Error analysis of quadrilateral Wilson element for Reissner-Mindlin plate

Computer Methods in Applied Mechanics and Engineering

Volumn 197, Issue 6-8, 2008, Pages 464-475

  Hu, Jun ^a   Shi, Zhong Ci ^b  

^a PEKING UNIVERSITY   (China)

^b INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

Locking free; MITC4; Reissner Mindlin plate; Wilson

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; MESH GENERATION; PLATES (STRUCTURAL COMPONENTS); STRUCTURAL ANALYSIS;

REISSNER-MINDLIN PLATE; WILSON ELEMENT METHOD;

ERROR ANALYSIS;

CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; MESH GENERATION; PLATES (STRUCTURAL COMPONENTS); STRUCTURAL ANALYSIS;

EID: 36148960544     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.06.006     Document Type: Article

References (21)

1. Adams R.A. Sobolev Space (1978), Academic Press, New York
2. Arnold D.N., and Falk R.S. A uniformly accurate finite element method for Reissner-Mindlin plate. SIAM J. Numer. Anal. 26 (1989) 1276-1290
3. Arnold D.N., and Falk R.S. Analysis of a linear-linear element for the Reissner-Mindlin model. Math. Models Methods Appl. Sci. 7 (1997) 486-514
4. Babuska I., and Scapolla T. Benchmark computation and performance evaluation for rhombic plate bending problem. Int. J. Numer. Methods. Engrg. 28 (1989) 155-179
5. K.J. Bathe, F. Brezzi, On the convergence of a four-node plate bending element based on Mindlin-Reissner plate theory and a mixed interpolation, in: J.R. Whiteman (Ed.), MAFELAP V (London, 1985), pp. 491-503.
6. Bathe K.J., and Dvorkin E. A four-node plate bending element based on Mindlin-Reissner plate theory and a mixed interpolation. Int. J. Numer. Methods Engrg. 21 (1985) 367-383
7. Brezzi F., and Fortin M. Numerical approximation of Reissner-Mindlin plates. Math Comput. 47 (1986) 151-158
8. Brezzi F., and Fortin M. Mixed and Hybrid Finite Element Methods (1991), Springer-Verlag
9. Brezzi F., Fortin M., and Stenberg R. Error analysis of mixed-interpolated elements for Reissner-Mindlin plate. Math. Models Methods Appl. Sci. 1 (1991) 125-151
10. Ciarlet P.G. The Finite Element Method for Elliptic Problems (1978), North Holland, Amsterdam
11. Clément P. Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 9 (1975) 77-84
12. Duran R., Hernández E., Hervella-Nieto L., Liberman E., and Rodríguez R. Error estimates for lower-order isoparametric quadrilateral finite elements for plates. SIAM J. Numer. Anal. 41 (2003) 1771-1772
13. Girault V., and Raviart P.A. Finite Element Methods for Navier-Stokes Equations, Theory and Algorithm (1986), Springer
14. J. Hu, Quadrilateral locking free elements in elasticity, Doctorate Dissertation, Institute of Computational Mathematics, CAS, 2004.
15. J. Hu, Z.C. Shi, Analysis for quadrilateral MITC elements for Reissner-Mindlin plate, Math. Comput., submitted for publication.
16. Lesaint P., and Z lámal M. Convergence of the nonconforming Wilson element for arbitrary quadrilateral meshes. Numer. Math. 36 (1980) 33-52
17. Pitkäranta J., and Stenberg R. Error bounds for the approximation of the Stokes problem using bilinear/constant elements on irregular quadrilateral meshes. In: Whiteman J.R. (Ed). The Mathematics of Finite Elements and Applications V. MAFELAP 1984 (1985), Academic Press 325-334
18. Shi Z.C. A convergence condition for quadrilateral Wilson element. Numer. Math. 44 (1984) 349-361
19. Stenberg R., and Süri M. An hp error analysis of MITC plate elements. SIAM J. Numer. Anal. 34 (1997) 544-568
20. Zhang Z., and Zhang S. Wilson element for the Reissner-Mindlin plate. Comput. Methods Appl. Mech. Engrg. 113 (1994) 55-65
21. Zienkiewicz O.C., and Xu Z. Linked interpolation for Reissner-Mindlin plate elements: Part I - A simple quadrilateral. Int. J. Numer. Methods Engrg. 36 (1993) 3043-3056