Numerical approximation of MindlinReissner plates
Authors:
F. Brezzi and M. Fortin
Journal:
Math. Comp. 47 (1986), 151158
MSC:
Primary 73K25; Secondary 65N30
MathSciNet review:
842127
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Abstract 
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Abstract: We consider a finite element approximation of the socalled MindlinReissner formulation for moderately thick elastic plates. We show that stability and optimal error bounds hold independently of the value of the thickness.
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 D. N. Arnold, "Discretization by finite elements of a model parameter dependent problem," Numer. Math., v. 37, 1981, pp. 405421. MR 627113 (82h:65077)
 [2]
 D. N. Arnold, F. Brezzi & M. Fortin, "A stable finite element for the Stokes equations," Calcolo, v. 21, 1984, pp. 337344. MR 799997 (86m:65136)
 [3]
 K. J. Bathe, Finite Element Procedures in Engineering Analysis, PrenticeHall, Englewood Cliffs, N.J., 1982.
 [4]
 K. J. Bathe & F. Brezzi, "On the convergence of a fournode plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation," in MAFELAP V (J. R. Whiteman, ed.), Academic Press, London, 1985, pp. 491503. MR 811058 (87f:65125)
 [5]
 K. J. Bathe & E. N. Dvorkin, A Formulation of General Shell ElementsThe 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]
 P. G. Ciarlet, The Finite Element Method for Elliptic Problems, NorthHolland, Amsterdam, 1978. MR 0520174 (58:25001)
 [8]
 M. A. Crisfield, "A quadratic Mindlin element using shear constraints," Comput. & Structures, v. 18, no. 5, 1984, pp. 833852.
 [9]
 P. Destuynder, Thèse d'état, Université P. et M. Curie, Paris, 1980.
 [10]
 O. A. Ladyzhenskaya, The Mathematical Theory of Viscous incompressible Flows, Gordon and Breach, New York, 1963. MR 0155093 (27:5034b)
 [11]
 G. Strang & G. Fix, An Analysis of the Finite Element Method, PrenticeHall, Englewood Cliffs, N.J., 1973. MR 0443377 (56:1747)
 [12]
 R. Temam, NavierStokes Equations, NorthHolland, Amsterdam, 1978.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198608421277
PII:
S 00255718(1986)08421277
Article copyright:
© Copyright 1986
American Mathematical Society
