Comptes Rendus
no. 12
Weighted Korn inequalities for thin-walled elastic structures
[Inégalités de Korn avec poids pour des structures élastiques de plaques minces]

Présenté par : Évariste Sanchez-Palencia

O.V. Izotova1 ; Serguei A. Nazarov1 ; Guido H. Sweers2, 3 
1 Institute of Mechanical Engineering Problems, V.O., Bolshoi pr., 61, 199178 St.-Petersburg, Russia
2 Delft Institute of Applied Mathematics, TU Delft, P.O. Box 5031, 2600 GA Delft, The Netherlands
3 Mathematisches Institut, Universität zu Köln, Weyertal 86–90, 50931 Köln, Germany
Comptes Rendus. Mécanique, Volume 334 (2006) no. 12, pp. 707-712.

Des normes dans H1 avec poids appropriés sont présentées tels que l'inégalité du type Korn soit asymptotiquement exacte en ce qui concerne l'épaisseur et la rigidité des plaques élastiques. Les poids dépendent crucialement de la structure géométrique de la jonction des plaques.

Appropriate weighted norms in H1 are presented such that the Korn type inequality is asymptotically sharp with respect to relative thickness and stiffness of the elastic plates. The weights depend crucially on the geometric structure of the plates' junction.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2006.10.002
Keywords: Computational solid mechanics, Korn's inequality, Elastic junction, Thin plates
Mot clés : Mécanique des solides numérique, Inégalité de Korn, Jonction élastique, Plaques minces

O.V. Izotova 1 ; Serguei A. Nazarov 1 ; Guido H. Sweers 2, 3

1 Institute of Mechanical Engineering Problems, V.O., Bolshoi pr., 61, 199178 St.-Petersburg, Russia
2 Delft Institute of Applied Mathematics, TU Delft, P.O. Box 5031, 2600 GA Delft, The Netherlands
3 Mathematisches Institut, Universität zu Köln, Weyertal 86–90, 50931 Köln, Germany 
@article{CRMECA_2006__334_12_707_0,
     author = {O.V. Izotova and Serguei A. Nazarov and Guido H. Sweers},
     title = {Weighted {Korn} inequalities for thin-walled elastic structures},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {707--712},
     publisher = {Elsevier},
     volume = {334},
     number = {12},
     year = {2006},
     doi = {10.1016/j.crme.2006.10.002},
     language = {en},
}
TY  - JOUR
AU  - O.V. Izotova
AU  - Serguei A. Nazarov
AU  - Guido H. Sweers
TI  - Weighted Korn inequalities for thin-walled elastic structures
JO  - Comptes Rendus. Mécanique
PY  - 2006
SP  - 707
EP  - 712
VL  - 334
IS  - 12
PB  - Elsevier
DO  - 10.1016/j.crme.2006.10.002
LA  - en
ID  - CRMECA_2006__334_12_707_0
ER  - 
%0 Journal Article
%A O.V. Izotova
%A Serguei A. Nazarov
%A Guido H. Sweers
%T Weighted Korn inequalities for thin-walled elastic structures
%J Comptes Rendus. Mécanique
%D 2006
%P 707-712
%V 334
%N 12
%I Elsevier
%R 10.1016/j.crme.2006.10.002
%G en
%F CRMECA_2006__334_12_707_0
O.V. Izotova; Serguei A. Nazarov; Guido H. Sweers. Weighted Korn inequalities for thin-walled elastic structures. Comptes Rendus. Mécanique, Volume 334 (2006) no. 12, pp. 707-712. doi : 10.1016/j.crme.2006.10.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.10.002/

[1] Ph.G. Ciarlet Mathematical Elasticity, vol. II. Theory of Plates, North-Holland, Amsterdam, 1997

[2] G. Duvaut; J.-L. Lions Inequalities in Mechanics and Physics, Springer-Verlag, Berlin–New York, 1976

[3] V.A. Kondratiev; O.A. Oleĭnik Boundary value problems for a system in elasticity theory in unbounded domains. Korn inequalities, Uspekhi Mat. Nauk, Volume 43 (1988) no. 5, pp. 55-98 (239 Russ. Math. Surveys, 43, 1988, pp. 65-119)

[4] S.A. Nazarov Korn's inequalities for junctions of spatial bodies and thin rods, Math. Methods Appl. Sci., Volume 20 (1997) no. 3, pp. 219-243

[5] S.A. Nazarov Asymptotic Theory of Thin Plates and Rods, vol. 1. Dimension Reduction and Integral Estimates, Nauchnaya Kniga, Novosibirsk, 2001 (in Russian)

[6] S.A. Nazarov Weighted anisotropic Korn's inequality for a junction of a plate and a rod, Sb. Math., Volume 191 (2004) no. 4, pp. 97-126

[7] S.A. Nazarov Korn's inequalities for junctions of elastic bodies with thin plates, Siberian Math. J., Volume 46 (2005) no. 4, pp. 876-889

[8] J. Nečas Les méthodes en théorie des équations elliptiques, Masson Academia, Paris/Prague, 1967

[9] J. Sanchez-Hubert; E. Sanchez-Palencia Coques élastiques minces: propriétés asymptotiques, Masson, Paris, 1997

[10] B.A. Shoikhet On asymptotically exact equations of thin plates of complex structure, J. Appl. Math. Mech., Volume 37 ( 1973–1974 ), pp. 914-924

Cité par Sources :

⁎ The authors gratefully acknowledge the support by N.W.O., the Netherlands Organisation for Scientific Research.

Commentaires - Politique