Free access
Issue
ESAIM: COCV
Volume 13, Number 3, July-September 2007
Page(s) 419 - 457
DOI http://dx.doi.org/10.1051/cocv:2007036
Published online 26 July 2007
  1. E. Acerbi, G. Buttazzo and D. Percivale, A variational definition of the strain energy for an elastic string. J. Elasticity 25 (1991) 137–148. [CrossRef] [MathSciNet]
  2. D.R. Adams and L.I. Hedberg, Fonctions Spaces and Potential Theory. Springer Verlag, Berlin (1996).
  3. G. Anzellotti, S. Baldo and D. Percivale, Dimension reduction in variational problems, asymptotic development in Formula -convergence and thin structures in elasticity. Asymptot. Anal. 9 (1994) 61–100.
  4. D. Caillerie, Thin elastic and periodic plates. Math. Methods Appl. Sci. 6 (1984) 159–191. [CrossRef] [MathSciNet]
  5. P.G. Ciarlet, Plates and Junctions in Elastic Multi-Structures: An Asymptotic Analysis. Masson, Paris (1990).
  6. P.G. Ciarlet, Mathematical Elasticity, Volume II: Theory of Plates. North-Holland, Amsterdam (1997).
  7. P.G. Ciarlet and P. Destuynder, A justification of the two-dimensional linear plate model. J. Mécanique 18 (1979) 315–344.
  8. A. Cimetière, G. Geymonat, H. Le Dret, A. Raoult, Z. Tutek, Asymptotic theory and analysis for displacements and stress distribution in nonlinear elastic straight slender rods. J. Elasticity 19 (1988) 111–161. [CrossRef] [MathSciNet]
  9. D. Cioranescu and J. Saint Jean Paulin, Homogenization of Reticulated Structures. Springer-Verlag, New York (1999).
  10. M. Dauge and I. Gruais, Asymptotics of arbitrary order for a thin elastic clamped plate, I: Optimal error estimates. Asymptot. Anal. 13 (1996) 167–197.
  11. G. Friesecke, R.D. James and S. Müller, A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity. Comm. Pure Appl. Math. 55 (2002) 1461–1506. [CrossRef] [MathSciNet]
  12. G. Friesecke, R.D. James and S. Müller, A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence. Arch. Rat. Mech. Anal. 180 (2006) 183–236. [CrossRef] [MathSciNet]
  13. A. Gaudiello, B. Gustafsson, C. Lefter and J. Mossino, Asymptotic analysis of a class of minimization problems in a thin multidomain. Calc. Var. Part. Diff. Eq. 15 (2002) 181–201. [CrossRef]
  14. A. Gaudiello, B. Gustafsson, C. Lefter and J. Mossino, Asymptotic analysis for monotone quasilinear problems in thin multidomains. Diff. Int. Eq. 15 (2002) 623–640.
  15. A. Gaudiello, R. Monneau, J. Mossino, F. Murat and A. Sili, On the junction of elastic plates and beams. C.R. Acad. Sci. Paris Sér. I 335 (2002) 717–722.
  16. A. Gaudiello and E. Zappale, Junction in a thin multidomain for a fourth order problem. M3AS: Math. Models Methods Appl. Sci. 16 (2006) 1887–1918. [CrossRef]
  17. I. Gruais, Modélisation de la jonction entre une plaque et une poutre en élasticité linéarisée. RAIRO: Modél. Math. Anal. Numér. 27 (1993) 77–105. [MathSciNet]
  18. I. Gruais, Modeling of the junction between a plate and a rod in nonlinear elasticity. Asymptotic Anal. 7 (1993) 179–194. [MathSciNet]
  19. V.A. Kozlov, V.G. Ma'zya and A.B. Movchan, Asymptotic representation of elastic fields in a multi-structure. Asymptot. Anal. 11 (1995) 343–415.
  20. H. Le Dret, Problèmes Variationnels dans les Multi-domaines: Modélisation des Jonctions et Applications. Masson, Paris (1991).
  21. H. Le Dret, Convergence of displacements and stresses in linearly elastic slender rods as the thickness goes to zero. Asymptot. Anal. 10 (1995) 367–402.
  22. H. Le Dret and A. Raoult, The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity. J. Math. Pures Appl. 74 (1995) 549–578. [MathSciNet]
  23. H. Le Dret and A. Raoult, The membrane shell model in nonlinear elasticity: a variational asymptotic derivation. J. Nonlinear Sci. 6 (1996) 59–84. [CrossRef] [MathSciNet]
  24. R. Monneau, F. Murat and A. Sili, Error estimate for the transition 3d-1d in anisotropic heterogeneous linearized elasticity. To appear.
  25. M.G. Mora and S. Müller, Derivation of the nonlinear bending-torsion theory for inextensible rods by Formula -convergence. Calc. Var. Part. Diff. Eq. 18 (2003) 287–305. [CrossRef]
  26. M.G. Mora and S. Müller, A nonlinear model for inextensible rods as a low energy Formula -limit of three-dimensional nonlinear elasticity. Ann. Inst. H. Poincaré Anal. Non Linéaire 21 (2004) 271–293. [CrossRef] [MathSciNet]
  27. F. Murat and A. Sili, Comportement asymptotique des solutions du sytème de l'élasticité linéarisée anisotrope hétérogène dans des cylindres minces. C.R. Acad. Sci. Paris Sér. I 328 (1999) 179–184.
  28. F. Murat and A. Sili, Anisotropic, heterogeneous, linearized elasticity problems in thin cylinders. To appear.
  29. O.A. Oleinik, A.S. Shamaev and G.A. Yosifian, Mathematical Problems in Elasticity and Homogenization. North-Holland, Amsterdam (1992).
  30. D. Percivale, Thin elastic beams: the variational approach to St. Venant's problem. Asymptot. Anal. 20 (1999) 39–60. [MathSciNet]
  31. L. Trabucho and J.M. Viano, Mathematical Modelling of Rods, Handbook of Numerical Analysis 4. North-Holland, Amsterdam (1996).