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

Full-text PDF Free Access

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]**Douglas N. Arnold,*Discretization by finite elements of a model parameter dependent problem*, Numer. Math.**37**(1981), no. 3, 405–421. MR**627113**, 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**, 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****[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****[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****[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****[12]**R. Temam,*Navier-Stokes Equations*, North-Holland, Amsterdam, 1978.

Retrieve articles in *Mathematics of Computation*
with MSC:
73K25,
65N30

Retrieve articles in all journals with MSC: 73K25, 65N30

Additional Information

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

Article copyright:
© Copyright 1986
American Mathematical Society