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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Numerical approximation of Mindlin-Reissner plates


Authors: F. Brezzi and M. Fortin
Journal: Math. Comp. 47 (1986), 151-158
MSC: Primary 73K25; Secondary 65N30
MathSciNet review: 842127
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Abstract: We consider a finite element approximation of the so-called Mindlin-Reissner formulation for moderately thick elastic plates. We show that stability and optimal error bounds hold independently of the value of the thickness.


References [Enhancements On Off] (What's this?)

  • [1] Douglas N. Arnold, Discretization by finite elements of a model parameter dependent problem, Numer. Math. 37 (1981), no. 3, 405–421. MR 627113 (82h:65077), http://dx.doi.org/10.1007/BF01400318
  • [2] D. N. Arnold, F. Brezzi, and M. Fortin, A stable finite element for the Stokes equations, Calcolo 21 (1984), no. 4, 337–344 (1985). MR 799997 (86m:65136), http://dx.doi.org/10.1007/BF02576171
  • [3] K. J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, N.J., 1982.
  • [4] K.-J. Bathe and F. Brezzi, On the convergence of a four-node plate bending element based on Mindlin-Reissner plate theory and a mixed interpolation, The mathematics of finite elements and applications, V (Uxbridge, 1984), Academic Press, London, 1985, pp. 491–503. MR 811058 (87f:65125)
  • [5] K. J. Bathe & E. N. Dvorkin, A Formulation of General Shell Elements--The Use of Mixed Interpolation of Tensorial Components, Proc. Conf. Numerical Methods in Engineering: Theory and Applications (Swansea, Jan. 1985). (To appear.)
  • [6] F. Brezzi & M. Fortin, Book in preparation.
  • [7] Philippe G. Ciarlet, The finite element method for elliptic problems, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978. Studies in Mathematics and its Applications, Vol. 4. MR 0520174 (58 #25001)
  • [8] M. A. Crisfield, "A quadratic Mindlin element using shear constraints," Comput. & Structures, v. 18, no. 5, 1984, pp. 833-852.
  • [9] P. Destuynder, Thèse d'état, Université P. et M. Curie, Paris, 1980.
  • [10] O. A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Revised English edition. Translated from the Russian by Richard A. Silverman, Gordon and Breach Science Publishers, New York-London, 1963. MR 0155093 (27 #5034b)
  • [11] Gilbert Strang and George J. Fix, An analysis of the finite element method, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1973. Prentice-Hall Series in Automatic Computation. MR 0443377 (56 #1747)
  • [12] R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam, 1978.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1986-0842127-7
PII: S 0025-5718(1986)0842127-7
Article copyright: © Copyright 1986 American Mathematical Society