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
Mots-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 
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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/

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  • Patrizio Neff; Dirk Pauly; Karl-Josef Witsch Poincaré meets Korn via Maxwell: Extending Korn's first inequality to incompatible tensor fields, Journal of Differential Equations, Volume 258 (2015) no. 4, p. 1267 | DOI:10.1016/j.jde.2014.10.019
  • Andrea Cianchi Korn type inequalities in Orlicz spaces, Journal of Functional Analysis, Volume 267 (2014) no. 7, p. 2313 | DOI:10.1016/j.jfa.2014.07.012
  • Sergey A. Nazarov; Andrey S. Slutskij; Guido H. Sweers Korn Inequalities for a Reinforced Plate, Journal of Elasticity, Volume 106 (2012) no. 1, p. 43 | DOI:10.1007/s10659-010-9289-y
  • O. V. Izotova; S. A. Nazarov; G. H. Sweers Asymptotically sharp weight Korn’s inequality for thin-walled elastic structures, Journal of Mathematical Sciences, Volume 150 (2008) no. 1, p. 1807 | DOI:10.1007/s10958-008-0098-9
  • Сергей Александрович Назаров; Sergei Aleksandrovich Nazarov Неравенства Корна для упругих сочленений массивных тел, тонких пластин и стержней, Успехи математических наук, Volume 63 (2008) no. 1, p. 37 | DOI:10.4213/rm8545

Cité par 5 documents. Sources : Crossref

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

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