Fundamental considerations for the finite element analysis of shell structures

Computers and Structures

Volumn 66, Issue 1, 1998, Pages 19-36

  Chapelle, D ^b,c   Bathe, K J ^a  

^a CNRS   (France)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; COMPUTATIONAL GEOMETRY; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL MODELS; OPTIMIZATION; SHELLS (STRUCTURES);

SHELL GEOMETRY; SHELL THICKNESS;

FINITE ELEMENT METHOD;

EID: 0031628614     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7949(97)00078-3     Document Type: Article

References (34)

1. Bathe, K. J., Finite Element procedures. Prentice Hall, Englewood Cliffs, NJ, 1996.
2. Goldenweizer A. L., Theory of Elastic Thin Shells. Pergamon Press, Oxford, 1961.
3. Novozhilov, V. V., Thin Shell Theory. Wolters-Noordhoff Publishing, Groningen, 1970.
4. Flügge, W., Stresses in Shells, 2nd edn. Springer, Berlin, 1973.
5. Ciarlet, P. G. and Lods, V. Analyse asymptotique des coques linéairement élastiques. I. Coques "membranaires". Comptes Rendus de l'Academie des Science, Paris, Série I, 1994, 318, 863-868.
6. Ciarlet, P. G., Lods, V. and Miara, B. Analyse asymptotique des coques linéairement élastiques. II. Coques "en flexion". Comptes Rendus de l'Academie des Science, Paris, Série I, 1994, 319, 95-100.
7. Piila, J. and Pitkäranta, J., Energy estimates relating different linear elastic models of a thin cylindrical shell. I. The membrane-dominated case. SIAM Journal of Mathematical Analysis, 1993, 24(1), 1-22.
8. Piila, J. and Pitkäranta, J., Energy estimates relating different linear elastic models of a thin cylindrical shell. II: The case of free boundary. SIAM Journal of Mathematical Analysis, 1995, 26(4), 820-849.
9. Bernadou M., Finite Element Methods for Thin Shell Problems. John Wiley and Sons, New York, 1996.
10. Green A. E. and Zerna W., Theoretical Elasticity, 2nd edn. Oxford University Press, Oxford, 1968.
11. Naghdi P. M., Foundations of elastic shell theory. In Progress in Solid Mechanics, Vol. 4. North-Holland, Amsterdam, 1963, pp. 1-90.
12. Koiter, W. T., On the nonlinear theory of thin elastic shells. Koninklijke Nederlandse Akademie van Wetenschappen-Proceedings, 1965, B69, 1-54.
13. Bernadou M. and Ciarlet P. G., Sur l'ellipticité du modèle linéaire de coques de W. T. Koiter. In Computing Methods in Applied Sciences and Engineering, ed. R. Glowinski and J. L. Lions, Springer Verlag, Berlin. 1975.
14. Coutris, N., Théorème d'existence et d'unicité pour un problème de coque élastique dans le cas d'un modèle linéaire de P. M. Naghdi. RAIRO Analyse Numérique, 1978, 12, 51-57.
15. Sanchez-Palencia, E., Statique et dynamique des coques minces. I. Cas de flexion pure non inhibée. Comptes Rendus de l'Academie des Science, Paris, Série I, 1989, 309, 411-417.
16. Sanchez-Palencia, E. Statique et dynamique des coques minces. II. Cas de flexion pure inhibée -Approximation membranaire. Comptes Rendues Academie de Science, Paris, Serie I, 1989, 309, 531-537.
17. Brezzi F. and Fortin M., Mixed and Hybrid Finite Element Methods. Springer, Berlin, 1991.
18. Bathe, K. J. and Brezzi F., On the convergence of a four-node plate bending element based on Mindlin-Reissner plate theory and a mixed interpolation. In The Mathematics of Finite Elements and Applications V, ed. J. R. Whiteman. Academic Press, NY, 1985, pp. 491-503.
19. Chenais, D. and Paumier, J.-C., On the locking phenomenon for a class of elliptic problems. Numerische Mathematik, 1994, 67, 427-440.
20. Pitkäranta, J., The problem of membrane locking in finite element analysis of cylindrical shells. Numerische Mathematik, 1992, 61, 523-542.
21. Sanchez-Palencia, E. Asymptotic and spectral properties of a class of singular-stiff problems. Journal de Mathématiques, Pures et Appliquées, 1992, 71, 379-406.
22. Ciarlet, P. G. and Lods, V., Ellipticité des équations membranaires d'une coque uniformément elliptique. Comptes Rendus de l'Academie des Science, Paris, Série I, 1994, 318, 195-200.
23. Ciarlet, P. G. and Sanchez-Palencia, E., Un théorème d'existence et d'unicité pour les équations de coques membranaires. Comptes Rendus de l'Academie des Science, Paris, Série I, 1993, 317, 801-805.
24. Lions J. L., Perturbations Singulières dans les Problèmes aux Limites et en Contrôle Optimal. Springer, Berlin, 1973.
25. Sanchez-Palencia, E., Surfaces et coques élastiques mince: problèmes et défis. La Vie des Sciences, 1995, 12(3), 239-258.
26. Kirmse, A., Bending-dominated deformation of thin spherical shells: analysis and finite element approximation. SIAM Journal of Numerical Analysis, 1993, 30(4), 1015-1040.
27. Arnold, D. N., Discretization by finite elements of a model parameter dependent problem. Numerische Mathematik, 1981, 37, 405-421.
28. Paumier J. C., On the locking phenomenon for a linearly elastic clamped plate. Research Report 76, L.M.C., 1992.
29. Bathe, K. J., Bucalem, M. L. and Brezzi, F., Displacement and stress convergence of our MITC plate bending elements. Engineering Computations, 1990, 7(4), 291-302.
30. Iosilevich A., Bathe K. J. and Brezzi F., Numerical inf-sup analysis of MITC plate bending elements. Proceedings Symposium on Plates and Shells. Université Laval, July 1996.
31. Arnold, D. N. and Brezzi, F., Locking-free finite element methods for shells. Mathematics Computations, 1977, 66(217), 1-14.
32. Chapelle D. and Stenberg R., Stabilized finite element formulations for shells in a bending dominated state. Submitted to SIAM Journal of Numerical Analysis.
33. Clément, P., Approximation by finite element functions using local regularization. R.A.I.R.O., 1975, R-2, 77-84.
34. Pitkäranta, J., Leino, Y., Ovaskainen, O. and Piila, J., Shell deformation states and the finite element method: a benchmark study of cylindrical shells. Computer Methods in Applied Mechanics and Engineering, 1995, 128, 81-121.