Approximation of the buckling problem for Reissner-Mindlin plates

SIAM Journal on Numerical Analysis

Volumn 48, Issue 2, 2010, Pages 603-632

  Lovadina, Carlo ^a   Mora, David ^b   Rodríguez, Rodolfo ^c  

^a UNIVERSITY OF PAVIA   (Italy)

^b UNIVERSIDAD DEL BÍO BÍO   (Chile)

^c UNIVERSITY OF CONCEPCIÓN   (Chile)

Author keywords

Buckling; Finite elements; Noncompact spectral problems; Reissner Mindlin plates

Indexed keywords

CLAMPED PLATES; CLASSICAL APPROXIMATION; EIGEN FUNCTION; EIGENVALUES; ERROR ESTIMATES; FINITE ELEMENT; LOCKING-FREE; MIXED INTERPOLATIONS; NUMERICAL COMPUTATIONS; NUMERICAL EXPERIMENTS; PLATE THICKNESS; REDUCED INTEGRATION; REISSNER-MINDLIN; REISSNER-MINDLIN PLATES; SPECTRAL CHARACTERIZATION; SPECTRAL PROBLEM; THEORETICAL RESULT; VIBRATION PROBLEM;

APPROXIMATION THEORY; BUCKLING; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL OPERATORS; SPECTRUM ANALYZERS;

MINDLIN PLATES;

EID: 77954204489     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/090747336     Document Type: Article

References (24)

1. D. N. ARNOLD AND R. S. FALK, A uniformly accurate.nite element method for the Reissner-Mindlin plate, SIAM J. Numer. Anal., 26 (1989), pp. 1276-1290.
2. I. BABU. SKA AND J. OSBORN, Eigenvalue Problems, Handb. Numer. Anal. 2, P. G. Ciarlet and J. L. Lions, eds., North-Holland, Amsterdam, 1991, pp. 641-787.
3. A. BERMÚDEZ, R. DURÁN, M. A. MUSCHIETTI, R. RODRÍGUEZ, AND J. SOLOMIN, Finite element vibration analysis of.uid-solid systems without spurious modes, SIAM J. Numer. Anal., 32 (1995), pp. 1280-1295.
4. F. BREZZI AND M. FORTIN, Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991.
5. C. CANUTO, Eigenvalue approximations by mixed methods, RAIRO Anal. Numér., 12 (1978), pp. 27-50.
6. P. G. CIARLET AND P. A. RAVIART, A mixed.nite element method for the biharmonic equation, in Mathematical Aspects of Finite Elements in Partial Di.erential Equations, C. de Boor, ed., Academic Press, New York, 1974, pp. 125-145.
7. M. DAUGE AND M. SURI, Numerical approximation of the spectra of non-compact operators arising in buckling problems, J. Numer. Math., 10 (2002), pp. 193-219.
8. J. DESCLOUX, N. NASSIF, AND J. RAPPAZ, On spectral approximation. Part 1: The problem of convergence, RAIRO Anal. Numér., 12 (1978), pp. 97-112.
9. J. DESCLOUX, N. NASSIF, AND J. RAPPAZ, On spectral approximation. Part 2: Error estimates for the Galerkin method, RAIRO Anal. Numér., 12 (1978), pp. 113-119.
10. R. DURÁN, L. HERVELLA-NIETO, E. LIBERMAN, R. RODRÍGUEZ, AND J. SOLOMIN, Approximation of the vibration modes of a plate by Reissner-Mindlin equations, Math. Comp., 68 (1999), pp. 1447-1463.
11. R. DURÁN AND E. LIBERMAN, On mixed.nite elements methods for the Reissner-Mindlin plate model, Math. Comp., 58 (1992), pp. 561-573.
12. R. FALK, Finite Elements for the Reissner-Mindlin Plate, in Mixed Finite Elements, Compatibility Conditions, and Applications, D. Bo. and L. Gastaldi, eds., Springer-Verlag, Berlin, 2008, pp. 195-230.
13. K. ISHIHARA, On the mixed.nite element approximation for the buckling of plates, Numer. Math., 33 (1979), pp. 195-210.
14. T. KATO, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1966.
15. S. KITIPORNCHAI, Y. XIANG, C. M. WANG, AND K. M. LIEW, Buckling of thick skew plates, Internat. J. Numer. Methods Engrg., 36, (1993), pp. 1299-1310.
16. B. MERCIER, J. OSBORN, J. RAPPAZ, AND P. A. RAVIART, Eigenvalue approximation by mixed and hybrid methods, Math. Comp., 36 (1981), pp. 427-453.
17. D. MORA AND R. RODRÍGUEZ, A piecewise linear.nite element method for the buckling and the vibration problems of thin plates, Math. Comp., 78 (2009), pp. 1891-1917.
18. R. RANNACHER, Nonconforming.nite element methods for eigenvalue problems in linear plate theory, Numer. Math., 33 (1979), pp. 23-42.
19. J. N. REDDY, Energy and Variational Methods in Applied Mechanics, Wiley, New York, 1984.
20. J. N. REDDY, Mechanics of Laminated Composite Plates-Theory and Analysis, CRC Press, Boca Raton, 1997.
21. G. SAVARÉ, Regularity results for elliptic equations in Lipschitz domains, J. Funct. Anal., 152 (1998), pp. 176-201.
22. J. P. SMITH, Buckling of shear deformable plates using the p-version of the.nite element method, Comput. & Structures, 57 (1995), pp. 527-532.
23. B. SZABO AND G. KIRALYFALVI, Linear models of buckling and stress-sti.ening, Comput. Methods Appl. Mech. Engrg., 171 (1999), pp. 43-59.
24. H. ZHONG AND C. GU, Buckling of simply supported rectangular Reissner-Mindlin plates subjected to linearly varying in-plane loading, J. Engrg. Mech., 132 (2006), pp. 578-581.