A nonconforming element for the Reissner-Mindlin plate

Computers and Structures

Volumn 81, Issue 8-11, 2003, Pages 515-522

  Brezzi, F ^a   Marini, L D ^a  

^a UNIVERSITY OF PAVIA   (Italy)

Author keywords

Discontinuous finite element methods; Reissner Mindlin plates

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); FINITE ELEMENT METHOD; GALERKIN METHODS; SHELLS (STRUCTURES);

NONCONFORMING ELEMENTS;

PLATES (STRUCTURAL COMPONENTS);

EID: 0037401609     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7949(02)00418-2     Document Type: Article

References (26)

1. Agmon S. Lectures on elliptic boundary value problems. 1965;Van Nostrand Mathematical Studies, Princeton, NJ.
2. Arnold D.N. An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19:1982;742-760.
3. Arnold D.N., Brezzi F. Locking-free finite element methods for shells. Math. Comp. 66:1997;1-14.
4. Arnold D.N., Brezzi F., Cockburn B., Marini L.D. Discontinuous Galerkin methods for elliptic problems. Discontinuous Galerkin Methods (Newport, RI, 1999), Lect. Notes Comput. Sci. Eng. 11. 2000;89-101 Springer, Berlin.
5. Arnold D.N., Brezzi F., Cockburn B., Marini L.D. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39:2002;1749-1779.
6. Arnold DN, Brezzi F, Marini LD. New elements for the Reissner-Mindlin plate, in preparation.
7. Arnold D.N., Falk R.S. A uniformly accurate finite element method for the Reissner-Mindlin plate. SIAM J. Numer. Anal. 26:1989;1276-1290.
8. Arnold D.N., Falk R.S. Analysis of a linear-linear finite element for the Reissner-Mindlin plate model. Math. Models Meth. Appl. Sci. 7:1997;217-238.
9. Auricchio F., Lovadina C. Partial selective reduced integration schemes and kinematically linked interpolations for plate bending problems. Math. Models Meth. Appl. Sci. 9:1999;693-722.
10. Auricchio F., Lovadina C. Analysis of kinematic linked interpolation methods for Reissner-Mindlin plate problems. Comput. Meth. Appl. Mech. Engrg. 190:2001;18-19.
11. Auricchio F., Taylor R.L. A shear deformable plate element with an exact thin limit. Comput. Meth. Appl. Mech. Engrg. 118:1994;393-412.
12. Bathe K.J. Finite element procedures. 1996;Prentice-Hall.
13. Brezzi F., Bathe K.J., Fortin M. Mixed-interpolated elements for Reissner-Mindlin plates. Int. J. Numer. Meth. Engrg. 28:1989;1787-1801.
14. Brezzi F., Fortin M. Mixed and hybrid finite element methods. 1991;Springer, New York.
15. Brezzi F., Fortin M., Stenberg R. Error analysis of mixed-interpolated elements for Reissner-Mindlin plates. Math. Models Meth. Appl. Sci. 1:1991;125-151.
16. Bucalem M.L., Bathe K.J. Finite element analysis of shell structures. Arch. Comput. Meth. Engrg. 4:1997;3-61.
17. Bucalem M.L., Bathe K.J. Higher-order MITC general shell elements. Int. J. Numer. Meth. Engrg. 36:1993;3729-3754.
18. Chapelle D., Bathe K.J. Fundamental considerations for the finite element analysis of shell structures. Comput. Struct. 66:1998;19-36.
19. Chapelle D, Bathe KJ. The finite element analysis of shells, Springer Verlag, in press.
20. Chapelle D., Stenberg R. Stabilized finite element formulations for shells in a bending dominated state. SIAM J. Numer. Anal. 36:1999;32-73.
21. Duran R., Liberman E. On mixed finite-element methods for the Reissner-Mindlin plate model. Math. Comput. 58:1992;561-573.
22. Flores F.G., Oñate E., Zaráte F. New assumed strain triangles for nonlinear shell analysis. Comput. Mech. 17:1995;107-114.
23. Hansbo P, Larson MG. Discontinuous Galerkin and the Crouzeix-Raviart element: application to elasticity. Chalmers Finite Element Center Preprint 2000-9, Chalmers University of Technology, Sweden, 2000.
24. Lovadina C. A new class of mixed finite element methods for Reissner-Mindlin plates. SIAM J. Numer. Anal. 33:1996;2457-2467.
25. Lovadina C. Analysis of a mixed finite element method for the Reissner-Mindlin plate problems. Comput. Meth. Appl. Mech. Engrg. 163:1998;71-85.
26. 1 element for Reissner-Mindlin plate Math. Models Meth. Appl. Sci. 11:2001;1311-1342.