A model problem for boundary layers of thin elastic shells

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1. [1] M. Bernadou, Méthodes d'éléments finis pour les problèmes de coques minces. Masson, Paris (1994). 
2. [2] F. Brezzi and F. M. Fortin, Mixed and hybrid finite elements methods. Springer (1991). Zbl0788.73002MR1115205
3. [3] D. Choï, F.J. Palma, É. Sanchez Palencia and M.A. Vilariño, Remarks on membrane locking in the finite element computation of very thin elastic shells. Math. Modell. Num. Anal. 32 (1998) 131-152. Zbl0905.73066MR1622605
4. [4] P.G. Ciarlet, Mathematical elasticity, Vol. III, Theory of shells. North Holland, Amsterdam (to appear). Zbl0953.74004MR1757535
5. [5] D. Chapelle and K.J. Bathe, Fundamental considerations for the finite element analysis of shell structures, Computers and Structures 66 (1998) 19-36. Zbl0934.74073
6. [6] P. Gérard and É. Sanchez Palencia, Sensitivity phenomena for certain thin elastic shells with edges. Math. Meth. Appl. Sci. (to appear). Zbl0989.74047MR1740321
7. [7] A.L. Goldenveizer, Theory of elastic thin shells. Pergamon, New York (1962). Zbl0145.45504MR135763
8. [8] P. Karamian, Nouveaux résultats numériques concernant les coques minces hyperboliques inhibées: cas du paraboloïde hyperbolique. C. R. Acad. Sci. Paris Sér. IIb 326 (1998) 755-760. Zbl0969.74063
9. [9] P. Karamian, Réflexion des singularités dans les coques hyperboliques inhibées. C.R. Acad. Sci. Paris Sér. IIb 326 (1998) 609-614. Zbl0914.73029
10. [10] P. Karamian, Coques élastiques minces hyperboliques inhibées: calcul du problème limite par éléments finis et non reflexion des singularités. Thèse de l'Universté de Caen (1999). 
11. [11] D. Leguillon, J. Sanchez-Hubert and É. Sanchez Palencia, Model problem of singular perturbation without limit in the space of finite energy and its computation. C.R. Acad. Sci. Paris Sér. IIb 327 (1999) 485-492. Zbl0932.35064
12. [12] J.L. Lions and É. Sanchez Palencia, Problèmes sensitifs et coques élastiques minces. in Partial Differenhal Equations and Functional Analysis, in memory of P. Grisvard (J. Céa, D. Chesnais, G. Geymonat, J.L. Lions Eds.), Birkhäuser, Boston (1996) 207-220. Zbl0857.35033MR1399133
13. [13] J.L. Lions and É. Sanchez Palencia, Sur quelques espaces de la théorie des coques et la sensitivité, in Homogenization and applications to material sciences, Cioranescu, Damlamian, Doneto Eds., Gakkotosho, Tokyo (1995) 271-278. Zbl0895.73042MR1473993
14. [14] A. E. H. Love, A treatrise on tke mathematical theory of elasticity, Reprinted by Dover, New-York (1944). Zbl0063.03651JFM47.0750.09
15. [15] J. Pitkaranta and É. Sanchez Palencia, On the asymptotic behavior of sensitive shells with small thickness. C.R. Acad. Sci. Paris Sér. IIb 325 (1997) 127-134. Zbl0886.73031
16. [16] H.S. Rutten, Theory and design of shells on the basis of asymptotic analysis. Rutten and Kruisman, Voorburg (1973). 
17. [17] J. Sanchez-Hubert and É. Sanchez Palencia, Introduction aux méthodes asymptotiques et à l'homogénéisation, Masson, Paris (1992). 
18. [18] J. Sanchez-Hubert and É. Sanchez Palencia, Coques élastiques minces. Propriétés asymptotiques. Masson, Paris (1997). Zbl0881.73001
19. [19] J. Sanchez-Hubert and É. Sanchez Palencia, Pathological phenomena in computation of thin elastic shells. Transactions Can Soc. Mech. Engin. 22 (1998) 435-446. 
20. [20] M. Van Dyke, Perturbation methods in fluid mechanics. Academic Press, New-York (1964). Zbl0136.45001MR176702