A new hybrid-mixed variational approach for Reissner-Mindlin plates. The MiSP model

International Journal for Numerical Methods in Engineering

Volumn 42, Issue 7, 1998, Pages 1149-1179

  Ayad, Rezak ^a,d   Dhatt, Gouri ^b   Batoz, Jean Louis ^c  

^a UNIVERSITÉ DE REIMS CHAMPAGNE ARDENNE   (France)

^b UNIVERSITÉ ET INSA DE ROUEN   (France)

^c UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

^d Eole Sup d'Ing en Emballage et Con   (France)

Author keywords

Hybrid mixed; MiSP3; MiSP4; Plate bending; Reissner Mindlin; Shear locking; Transversal shear

Indexed keywords

APPROXIMATION THEORY; BENDING (DEFORMATION); FINITE ELEMENT METHOD; MATHEMATICAL MODELS; SHEAR DEFORMATION; VARIATIONAL TECHNIQUES;

TRANSVERSAL SHEAR;

PLATES (STRUCTURAL COMPONENTS);

EID: 0032137073     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19980815)42:7<1149::AID-NME391>3.0.CO;2-2     Document Type: Article

References (40)

1. M. M. Hrabok and T. M. Hrudey, 'A review and catalogue of plate bending finite elements', Comp. Struct., 19, 479-495 (1984).
2. T. Belytschko, 'A review of recent developments in plate and shells elements', Comp. Mech. Adv. and Trends AMD-75 ASME, New York, 1986.
3. T. Kerber, 'Revue des éléments finis de coques au travers des phénomènes de verrouillage et de leurs remèdes', La Recherche Aérospatiale, 3, 45-76 (1990).
4. R. Ayad, 'Eléments Finis de Plaque et Coque en Formulation Mixte avec Projection en Cisaillement', Thèse de Doctorat, UTC, 1993.
5. J. A. Stricklin, W. Haisler, P. Tisdale and R. Gunderson, 'A rapidly converging triangular plate element', AIAA J., 7, 180-181 (1969).
6. G. Dhatt, 'Numerical analysis of thin shells by curved triangular elements based discrete Kirchhoff hypothesis', ASCE Symposium, Nashville, November 1969, pp. 255-278
7. G. Dhatt and S. Venkatasubbu, 'Finite element analysis of intainment vessals', Int. Conf. on Structural Mechanics, in Reactor Technology, Berlin, Vol. 5, Part I, pp. 257-276, September 1971.
8. J. L. Batoz, K. J. Bathe and L. W. Ho, 'A study of three-node triangular plate bending elements', Int. J. Numer. Meth. Engng., 15, 1771-1812 (1980).
9. J. L. Batoz and M. Bentahar, 'Evaluation of a new thin plate quadrilateral element', Int. J. Numer. Meth. Engng., 18, 1655-1678 (1982).
10. J. L. Batoz and G. Dhatt, 'Revue et bilan des éléments de plaque de type Kirchhoff discret', in Fouet et al. (eds.), Calcul des Structures et Intelligence Artificielle, Vol. 2, Pluralis, 1988, pp. 137-160.
11. R. H. Macneal, 'Derivation of element stiffness matrices by assumed strain distributions', Nucl. Engng. Des., 70, 3-12 (1982).
12. T. J. R. Hughes and T. E. Tezduyar, 'Finite elements based upon Mindlin plate theory with particular reference to the four-node bilinear isoparametric element', J. Appl. Mech., 48, 587-596 (1981).
13. T. J. R Hughes and R. L. Taylor, 'The linear triangle bending elements', in The Mathematics of Finite Element and Application IV, MAFELAP 1981, Academic Press, London, 1982, pp. 127-142.
14. E. N. Dvorkin and K. J. Bathe, 'A continuum mechanics based four-node shell element for general non-linear analysis', Engng. Comput., 1, 77-78 (1984).
15. K. J. Bathe and E. N. Dvorkin, 'A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation', Int. J. Numer. Meth. Engng., 21, 367-383 (1985).
16. G. Prathap and B. R. Somashekar, 'Field, and edge-consistency synthesis of a 4-node quadrilateral plate bending element', Int. J. Numer Meth. Engng., 26, 1693-1708 (1988).
17. J. Donea and L. G. Lamain, 'A modified representation of transverse shear in C̊ quadrilateral plate elements', Comp. Meth. Appl. Mech. Engng., 63, 183-207 (1987).
18. J. L. Batoz and G. Dhatt, Modélisation des Structures par Eléments Finis, Vol. 2, Poutres et Plaques, Editions Hermès, Paris, 1990.
19. O. C. Zienkiewicz, R. L. Taylor, P. Papadopoulos and E. Onate, 'Plate bending elements with discrete constraints: new triangular elements', Comp. Struct., 35, 505-522 (1990).
20. P. Papadopoulos and R. L. Taylor, 'A triangular element based on Reissner-Mindlin plate theory', Int. J. Numer. Meth. Engng., 30, 1029-1049 (1990).
21. E. Onate, O. C. Zienkiewicz, B. Suarez and R. L. Taylor, 'A general methodology for deriving shear constrained Reissner-Mindlin plate elements', Int. J. Numer. Meth. Engng., 33, 345-367 (1992).
22. E. Onate and J. Castro, 'Derivation of plate based on assumed shear strain fields', in Ladevèze and Zienkiewicz (eds.), New Advances in Computational Structural Mechanics, Elsevier, Amsterdam, 1992, pp. 237-288.
23. J. Aalto, 'From Kirchhoff to Mindlin plate element', Comm. Appl. Numer. Meth., 4, 231-241 (1988).
24. J. L. Batoz and P. Lardeur, 'A discrete shear triangular nine dof element for the analysis of thick to very thin plates', Int. J. Numer. Meth. Engng., 28, 533-560 (1989).
25. P. Lardeur and J. L. Batoz, 'Composite plate analysis using a new discrete shear triangular finite element', Int. J. Numer. Meth. Engng., 27, 343-360 (1989).
26. P. M. Pinsky and R. V. Jasti, 'A mixed finite element formulation for Reissner-Mindlin plates based on the use of bubble functions', Int. J. Numer. Meth. Engng., 28, 1677-1702 (1989).
27. A. F. Saleeb and T. Y. Chang, 'An efficient quadrilateral element for plate bending analysis', Int. J. Numer. Meth. Engng., 24, 1123-1155 (1987).
28. A. F. Saleeb, T. Y. Chang and S. Yingyeunyong, 'A mixed formulation of C̊-Linear triangular plate-shell element - the role of edge shear constraints', Int. J. Numer. Meth. Engng., 26, 1101-1128 (1988).
29. J. L. Batoz and I. Katili, 'On a simple triangular Reissner/Mindlin plate element based on incompatible modes and discrete constraints', Int. J. Numer. Meth. Engng., 35, 1603-1632 (1992).
30. D. N. Arnold and R. S. Falk, 'A uniformly accurate finite element method for the Reissner-Mindlin plate', SIAM J. Numer. Anal., 26, 1276-1290 (1989).
31. O. C. Zienkiewicz and D. Lefebvre, 'A robust triangular plate bending element of the Reissner-Mindlin type', Int. J. Numer. Meth. Engng., 26, 1169-1184 (1988).
32. P. Lardeur, 'Dévelopement et evaluation de deux nouveaux eléments finis de plaques et coques composites avec influence du cisaillement transverse', Thèse de Doctorat, UTC, 1990.
33. E. Reissner, The effect of transverse shear deformation on the bending of plates', J. Appl. Mech., 12, A69-A77 (1945).
34. R. Ayad, J. L. Batoz and G. Dhat, 'Un élément quadrilatéral de plaque basé sur une formulation mixte-hybride avec projection en cisaillement', Revue Européenne des Eléments Finis, 4, 415-440 (1995).
35. B. Irons and M. Loikkanen, 'An engineer's defence of the patch test', Int. J. Numer. Meth. Engng., 19, 1391-1401 (1983).
36. R. L. Taylor, J. C. Simo, O. C. Zienkiewicz and A. C. H. Chan, 'The Patch-test - a condition for assessing FEM convergence', Int. J. Numer. Meth. Engng., 22, 39-62 (1986).
37. L. S. D. Morley, Skew Plates and Structures, Pergamon, Oxford, 1963.
38. I. Babuska and T. Scapolla, 'Benchmark computation and performance evaluation for a rhombic plate bending problem', Int. J. Numer. Meth. Engng., 28, 155-179 (1989).
39. A. Razzaque, 'Program for triangular bending elements with derivative smoothing', Int. J. Numer. Meth. Engng., 6, 333-343 (1973).
40. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, Vol. 2: Plates, Shells, Fluids and Non-Linear Problems, 4th Ed., McGraw-Hill, London, 1991.