DOI QR코드

DOI QR Code

An improved incompatible DST element using free formulation approach

  • Katili, Irwan (Civil Engineering Department, Universitas Indonesia)
  • 투고 : 2020.12.20
  • 심사 : 2021.05.12
  • 발행 : 2021.07.10

초록

This study proposes DSTK, a new incompatible triangular element formulated from a combination of discrete shear constraints, independent transverse shear strains and a free formulation approach. DSTK takes into account transverse shear effects and is valid for thin and thick plates. Furthermore, this element has 3 nodes and 3 DOFs per node (transverse displacement w and rotations βx and βy). The couple between lower order and higher order bending energy is assumed to be zero to fulfil the constant bending patch test. Unifying and integrating kinematic relationship, constitutive law, and equilibrium equations contribute to the independent transverse shear strain expression, which comprises merely the second derivatives of the rotations. The study performs validation based on individual element tests, patch tests, and convergence tests. This study shows that the DSTK element yields good results of various classical benchmark tests for thin to thick plates.

키워드

과제정보

The financial support from the Indonesian Ministry of Research and Technology (RISTEK-BRIN) through the World Class Research (WCR) program is gratefully acknowledged (NKB-384/UN2.RST/HKP.05.00/2021).

참고문헌

  1. Batoz, J.L. and Dhatt, G. (1990), Modelisation des Structures par Element Finis, Volume 2: Poutres et Plaques, Hermes, Paris, France.
  2. Batoz, J.L. and Katili, I. (1992), "On a simple triangular Reissner Mindlin plate element based on incompatible modes and discrete constraints", Int. J. Numer. Meth. Eng., 3, 1603-1632. https://doi.org/10.1002/nme.1620350805.
  3. 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, 533-560. https://doi.org/10.1002/nme.1620280305.
  4. Batoz, J.L., Bathe, K.J. and Ho, L.W. (1980), "A study of three-node triangular plate bending elements", Int. J. Numer. Meth. Eng., 15, 1771-1812. https://doi.org/10.1002/nme.1620151205.
  5. Bergan, P.G. (1980), "Finite elements based on energy orthogonal functions", Int. J. Numer. Meth. Eng., 15. 1541-1555. https://doi.org/10.1002/nme.1620151009.
  6. Dinh, T.C., Duc, T.T., Trung, K.N. and Van, H.N. (2017b), "A node-based mitc3 element for analyses of laminated composite plates using the higher-order shear deformation theory", Proceedings of the International Conference on Advances in Computational Mechanics, 409-429.
  7. Dinh, T.C., Duy, Q.N. and Xuan, H.N. (2017a), "Improvement on MITC3 plate finite element using edge-based strain smoothing enhancement for plate analysis", Acta Mechanica, 228, 2141-2163. https://doi.org/10.1007/s00707-017-1818-3.
  8. 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.
  9. Katili, A.M., Maknun, I.J. and Katili, I. (2019b), "Theoretical equivalence and numerical performance of T3γs and MITC3 plate finite elements", Struct. Eng. Mech., 69, 527-536. https://doi.org/10.12989/sem.2019.69.5.527.
  10. 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, 1859-1883. https://doi.org/10.1002/nme.1620361107.
  11. Katili, I., Aristio, R. and Setyanto, S.B. (2020), "Isogeometric collocation method to solve the strong form equation of UI-RM Plate Theory", Struct. Eng. Mech., 76, 435-449. https://doi.org/10.12989/sem.2020.76.4.435.
  12. Katili, I., Maknun, I.J., Batoz, J.L. and Katili, A.M. (2018), "Asymptotic equivalence of DKMT and MITC3 elements for Thick Compos. Plates, 206, 363-379. https://doi.org/10.1016/j.compstruct.2018.08.017
  13. Katili, I., Maknun, I.J., Batoz, J.L. and Katili, A.M. (2019a), "A comparative formulation of T3γs, DST, DKMT and MITC3+ triangular plate elements with new numerical results based on s-norm tests", Eur. J. Mech./A Solid., 78, 103826. https://doi.org/10.1016/j.euromechsol.2019.103826
  14. Kirchhoff, G. (1950), "Uber das Gleichgewicht und die Bewegung einer elastischen Scheibe", J. Reine Angew. Math., 40, 51-58.
  15. Lardeur, P. and Batoz, J.L. (1989), "Composite plate analysis using a new discrete shear triangular plate bending element", Int. J. Numer. Meth. Eng., 27, 343-360. https://doi.org/10.1002/nme.1620270209.
  16. Lee, P.S. and Bathe, K.J. (2004), "Development of MITC isotropic triangular shell finite elements", Comput. Struct., 82, 945-962. https://doi.org/10.1016/j.compstruc.2004.02.004.
  17. 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, 404-418. https://doi.org/10.1016/j.compstruc.2006.10.006.
  18. Lee, Y., Jeon, H.M., Lee, P.S. and Bathe, K.J. (2015), "The modal behavior of the MITC3+ triangular shell element", Comput. Struct., 153, 148-164. https://doi.org/10.1016/j.compstruc.2015.02.033.
  19. 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.
  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, 93-106. https://doi.org/10.1016/j.compstruc.2012.07.004.
  21. Liew, K.M. and Han, J.B. (1997), "Bending analysis of simply supported shear deformable skew plates", J. Eng. Mech., 123, 214-221. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:3(214).
  22. MacNeal, R.H. (1982), "Derivation of element stiffness matrices by assumed strain distributions", Nucl. Eng. Des., 70, 3-12. https://doi.org/10.1016/0029-5493(82)90262-X.
  23. Maknun, I.J., Katili, I., Ibrahimbegovic, A. and Katili, A.M. (2020), "A new triangular shell element for composites accounting for shear deformation", Comput. Struct., 243, 112214. https://doi.org/10.1016/j.compstruct.2020.112214.
  24. Mindlin, R.D. (1951), "Influence of rotation inertia and shear on flexural motion of isotropic elastic plates", J. Appl. Mech., 18, 31-38. https://doi.org/10.1115/1.4010217.
  25. Morley, L.S.D. (1963), Skew Plates and Structures, Pergamon Press, New York, USA.
  26. Nguyen, T.K., Nguyen, V.H. and Dinh, T.C. (2018), "Cell- and node-based smoothing mitc3-finite elements for static and free vibration analysis of laminated composite and functionally graded plates", Int. J. Comput. Meth., 15(03), 1850123. https://doi.org/10.1142/S0219876218501232.
  27. Razzaque, A. (1973), "Program for triangular bending elements with derivative smoothing", Int. J. Numer. Meth. Eng., 6, 333-345. https://doi.org/10.1002/nme.1620060305.
  28. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech. Eng., ASME, 12, A69-A77. https://doi.org/10.1115/1.4009435.
  29. Sengupta, D. (1995), "Performance study of a simple finite element in the analysis of skew rhombic plates", Comput. Struct., 54, 1173-82. https://doi.org/10.1016/0045-7949(94)00405-R.