  2. Belytschko, T. and Tsay, C.S. (1983), "A stabilization procedure for the quadrilateral plate element with one-point quadrature", Int. J. for Numerical Methods in Engineering, 19, 405-419. https://doi.org/10.1002/nme.1620190308
  3. Belytschko, T. and Ong, J.S. (1984), "Hourglass control in linear and nonlinear problems" , Computer Methods in Applied Mechanics and Engineering, 43, 251-276. https://doi.org/10.1016/0045-7825(84)90067-7
  4. Belytschko, T. and Leviathan, I. (1994), "Physical stabilization of the 4-node shell element with one point quadrature", Computer Methods in Applied Mechanics and Engineering, 113, 321-350. https://doi.org/10.1016/0045-7825(94)90052-3
  5. Cook, R.D. (1981), Concepts and Applications of Finite Element Analysis, John Wiley & Sons, Inc. New York.
  6. Hughes, T.J.R. (1987), "Linear static and dynamic finite element analysis", The Finite Element Method, Prentice-Hall, Inc.
  7. Jacquotte, O.P. and Oden, J.T. (1983), "Analysis of hourglass instabilities and control in underintegrated finite element methods", Computer Methods in Applied Mechanics and Engineering, 19, 405-419.
  8. Jacquotte, O.P. and Oden, J.T. (1986), "An accurate and efficient control of hourgalss instabilities in under-integrated linear and nonlinear elasticity" , Computer Methods in Applied Mechanics and Engineering, 55, 105-128. https://doi.org/10.1016/0045-7825(86)90088-5
  9. Liu, W.K, Ong, J.S. and Uras, R.A. (1985), "Finite element stabilization matrices-a unification approach", Computer Methods in Applied Mechanics and Engineering, 53, 13-46. https://doi.org/10.1016/0045-7825(85)90074-X
  10. Noor, A.K., Belytschko, T. and Simo, J.C.(1989), "Analytical and computational models for shells" , CED-3, ASME.
  11. Oldenburg, M. (1988), "Finite element analysis of thin walled structures subjected to impact loading" , Doctoral Thesis 1988:69D, Lulea University of Technology, Lulea, Sweden.
  12. Parisch, H. (1995), "A continuum based shell theory for nonlinear applications" , Int. J. for Numerical Methods in Engineering, 38, 1855-1883. https://doi.org/10.1002/nme.1620381105
  13. Park, K.C., Stanley, G.M. and Flaggs, D.L. (1985), A uniformly reduced, four-node shell element with consistent rank corrections" , Computers & Structures, 20, 129-13. https://doi.org/10.1016/0045-7949(85)90062-8
  14. Pugh, E.D, Hinton, E. and Zienkiewicz, O.C. (1978), "A study of quadrilateral plate bending elements with reduced integration", Int. J. for Numerical Methods in Engineering, 12, 1059-1079. https://doi.org/10.1002/nme.1620120702
  15. Vu-Quoc, L. and More, J.A. (1989), "A class of simple and efficient degenerated shell elements-Analysis of global spurious mode filtering", Computer Methods in Applied Mechanics and Engineering, 74, 117-175. https://doi.org/10.1016/0045-7825(89)90101-1
  16. Vu-Quoc, L. (1990), "A perturbation method for dynamic analysis of under-integrated shell elements" , Computer Methods in Applied Mechanics and Engineering, 79, 129-172. https://doi.org/10.1016/0045-7825(90)90130-E
  17. Wissmann, J.W., Becker, T. and Moller, H. (1987), "Stabilization of the zero energy modes of under-integrated isoparametric finite elements" , Computational Mechanics, 2, 289-306. https://doi.org/10.1007/BF00296423
  18. Zhong, Z.H. (1991), "A cross reduced integration technique for a bilinear shell element without zero energy modes" , Int. J. Communication of Applied Numerical Methods, 7, 569-575. https://doi.org/10.1002/cnm.1630070708
  19. Zienkiewicz, O.C. (1977), The Finite Element Method, Third edition, McGRAW HILL.
  20. Zienkiewicz, O.C., Taylor, R.L. and Too, J.M. (1971), "Reduced integration technique in general analysis of plates and shells" , Int. J. for Numerical Methods in Engineering, 3, 275-290. https://doi.org/10.1002/nme.1620030211

Cited by

  1. Finite- and boundary-element linear and nonlinear analyses of shells and shell-like structures vol.38, pp.8, 2002, https://doi.org/10.1016/S0168-874X(01)00103-2
  2. Finite element linear and nonlinear, static and dynamic analysis of structural elements, an addendum vol.19, pp.5, 2002, https://doi.org/10.1108/02644400210435843