Structural Engineering and Mechanics

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Theoretical equivalence and numerical performance of T3γs and MITC3 plate finite elements

  • Received : 2018.06.14
  • Accepted : 2019.01.23
  • Published : 2019.03.10
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Abstract

This paper will compare $T3{\gamma}_s$ and MITC3 elements, both these two elements are three-node triangular plate bending elements with three degrees of freedom per node. The formulation of the $T3{\gamma}_s$ and MITC3 elements is rather simple and has already been widely used. This paper will prove that the shear strain formulation of these two elements is identical even though they are obtained from two different methods. A single element is used to test the formulation of shear strain matrices. Numerical tests for circular plate cases compared with the exact solutions and with DKMT element will complete this review to verify the performances and show the convergence of these two elements.

Keywords

Acknowledgement

Supported by : Universitas Indonesia

References

  1. Katili, I., Batoz, J.L., Maknun, I.J., Hamdouni, A. and Millet, O. (2014), "The development of DKMQ plate bending element for thick to thin shell analysis based on Naghdi/Reissner/Mindlin shell theory", Fin. Elem. Anal. Des., 100, 12-27. https://doi.org/10.1016/j.finel.2015.02.005
  2. Katili, I., Maknun, I.J., Millet, O. and Hamdouni, A. (2015), "Application of DKMQ element for composite plate bending structures", Compos. Struct., 132, 166-174. https://doi.org/10.1016/j.compstruct.2015.04.051
  3. Mahjudin, M., Lardeur, P., Druesne, F. and Katili, I. (2016), "Stochastic finite element analysis of plates with the certain generalized stresses method", Struct. Saf., 61, 12-21. https://doi.org/10.1016/j.strusafe.2016.02.006
  4. Maknun, I.J., Katili, I., Millet, O. and Hamdouni, A. (2016), "Application of DKMQ element for a twist of thin-walled beams: Comparison with Vlasov theory", Int. J. Comput. Meth. Eng. Sci. Mech., 17, 391-400. https://doi.org/10.1080/15502287.2016.1231240
  5. Wong, F.T., Richard, A. and Katili, I. (2017), "Development of the DKMQ element for buckling analysis of shear-deformable plate bending", Proc. Eng., 171, 805-812. https://doi.org/10.1016/j.proeng.2017.01.368
  6. Katili, I., Batoz, J.L., Maknun, I.J. and Lardeur, P. (2018), "A comparative formulation of DKMQ, DSQ and MITC4 quadrilateral plate elements with new numerical results based on s-norm tests", Comput. Struct., 204, 48-64. https://doi.org/10.1016/j.compstruc.2018.04.001
  7. Katili, I., Maknun, I.J., Batoz, J.L. and Ibrahimbegovic, A. (2018), "Shear deformable shell element DKMQ24 for composite structures", Compos. Struct., 202, 182-200. https://doi.org/10.1016/j.compstruct.2018.01.043
  8. Katili, I., Maknun, I.J., Batoz, J.L. and Katili, A.M. (2018), "Asymptotic equivalence of DKMT and MITC3 elements for thick composite plates", Compos. Struct., 206, 363-379. https://doi.org/10.1016/j.compstruct.2018.08.017
  9. Ko, Y., Lee, P.S. and Bathe, K.J. (2017), "A new MITC4+ shell element", Comput. Struct., 182, 404-418. https://doi.org/10.1016/j.compstruc.2016.11.004
  10. Banh, T.T. and Lee, D. (2018), "Multi-material topology optimization of Reissner-Mindlin plates using MITC4", Steel Compos. Struct., 27, 27-33. https://doi.org/10.12989/SCS.2018.27.1.027
  11. Hughes, T.J.R. and Tezduyar, T.E. (1981), "Finite elements based upon Mindlin plate theory with particular reference to the fournode bilinear isoparametric element", Trans. ASME J. App. Mech., 48(3), 587-596. https://doi.org/10.1115/1.3157679
  12. MacNeal, R.H. (1982), "Derivation of element stiffness matrices by assumed strain distributions", Nucl. Eng. Des., 70(1), 3-12. https://doi.org/10.1016/0029-5493(82)90262-X
  13. Hughes, T.J.R. and Taylor, R.L. (1982), The Linear Triangle Bending Elements, The Mathematics of Finite Element and Application IV, MAFELAP, Academic Press, London, U.K.
  14. Ayad, R., Batoz, J.L., Dhatt, G. and Katili, I. (1992), A Study of Recent Triangular Elements for Thin and Thick Plates, Elsevier.
  15. Batoz, J.L., Bathe, K.J. and Ho, L.W. (1980), "A study of threenode triangular plate bending elements", Int. J. Numer. Meth. Eng., 15(12), 1771-1812. https://doi.org/10.1002/nme.1620151205
  16. Batoz, J.L. and Lardeur, P. (1989), "A discrete shear triangular nine dof element for the analysis of thick to very thin plates", Int. J. Numer. Meth. Eng., 28(3), 533-560. https://doi.org/10.1002/nme.1620280305
  17. Katili, I. (1993), "A new discrete Kirchhoff-Mindlin element based on Mindlin-Reissner plate theory and assumed shear strain fields-part I: An extended DKT element for thick-plate bending analysis", Int. J. Numer. Meth. Eng., 36(11), 1859-1883. https://doi.org/10.1002/nme.1620361106
  18. Lee, P.S. and Bathe, K.J. (2004), "Development of MITC isotropic triangular shell finite elements", Comput. Struct., 82(11-12), 945-962. https://doi.org/10.1016/j.compstruc.2004.02.004
  19. Lee, P.S., Noh, H.C. and Bathe, K.J. (2007), "Insight into 3-node triangular shell finite elements: The effect of element isotropy and mesh pattern", Comput. Struct., 85(7-8), 404-418. https://doi.org/10.1016/j.compstruc.2006.10.006
  20. Lee, Y., Yoon, K. and Lee, P.S. (2012), "Improving the MITC3 shell finite element by using the Hellinger-Reissner principle", Comput. Struct., 110-111, 93-106. https://doi.org/10.1016/j.compstruc.2012.07.004
  21. Lee, Y., Lee, P.S. and Bathe, K.J. (2014), "The MITC3+ shell element and its performance", Comput. Struct., 138, 12-23. https://doi.org/10.1016/j.compstruc.2014.02.005
  22. Jeon, H.M., Lee, Y., Lee, P.S. and Bathe, K.J. (2015), "The MITC3+ shell element in geometric nonlinear analysis", Comput. Struct., 146, 91-104. https://doi.org/10.1016/j.compstruc.2014.09.004
  23. Ko, Y., Lee, Y., Lee, P.S. and Bathe, K.J. (2017), "Performance of MITC3+ and MITC4+ shell elements in widely-used benchmark problems", Comput. Struct., 193, 187-206. https://doi.org/10.1016/j.compstruc.2017.08.003
  24. Batoz, J.L. and Dhatt, G. (1990), Modelisation des Structures par Element Finis, Poutres et Plaques, Hermes, Paris, France.

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