Optimal Rectangular MITC Finite Elements for Reissner-Mindlin Plates

Numerical Methods for Partial Differential Equations

Volumn 13, Issue 5, 1997, Pages 575-585

  Perugia, Ilaria ^a   Scapolla, Terenzio ^a,b,c  

^a UNIVERSITY OF PAVIA   (Italy)

^b UNIVERSITY OF TURIN   (Italy)

^c CNR   (Italy)

Author keywords

Finite elements; Plates 65N30, 73K10

Indexed keywords

EID: 0039151140     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2426(199709)13:5<575::AID-NUM8>3.0.CO;2-G     Document Type: Article

References (22)

1. K.-J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Clififs, New Jersey, 1982.
2. T. J. R. Hughes, The Finite Element Method, Prentice-Hall, Englewood Clififs, New Jersey, 1987.
3. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, McGraw-Hill, London, Vol. I, 1989, Vol. i, 1991.
4. E. N. Dvorkin and K.-J. Bathe, "A continuum mechanics based four-node shell element for general nonlinear analysis," Engng. Comp. 1, 77-88 (1984).
5. K.-J. Bathe and E. N. Dvorkin, "A four-node plate bending element based on Mindlin-Reissner plate theory and mixed interpolation," Int. J. Num. Meth. Engng. 21, 367-383 (1985).
6. K.-J. Bathe and E. N. Dvorkin, "A formulation of general shell elements. The use of mixed interpolation of tensorial components," Int. J. Num. Meth. Engng. 22, 697-722 (1986).
7. K.-J. Bathe, F. Brezzi, and S. W. Cho, "The MITC7 and MITC9 plate bending elements," Comput. & Structures 32, 797-814 (1989).
8. K.-J. Bathe, S. W. Cho, and M. L. Bucalem, "On our MITC plate bending/shell elements," in Analytical and Computational Models of Shells, A. K. Noor, T. Belytschko, and J. C. Simo, Eds., AMSE, New York, 1990, Vol. iI, pp. 261-278.
9. F. Brezzi, K.-J. Bathe, and M. Fortin, "Mixed-interpolated elements for Reissner-Mindlin plates," Int. J. Num. Met. Eng. 28, 1787-1801 (1989).
10. F. Brezzi and M. Fortin, "Analysis of some low order finite element schemes for Mindlin-Reissner plates," Math. Comp. 47, 151-158 (1986).
11. F. Brezzi, M. Fortin, and R. Stenberg, "Error analysis of mixed-interpolated elements for Reissner-Mindlin plates," Math. Mod. and Meth. in Appl. Sci. 1, 125-151 (1991).
12. F. Brezzi, J. Douglas, M. Fortin, and L. D. Marini, "Efificient rectangular mixed finite elements in two and three space variables," Math. Model. Numer. Anal. 21, 581-604 (1987).
13. I. Perugia, "A class of quadrilateral finite elements for the Stokes problem," Appl. Math. Lett. 6, 27-30 (1993).
14. F. Brezzi, "On the existence, uniqueness and approximation of saddle point problems arising from Lagrangian multipliers," RAIRO Anal. Numér. 2, 129-151 (1974).
15. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991.
16. M. Fortin, "Old and new finite elements for incompressible flows," Int. J. Numer. Meth. Fluids, 1, 347-364 (1981).
17. T. Dupont and L. R. Scott, "Polynomial approximation of functions in Sobolev spaces," Math. Comp. 34, 441-463 (1980).
18. P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.
19. L. Gastaldi, "Uniform interior error estimates for Reissner-Mindlin plate model," Math. Comp., 61, 539-567 (1993).
20. T. Scapolla and L. Della Croce, "Hierarchic and mixed-interpolated finite elements for Reissner-Mindlin plate problems," Comm. Numer. Methods in Eng. 11, 549-562 (1995).
21. L. Della Croce and T. Scapolla, "High order finite elements for thin to moderately thick plates," Comput. Mech. 10, 263-279 (1992).
22. S. Timoshenko and S. Woinowski-Krieger, Theory of Plates and Shells, McGraw-Hill, Singapore, 1970.