Partial selective reduced integration schemes and kinematically linked interpolations for plate bending problems

Mathematical Models and Methods in Applied Sciences

Volumn 9, Issue 5, 1999, Pages 693-722

  Auricchio, Ferdinando ^a   Lovadina, Carlo ^b  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b UNIVERSITY OF TRENTO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033460849     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021820259900035X     Document Type: Article

References (29)

1. D. N. Arnold, Innovative finite element methods for plates, Math. Appl. Comput. 10 (1991) 77-88.
2. D. N. Arnold and F. Brezzi, Some new elements for the Reissner-Mindlin plate model, in Boundary Value Problems for Partial Differential Equations and Applications, eds. J. L. Lions and C. Baiocchi (Masson, 1993), pp. 287-292.
3. D. N. Arnold and R. S. Falk, A uniformly accurate finite element method for the Reissner-Mindlin plate model, SIAM J. Numer. Anal 26 (1989) 1276-1290.
4. F. Auricchio and E. Sacco, Augmented Lagrangian finite-elements for plate contact problems, Internat. J. Numer. Methods Engrg. 39 (1996) 4141-4158.
5. F. Auricchio and R. L. Taylor, 3-node triangular elements based on Reissner-Mindlin plate theory, Report No. UCB/SEMM-91/04, Department of Civil Engineering, University of California at Berkeley (1991).
6. F. Auricchio and R. L. Taylor, A shear deformable plate element with an exact thin limit, Comput. Methods Appl. Mech. Engrg. 118 (1994) 393-412.
7. F. Auricchio and C. Lovadina, Analysis of kinematic linked interpolation methods for Reissner-Mindlin plate problems, submitted to Comput. Methods Appl. Mech. Engrg.
8. C. Baiocchi, F. Brezzi and L. P. Franca, Virtual bubbles and Galerkin-least-squares type methods (Ga.L.S.), Comput. Methods Appl. Mech. Engrg. 105 (1993) 125-141.
9. K.-J. Bathe, Finite Element Procedures (Prentice Hall, 1996).
10. K.-J. Bathe and F. Brezzi, On the convergence of a four node plate bending element based on Reissner-Mindlin theory, The Mathematics of Finite Elements and Applications, ed. J. R. Whiteman (Academic Press, 1985), pp. 491-503.
11. D. Boffi and C. Lovadina, Analysis of new augmented Lagrangian formulations for mixed finite element schemes, Numer. Math. 75 (1997) 405-419.
12. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods (Springer-Verlag, 1991).
13. F. Brezzi, K.-J. Bathe and M. Fortin, Mixed-interpolated elements for Reissner-Mindlin plates, Internat. J. Numer. Methods Engrg. 28 (1989) 1787-1801.
14. F. Brezzi, M. Fortin and R. Stenberg, Error analysis of mixed-interpolated elements for Reissner-Mindlin plates, Math. Models Methods Appl. Sci. 1 (1991) 125-151.
15. D. Chapelle and R. Stenberg, An optimal low-order locking-free finite element method for Reissner-Mindlin plates, Math. Models Methods Appl. Sci. 8 (1998) 407-430.
16. C. Chinosi and C. Lovadina, Numerical analysis of some mixed finite elements methods for Reissner-Mindlin plates, Comput. Mech. 16 (1995) 36-44.
17. P. G. Ciarlet, The Finite Element Method for Elliptic Problems (North Holland, 1978).
18. R. G. Duran and E. Liberman, On the convergence of a triangular mixed finite element method for Reissner-Mindlin plates, Math. Models Methods Appl. Sci. 6 (1996) 339-352.
19. T. J. R. Hughes, The Finite Element Method (Prentice Hall, 1987).
20. C. Lovadina, A new class of mixed finite element methods for Reissner-Mindlin plates, SIAM J. Numer. Anal. 33 (1996) 2457-2467.
21. C. Lovadina, Some rectangular finite element methods for Reissner-Mindlin plates, Math. Models Methods Appl. Sci. 5 (1995) 777-787.
22. C. Lovadina, Analysis of a mixed finite element method for Reissner-Mindlin plate problem, submitted to Comput. Methods Appl. Mech. Engrg.
23. M. Lyly, On the connection between some linear triangular Reissner-Mindlin plate bending elements, to appear in Numer. Math.
24. J. Pitkäranta, Analysis of some low-order finite element schemes for Reissner-Mindlin and Kirchhoff plates, Numer. Math. 53 (1988) 237-254.
25. J. Pitkäranta, The problem of membrane locking infinite element analysis of cylindrical shells, Numer. Math. 61 (1992) 523-542.
26. R. L. Taylor and F. Auricchio, Linked interpolation for Reissner-Mindlin plate elements: Part II - A simple triangle, Internat. J. Numer. Methods Engrg. 36 (1993) 3057-3066.
27. Z. Xu, A simple and efficient triangular finite element for plate bending, Acta Mech. Sin. 2 (1986) 185-192.
28. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method (McGraw-Hill, 1989).
29. O. C. Zienkiewicz, Z. Xu, L. F. Zeng, A. Samuelsson and N.-E. Wiberg, Linked interpolation for Reissner-Mindlin plate elements: Part I - A simple quadrilateral, Internat. J. Numer. Methods Engrg. 36 (1993) 3043-3056.