On the characterizations of matrix fields as linearized strain tensor fields

Journal des Mathematiques Pures et Appliquees

Volumn 86, Issue 2, 2006, Pages 116-132

  Amrouche, Cherif ^a   Ciarlet, Philippe G ^b   Gratie, Liliana ^b   Kesavan, Srinivasan ^c  

^a UNIVERSITÉ DE PAU ET DES PAYS DE L'ADOUR   (France)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^c INSTITUTE OF MATHEMATICAL SCIENCES   (India)

Author keywords

Donati's theorem; Korn's inequality; Linearized elasticity; Poincar 's lemma; Saint Venant compatibility conditions

Indexed keywords

EID: 33746659459     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2006.04.004     Document Type: Article

References (27)

1. Adams R.A. Sobolev Spaces (1975), Academic Press, San Diego, CA
2. Amrouche C., Ciarlet P.G., Gratie L., and Kesavan S. New formulations of linearized elasticity problems, based on extensions of Donati's theorem. C. R. Acad. Sci. Paris, Ser. I 342 (2006) 785-789
3. Amrouche C., Ciarlet P.G., Gratie L., and Kesavan S. On Saint Venant's compatibility conditions and Poincaré's lemma. C. R. Acad. Sci. Paris, Ser. I 342 (2006) 887-891
4. Amrouche C., and Girault V. Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension. Czechoslovak Math. J. 44 (1994) 109-140
5. Babuška I. Error-bounds for finite element methods. Numer. Math. 16 (1971) 322-333
6. Bolley P., and Camus J. Régularité pour une classe de problèmes aux limites dégénérés variationnels. C. R. Acad. Sci. Paris, Sér. A 282 (1976) 45-47
7. Borchers W., and Sohr H. On the equations rot v = g and div u = f with zero boundary conditions. Hokkaido Math. J. 19 (1990) 67-87
8. Brezzi F. On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers. Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge Anal. Numér. R-2 (1974) 129-151
9. Ciarlet P.G. Mathematical Elasticity, vol. I: Three-Dimensional Elasticity (1988), North-Holland, Amsterdam
10. Ciarlet P.G., and Ciarlet Jr. P. Another approach to linearized elasticity and a new proof of Korn's inequality. Math. Models Methods Appl. Sci. 15 (2005) 259-271
11. P.G. Ciarlet, S. Sauter, Direct computation of stresses in linearized elasticity, in preparation
12. Dautray R., and Lions J.L. Mathematical Analysis and Numerical Methods for Science and Technology, vol. 2: Functional and Variational Methods (1988), Springer-Verlag, Berlin/New York
13. Duvaut G., and Lions J.L. Les Inéquations en Mécanique et en Physique (1972), Dunod, Paris
14. G. Geymonat, F. Krasucki, Some remarks on the compatibility conditions in elasticity, Accad. Naz. Sci. XL Mem. Math. Appl., submitted for publication
15. Geymonat G., and Krasucki F. Beltrami's solutions of general equilibrium equations in continuum mechanics. C. R. Acad. Sci. Paris, Ser. I 342 (2006) 359-363
16. Geymonat G., and Suquet P. Functional spaces for Norton-Hoff materials. Math. Methods Appl. Sci. 8 (1986) 206-222
17. Girault V., and Raviart P.A. Finite Element Methods for Navier-Stokes Equations (1986), Springer-Verlag, Heidelberg
18. Gurtin M.E. The linear theory of elasticity. In: Flügge S., and Truesdell C. (Eds). Handbuch der Physik vol. VIa/2 (1972), Springer-Verlag, Berlin/New York 1-295
19. Kesavan S. On Poincaré's and J.L. Lions' lemmas. C. R. Acad. Sci. Paris, Ser. I 340 (2005) 27-30
20. Magenes E., and Stampacchia G. I problemi al contorno per le equazioni differenziali di tipo ellitico. Ann. Scuola Norm. Sup. Pisa 12 (1958) 247-358
21. Moreau J.J. Duality characterization of strain tensor distributions in an arbitrary open set. J. Math. Anal. Appl. 72 (1979) 760-770
22. k (Ω) et sur la coercivité des formes formellement positives. Equations aux Dérivées Partielles (1965), Presses de l'Université de Montréal, Montréal
23. Nečas J. Les Méthodes Directes en Théorie des Equations Elliptiques (1967), Masson, Paris
24. Opoka S., and Pietraszkiewicz W. Intrinsic equations for non-linear deformation and stability of thin elastic shells. Internat. J. Solids Structures 41 (2004) 3275-3292
25. Peetre J. Espaces d'interpolation et théorème de Soboleff. Ann. Institut Fourier 16 (1966) 279-317
26. L. Tartar, Topics in Nonlinear Analysis, Publications Mathématiques d'Orsay No. 78.13, Université Paris-Sud, 1978
27. Ting T.W. St. Venant's compatibility conditions. Tensor, N.S. 28 (1974) 5-12