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Mixed-interpolated elements for Reissner-Mindlin plates. (English) Zbl 0705.73238

Summary: We present in this paper a procedure to establish Reissner-Mindlin plate bending elements. The procedure is based on the idea to combine known results on the approximation of Stokes problems with known results on the approximation of elliptic problems. The proposed elements satisfy the mathematical conditions of stability and convergence, and some of them promise to provide efficient elements for practical solutions.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K20 Plates
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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References:

[1] Dvorkin, J. Eng. Comp. 1 pp 77– (1984)
[2] Bathe, Int. j. numer. methods eng. 21 pp 367– (1985)
[3] and , ’A simplified analysis of two-plate bending elements– The MITC4 and MITC9 elements’, in and (eds.), Numeta 87, Vol. 1, Numerical Techniques for Engineering Analysis and Design, Martinus Nijhoff, Amsterdam, 1987.
[4] and , ’On the convergence of a four-node plate bending element based on Mindlin- Reissner plate theory and a mixed interpolation’, in (ed.), Proceedings of Conference on Mathematics of Finite Elements and Applications V, Academic Press, New York, 1985, pp. 491-503.
[5] Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, N.J., 1982.
[6] and , ’Studies of finite element procedures–The inf-sup condition, equivalent forms and applications’, in and (eds.), Reliability of Methods for Engineering Analysis, Pineridge Press, Swansea, 1986.
[7] and , Mixed and Hybrid Finite Element Methods, to appear.
[8] The Finite Element Method For Elliptic Problems, North-Holland, Amsterdam, 1978.
[9] and , ’A mixed finite element method for second-order elliptic problems’, in Mathematical Aspects of Finite Element Methods, Lecture Notes in Mathematics, Vol. 606, Springer-Verlag, New York, 1975, pp. 292-315.
[10] Breezi, RAIRO M2AN 21 pp 581– (1987)
[11] Bathe, Int. j. numer. methods eng. 22 pp 697– (1986)
[12] and , ’Conforming and nonconforming finite element methods for solving the stationary Stokes equations’, RAIRO Anal. Numer. R3, 33-76 ( 1976).
[13] Fortin, Int. j. numer. methods fluids 1 pp 347– (1981)
[14] Sussman, J. Comp. Struct. 26 pp 357– (1987)
[15] Brezzi, Math. Comp. 47 pp 151– (1986)
[16] Douglas, Math. Comp. 44 pp 39– (1985)
[17] and , Finite Element Approximation of the Navier-Stokes Equations, Lecture Notes in Mathematics, Vol. 749, Springer-Verlag, New York, 1979.
[18] Nedelec, Numer. Math. 35 pp 315– (1980)
[19] Brezzi, Numer. Math. 47 pp 217– (1985)
[20] and , ’The MITC7 and MITC9 plate bending elements’, Comp. Struct., in press. · Zbl 0705.73241
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