Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A new finite element based on the strain approach with transverse shear effect

  • Received : 2013.03.26
  • Accepted : 2014.02.01
  • Published : 2014.03.25
⟨ Previous Next ⟩

Abstract

This research work deals with the development of a new Triangular finite element for the linear analysis of plate bending with transverse shear effect. It is developed in perspective to building shell elements. The displacements field of the element has been developed by the use of the strain-based approach and it is based on the assumed independent functions for the various components of strain insofar as it is allowed by the compatibility equations. Its formulation uses also concepts related to the fourth fictitious node, the static condensation and analytic integration. It is based on the assumptions of tick plate.s theory (Reissner-Mindlin theory). The element possesses three essential external degrees of freedom at each of the four nodes and satisfies the exact representation of the rigid body modes of displacements. As a result of this approach, a new bending plate finite element (Pep43) which is competitive, robust and efficient.

Keywords

References

  1. Argyris, J.H., Dune, P.C., Malejannakis, G.A. and Schelkle, E. (1977), "A simple triangular facet shell element with applications to linear and non linear equilibrium and elastic stability problems", Comput. Method. Appl. Mech. Eng., 10(3), 371-403. https://doi.org/10.1016/0045-7825(77)90080-9
  2. Barik, M. and Mukhopadhyay, M. (2002), "A new stiffened plate element for the analysis of arbitrary plates", Thin Wall. Struct., 40(7-8), 625-639. https://doi.org/10.1016/S0263-8231(02)00016-2
  3. Batoz, J.L., Bath, K.J. and Ho, L.W. (1980), "A study of three nodes triangular plate bending elements", Int. J. Numer. Meth. Eng., 15, 1771-812. https://doi.org/10.1002/nme.1620151205
  4. Batoz, J.L. and Dhatt, G. (1990), Modelisation des structures par elements finis, Vol.1, Solides Elastiques, Vol 2 : Poutres et plaques, Hermes, Paris.
  5. Belarbi, M.T. and Charif, A. (1999), "Developpement d'un nouvel element hexaedrique simple base sur le modele en deformation pour l'etude des plaques minces et epaisses", Revue Europeenne des Elements Finis, 135-157.
  6. Belounar, L. and Guenfoud, M. (2005), "A new rectangular finite element based on the strain approach for plate bending", Thin Wall. Struct., 43, 47-63. https://doi.org/10.1016/j.tws.2004.08.003
  7. Belytschko, T., Ong, J.S.J., Liu, W.K. and Kennedy, J.M. (1984), "Hourglass control in linear and nonlinear problems", Compute Method. Appl. Mech. Eng., 43, 251-276. https://doi.org/10.1016/0045-7825(84)90067-7
  8. Brasile, S. (2008), "An isostatic assumed stress triangular element for the Reissner-Mindlin plate bending problem", Int. J. Numer. Meth. Eng., 74, 971-995. https://doi.org/10.1002/nme.2194
  9. Chinosi, C. (2005), "PSRI elements for the Reissner-Mindlin free plate", Comput. Struct., 83 (31-32), 559-2572.
  10. Clough, R.W. and Tocher, J.L. (1965), "Finite element stiffness matrixes for analysis of plate bending", Proceeding of first conference Matrix methods in structural mechanics, Wright-Patterson Air force baseman, Ohio.
  11. Boutagouga, D., Gouasmia, A. and Djeghaba, K. (2010), "Geometrically non-linear analysis of thin shell by a quadrilateral finite element with in-lane rotational degrees of freedom", European Journal of Computational Mechanics/Revue Europeenne de Mecanique Numerique, 19 (8), 707-724.
  12. Kim, D.N. and Bathe, K.J. (2009), "A triangular six-node shell element", Comput. Struct., 87(23-24), 1451-1460. https://doi.org/10.1016/j.compstruc.2009.05.002
  13. Frey, F. (1998), "Traite de genie civil de l'ecole polytechnique federale de Lausane", Volume 3, Analyse des structures et milieux continus - mecanique des solides, Presses polytechniques et universitaires romandes CH-1015.
  14. Guenfoud, M. (1990), "Deux elements triangulaires nouveaux pour l‟analyse lineaire et non lineaire geometrique des coques", These de doctorat, Institut national des sciences appliquees de Lyon, France
  15. Hamadi, D.J. and Belarbi, M.T. (2006), "Integration solution routine to evaluate the element stiffness matrix for distorted shape", Asian J. Civil Eng., 7(5), 525-549.
  16. Han, S.C., Ham, H.D. and Nuklchaic, W.K. (2008), "Geometrically non-linear analysis of arbitrary elastic supported plates and shells using an element-based Lagrangian shell element", Int. J. Nonlin. Mech., 43, 53-64. https://doi.org/10.1016/j.ijnonlinmec.2007.09.011
  17. Himeur, M. (2008), "Developpement d‟elements membranaires nouveaux d'elasticite plane bases sur la formulation en deformation", These de magistere, Universite de Guelma (Algerie), Departement de Genie Civil, 104p
  18. Himeur, M. and Guenfoud, M. (2011), "Bending triangular finite element with a fictitious fourth node based on the strain approach", European Journal of Computational Mechanics/Revue Europeenne de Mecanique Numerique, 20(7-8), 455-485.
  19. Maalem, T. (2007), "Contribution au modele en deformation dans l‟analyse des structures", These de Doctorat, Universite de Batna (Algerie).
  20. Man, H., Song, C., Xiang, T., Gao, W. and Tin-Loi, F. (2013), "High-order plate bending based on the boundary finite element method", Int. J. Numer. Meth. Eng., 95, 331-360. https://doi.org/10.1002/nme.4519
  21. Providas, E. and Kattis, M.A. (2000), "An assessment of two fundamental flat triangular shell elements with drilling rotation", Comput. Struct., 77, 129-139. https://doi.org/10.1016/S0045-7949(99)00215-1
  22. Sabourin, F.M. and Salle, F. (2000), "Calcul des structures par elements finis, Barres" - Poutres Elasticite plane Axisymetrique Plaques - coques non linearite", Chapitre IV, INSA Lyon, France.
  23. Yuan, F. and Miller, R.E. (1988), "A rectangular finite element for moderately thick flat plate", Comput. Struct., 30, 1375-87. https://doi.org/10.1016/0045-7949(88)90202-7

Cited by

  1. Use of design optimization techniques in solving typical structural engineering related design optimization problems vol.55, pp.6, 2015, https://doi.org/10.12989/sem.2015.55.6.1121
  2. Strain based triangular finite element for plate bending analysis pp.1537-6532, 2018, https://doi.org/10.1080/15376494.2018.1488310
  3. Using Higher-Order Strain Interpolation Function to Improve the Accuracy of Structural Responses vol.12, pp.3, 2014, https://doi.org/10.1142/s175882512050026x