Numerical approximation of Mindlin-Reissner plates

Authors:
F. Brezzi and M. Fortin

Journal:
Math. Comp. **47** (1986), 151-158

MSC:
Primary 73K25; Secondary 65N30

DOI:
https://doi.org/10.1090/S0025-5718-1986-0842127-7

MathSciNet review:
842127

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Abstract | References | Similar Articles | Additional Information

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.

**[1]**D. N. Arnold, "Discretization by finite elements of a model parameter dependent problem,"*Numer. Math.*, v. 37, 1981, pp. 405-421. 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. 337-344. MR**799997 (86m:65136)****[3]**K. J. Bathe,*Finite Element Procedures in Engineering Analysis*, Prentice-Hall, Englewood Cliffs, N.J., 1982.**[4]**K. J. Bathe & F. Brezzi, "On the convergence of a four-node 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. 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]**P. G. Ciarlet,*The Finite Element Method for Elliptic Problems*, North-Holland, 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. 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 Flows*, Gordon and Breach, New York, 1963. MR**0155093 (27:5034b)****[11]**G. Strang & G. Fix,*An Analysis of the Finite Element Method*, Prentice-Hall, Englewood Cliffs, N.J., 1973. MR**0443377 (56:1747)****[12]**R. Temam,*Navier-Stokes Equations*, North-Holland, Amsterdam, 1978.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1986-0842127-7

Article copyright:
© Copyright 1986
American Mathematical Society