Numerical approximation of Mindlin-Reissner plates
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- by F. Brezzi and M. Fortin PDF
- Math. Comp. 47 (1986), 151-158 Request permission
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
- Douglas N. Arnold, Discretization by finite elements of a model parameter dependent problem, Numer. Math. 37 (1981), no. 3, 405–421. MR 627113, DOI 10.1007/BF01400318
- 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, DOI 10.1007/BF02576171 K. J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, N.J., 1982.
- 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 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.) F. Brezzi & M. Fortin, Book in preparation.
- Philippe G. Ciarlet, The finite element method for elliptic problems, Studies in Mathematics and its Applications, Vol. 4, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978. MR 0520174 M. A. Crisfield, "A quadratic Mindlin element using shear constraints," Comput. & Structures, v. 18, no. 5, 1984, pp. 833-852. P. Destuynder, Thèse d’état, Université P. et M. Curie, Paris, 1980.
- O. A. Ladyženskaja, Matematicheskie voprosy dinamiki vyazkoĭneszhimaemoĭ zhidkosti, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1961 (Russian). MR 0155092
- Gilbert Strang and George J. Fix, An analysis of the finite element method, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1973. MR 0443377 R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam, 1978.
Additional Information
- © Copyright 1986 American Mathematical Society
- 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