Junction of a periodic family of elastic rods with a 3d plate. Part I

Journal des Mathematiques Pures et Appliquees

Volumn 88, Issue 1, 2007, Pages 1-33

  Blanchard, Dominique ^a,b   Gaudiello, Antonio ^c   Griso, Georges ^b  

^a UNIVERSITÉ DE ROUEN   (France)

^b SORBONNE UNIVERSITÉ   (France)

^c UNIVERSITY OF CASSINO AND SOUTHERN LAZIO   (Italy)

Author keywords

Linear elasticity; Rods; Rough boundary

Indexed keywords

EID: 34347237621     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2007.04.005     Document Type: Article

References (30)

1. Acerbi E., Buttazzo G., and Percivale D. A variational definition of the strain energy for an elastic string. J. Elasticity 25 (1991) 137-148
2. Amirat Y., Bodart O., De Maio U., and Gaudiello A. Asymptotic approximation of the solution of the Laplace equation in a domain with highly oscillating boundary. SIAM J. Math. Anal. 35 6 (2004) 1598-1616
3. Baffico L., and Conca C. Homogenization of a transmission problem in solid mechanics. J. Math. Anal. Appl. 233 2 (1999) 659-680
4. Blanchard D., Carbone L., and Gaudiello A. Homogenization of a monotone problem in a domain with oscillating boundary. M2AN Math. Model. Numer. Anal. 33 5 (1999) 1057-1070
5. D. Blanchard, A. Gaudiello, G. Griso, Junction of a periodic family of elastic rods with a 3d plate. Part II, J. Math. Pures Appl., in press
6. Brizzi R., and Chalot J.P. Boundary homogenization and Neumann boundary value problem. Ricerche Mat. 46 2 (1997) 341-387
7. Casado Diaz J., and Luna Laynez M. Homogenization of the anisotropic heterogeneous linearized elasticity system in thin reticulated structures. Proc. Royal Soc. Edinburgh 134A (2004) 1041-1083
8. Ciarlet P.G. Mathematical Elasticity, vol. 1: Three-Dimensional Elasticity (1988), North-Holland, Amsterdam
9. Cioranescu D., Damlamian A., and De Arcangelis R. Homogenization of quasiconvex integrals via the periodic unfolding method. SIAM J. Math. Anal. 37 5 (2006) 1435-1453
10. Cioranescu D., Damlamian A., and Griso G. Periodic unfolding and homogenization. C. R. Acad. Sci. Paris Sér. I Math. 335 (2002) 99-104
11. Cioranescu D., and Saint Jean Paulin J. Homogenization of Reticulated Structures. Applied Mathematical Sciences vol. 136 (1999), Springer-Verlag, New York
12. Corbo Esposito A., Donato P., Gaudiello A., and Picard C. Homogenization of the p-Laplacian in a domain with oscillating boundary. Comm. Appl. Nonlinear Anal. 4 4 (1997) 1-23
13. Damlamian A. An elementary introduction to periodic unfolding. GAKUTO Internat. Ser. Math. Sci. Appl. 24 (2005) 119-136
14. De Maio U., Gaudiello A., and Lefter C. Optimal control for a parabolic problem in a domain with highly oscillating boundary. Appl. Anal. 83 12 (2004) 1245-1264
15. Gaudiello A. Asymptotic behaviour of non-homogeneous Neumann problems in domains with oscillating boundary. Ricerche Mat. 43 2 (1994) 239-292
16. Gaudiello A. Homogenization of an elliptic transmission problem. Adv. Math. Sci. Appl. 5 2 (1995) 639-657
17. Griso G. Comportement asymptotique d'une grue. C. R. Acad. Sci. Paris Sér. I Math. 338 (2004) 261-266
18. Griso G. Décomposition des déplacements d'une poutre : simplification d'une problème d'élasticité. C. R. Acad. Sci. Paris Mecanique 333 (2005) 475-480
19. Griso G. Asymptotic behavior of curved rods by the unfolding method. Mod. Meth. Appl. Sci. 27 2004 (2005) 2081-2110
20. Keller J.B., and Nevard J. Homogenization of rough boundary and interfaces. SIAM J. Appl. Math. 57 6 (1997) 1660-1686
21. Kozlov V.A., Ma'zya V.G., and Movchan A.B. Asymptotic Analysis of Fields in a Multi-Structure. Oxford Mathematical Monographs (1999), Oxford Science Publications, The Clarendon Press, Oxford University Press, New York
22. Le Dret H. Problèmes variationnels dans les multi-domaines : modélisation des jonctions et applications. Res. Appl. Math. vol. 19 (1991), Masson, Paris
23. Le Dret H. Convergence of displacements and stresses in linearly elastic slender rods as the thickness goes to zero. Asymptot. Anal. 10 (1995) 367-402
24. Maz'ya V.G., Nazarov S.A., and Plamenevskii B.A. Asymptotic Behavior of Solution of Elliptic Boundary Value Problems under Singular Perturbations of the Domain (1981), Tbilis. Gos. Univ., Inst. Prikl. Mat., Tbilisi
25. Mel'nyk T.A. Homogenization of the Poisson equations in a thick periodic junction. Z. Anal. Anwendungen 18 4 (1999) 953-975
26. Mora M.G., and Muller S. A nonlinear model for inextensible rods as a low energy Γ-limit of three-dimensional nonlinear elasticity. Ann. Inst. H. Poincaré - AN 21 (2004) 271-293
27. Murat F., and Sili A. Comportement asymptotique des solutions du système de l'élasticité linéarisée anisotrope hétérogène dans des cylindres minces. C. R. Acad. Sci. Paris Sér. I Math. 328 (1999) 179-184
28. Percivale D. Thin elastic beams: the variational approach to St. Venant's problem. Asymptot. Anal. 20 (1999) 39-60
29. Tartar L. Cours Peccot, Collège de France (March 1977). Partially written in: F. Murat, H-Convergence, Séminaire d'analyse fonctionnelle et numérique de l'Université d'Alger (1977-78). English translation. In: Cherkaev A., and Kohn R.V. (Eds). Mathematical Modelling of Composite Materials. Progress in Nonlinear Differential Equations and their Applications (1997), Birkhäuser-Verlag 21-44
30. Trabucho L., and Viano J.M. Mathematical Modelling of Rods. Hand-book of Numerical Analysis vol. 4 (1996), North-Holland, Amsterdam