A model problem for boundary layers of thin elastic shells
Karamian, Philippe ; Sanchez-Hubert, Jacqueline ; Sanchez Palencia, Évarisite
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000), p. 1-30 / Harvested from Numdam
Publié le : 2000-01-01
@article{M2AN_2000__34_1_1_0,
     author = {Karamian, Philippe and Sanchez-Hubert, Jacqueline and Sanchez Palencia, \'Evarisite},
     title = {A model problem for boundary layers of thin elastic shells},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {34},
     year = {2000},
     pages = {1-30},
     mrnumber = {1735979},
     zbl = {1004.74050},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2000__34_1_1_0}
}
Karamian, Philippe; Sanchez-Hubert, Jacqueline; Sanchez Palencia, Évarisite. A model problem for boundary layers of thin elastic shells. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000) pp. 1-30. http://gdmltest.u-ga.fr/item/M2AN_2000__34_1_1_0/

[1] M. Bernadou, Méthodes d'éléments finis pour les problèmes de coques minces. Masson, Paris (1994).

[2] F. Brezzi and F. M. Fortin, Mixed and hybrid finite elements methods. Springer (1991). | MR 1115205 | Zbl 0788.73002

[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. | Numdam | MR 1622605 | Zbl 0905.73066

[4] P.G. Ciarlet, Mathematical elasticity, Vol. III, Theory of shells. North Holland, Amsterdam (to appear). | MR 1757535 | Zbl 0953.74004

[5] D. Chapelle and K.J. Bathe, Fundamental considerations for the finite element analysis of shell structures, Computers and Structures 66 (1998) 19-36. | Zbl 0934.74073

[6] P. Gérard and É. Sanchez Palencia, Sensitivity phenomena for certain thin elastic shells with edges. Math. Meth. Appl. Sci. (to appear). | MR 1740321 | Zbl 0989.74047

[7] A.L. Goldenveizer, Theory of elastic thin shells. Pergamon, New York (1962). | MR 135763

[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. | Zbl 0969.74063

[9] P. Karamian, Réflexion des singularités dans les coques hyperboliques inhibées. C.R. Acad. Sci. Paris Sér. IIb 326 (1998) 609-614. | Zbl 0914.73029

[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] 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. | Zbl 0932.35064

[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. | MR 1399133 | Zbl 0857.35033

[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. | MR 1473993 | Zbl 0895.73042

[14] A. E. H. Love, A treatrise on tke mathematical theory of elasticity, Reprinted by Dover, New-York (1944). | JFM 47.0750.09 | Zbl 0063.03651

[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. | Zbl 0886.73031

[16] H.S. Rutten, Theory and design of shells on the basis of asymptotic analysis. Rutten and Kruisman, Voorburg (1973).

[17] J. Sanchez-Hubert and É. Sanchez Palencia, Introduction aux méthodes asymptotiques et à l'homogénéisation, Masson, Paris (1992).

[18] J. Sanchez-Hubert and É. Sanchez Palencia, Coques élastiques minces. Propriétés asymptotiques. Masson, Paris (1997). | Zbl 0881.73001

[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] M. Van Dyke, Perturbation methods in fluid mechanics. Academic Press, New-York (1964). | MR 176702 | Zbl 0136.45001