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Abstract:

We analyze the convergence of a mixed finite element method introduced by Zienkiewicz, Taylor, Papadopoulos and Oñate for the Reissner-Mindlin plate model. In order to do this, we compare it with a method which is known to be convergent with optimal order uniformly in the plate thickness. We show that the difference between the solutions of both methods is of higher order than the error. In particular the method does not present locking and is optimal order convergent. We also present several numerical experiments which confirm the similar behavior of both methods.

Registro:

Documento: Artículo
Título:On the convergence of a triangular mixed finite element method for Reissner-Mindlin plates
Autor:Durán, R.G.; Liberman, E.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C.172, (1900) La Plata, Argentina
Año:1996
Volumen:6
Número:3
Página de inicio:339
Página de fin:352
DOI: http://dx.doi.org/10.1142/S0218202596000110
Título revista:Mathematical Models and Methods in Applied Sciences
Título revista abreviado:Math. Models Methods Appl. Sci.
ISSN:02182025
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182025_v6_n3_p339_Duran

Referencias:

  • Arnold, D.N., Brezzi, F., Fortin, M., A stable finite element for the Stokes equations (1984) Calcolo, 21, pp. 337-344
  • Arnold, D.N., Falk, R.S., A uniformly accurate finite element method for the Heissner-Mindlin plate (1989) SIAM J. Numer. Anal., 20, pp. 1276-1290
  • Arnold, D.N., Falk, R.S., Edge effects in the Reissner-Mindlin plate theory (1989) Analytical and Computational Models for Shells, pp. 71-90. , eds. A. K. Noor, T. Belytschko and T. Simo American Society of Mechanical Engineers
  • Bathe, K.J., Brezzi, F., (1985) On the Convergence of a Four-node Plate Bending Element Based on Mindlin-Reissner Plate Theory and a Mixed Interpolation, pp. 491-503. , MAFELAP V, ed. J. R. Witheman, London
  • Bathe, K.J., Brezzi, F., A simplified analysis of two plate bending elements - The MITC4 and MITC9 elements (1987) Numerical Techniques for Engineering Analysis and Design, 1. , NUMETA 87, eds. G. N. Pande and J. Middleton, Martinus Nijhoff
  • Bathe, K.J., Brezzi, F., Fortin, M., Mixed-interpolated elements for Reissner-Mindlin plates (1989) Internat. J. Numer. Methods Engrg., 28, pp. 1787-1801
  • Bathe, K.J., Dvorkin, E.N., A four-node plate bending element based on Mindlin-Reissner plate theory and a mixed interpolation (1985) Internat. J. Numer. Methods Engrg., 21, pp. 367-383
  • Brezzi, F., Bathe, K.J., Fortin, M., Mixed interpolated elements for Reissner-Mindlin plates (1989) Internat. J. Numer. Methods Engrg., 28, pp. 1787-1801
  • Brezzi, F., Fortin, M., Numerical approximation of Mindlin-Reissner plates (1986) Math. Comp., 47, pp. 151-158
  • Brezzi, F., Fortin, M., (1991) Hybrid and Mixed Finite Element Methods, , Springer-Verlag
  • Brezzi, F., Fortin, M., Stenberg, R., Error analysis of mixed interpolated elements for Reissner-Mindlin plates (1991) Math. Models Methods Appl. Sci., 1, pp. 125-151
  • Durán, R., Liberman, E., On mixed finite element methods for the Reissner-Mindlin plate model (1992) Math. Comp., 58, pp. 561-573
  • Papadopoulos, P., Taylor, R., A triangular element based on Reissner-Mindlin plate theory (1990) Internat. J. Numer. Methods Engrg., 30, pp. 1029-1049
  • Szabo, B., Babuska, I., (1991) Finite Element Analysis, , John Wiley & Sons
  • Zienkiewicz, O.C., Taylor, R.L., Papadopoulos, P., Oñate, E., (1989) Plate Bending Elements with Discrete Constraints: New Triangular Elements, , UCB/SEMM Report 89/09, Department of Civil Engineering, University of California, Berkeley, CA

Citas:

---------- APA ----------
Durán, R.G. & Liberman, E. (1996) . On the convergence of a triangular mixed finite element method for Reissner-Mindlin plates. Mathematical Models and Methods in Applied Sciences, 6(3), 339-352.
http://dx.doi.org/10.1142/S0218202596000110
---------- CHICAGO ----------
Durán, R.G., Liberman, E. "On the convergence of a triangular mixed finite element method for Reissner-Mindlin plates" . Mathematical Models and Methods in Applied Sciences 6, no. 3 (1996) : 339-352.
http://dx.doi.org/10.1142/S0218202596000110
---------- MLA ----------
Durán, R.G., Liberman, E. "On the convergence of a triangular mixed finite element method for Reissner-Mindlin plates" . Mathematical Models and Methods in Applied Sciences, vol. 6, no. 3, 1996, pp. 339-352.
http://dx.doi.org/10.1142/S0218202596000110
---------- VANCOUVER ----------
Durán, R.G., Liberman, E. On the convergence of a triangular mixed finite element method for Reissner-Mindlin plates. Math. Models Methods Appl. Sci. 1996;6(3):339-352.
http://dx.doi.org/10.1142/S0218202596000110