Free access
Issue
ESAIM: COCV
Volume 17, Number 2, April-June 2011
Page(s) 493 - 505
DOI http://dx.doi.org/10.1051/cocv/2010002
Published online 24 March 2010
  1. J.M. Ball, Some open problems in elasticity, in Geometry, mechanics, and dynamics, Springer, New York, USA (2002) 3–59.
  2. P.G. Ciarlet, Mathematical Elasticity, Vol. 3: Theory of Shells. North-Holland, Amsterdam (2000).
  3. G. Dal Maso, An introduction to Γ-convergence, Progress in Nonlinear Differential Equations and their Applications 8. Birkhäuser, USA (1993).
  4. G. Friesecke, R. 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]
  5. G. Friesecke, R. James and S. Müller, A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence. Arch. Ration. Mech. Anal. 180 (2006) 183–236. [CrossRef] [MathSciNet]
  6. H. LeDret and A. Raoult, The nonlinear membrane model as a variational limit of nonlinear three-dimensional elasticity. J. Math. Pures Appl. 73 (1995) 549–578.
  7. M. Lewicka and M. Pakzad, The infinite hierarchy of elastic shell models: some recent results and a conjecture. Preprint (2009) http://arxiv.org/abs/0907.1585.
  8. M. Lewicka, M.G. Mora and M.R. Pakzad, The matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells. Preprint (2008) http://arxiv.org/abs/0811.2238.
  9. M. Lewicka, M.G. Mora and M.R. Pakzad, A nonlinear theory for shells with slowly varying thickness. C. R. Acad. Sci. Paris, Sér. I 347 (2009) 211–216.
  10. M. Lewicka, M.G. Mora and M.R. Pakzad, Shell theories arising as low energy Γ-limit of 3d nonlinear elasticity. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (to appear).
  11. A.E.H. Love, A treatise on the mathematical theory of elasticity. 4th Edn., Cambridge University Press, Cambridge, UK (1927).
  12. M.G. Mora and S. Müller, Convergence of equilibria of three-dimensional thin elastic beams. Proc. Roy. Soc. Edinburgh Sect. A 138 (2008) 873–896. [MathSciNet]
  13. M.G. Mora and L. Scardia, Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density. Preprint (2008).
  14. M.G. Mora, S. Müller and M.G. Schultz, Convergence of equilibria of planar thin elastic beams. Indiana Univ. Math. J. 56 (2007) 2413–2438. [CrossRef] [MathSciNet]
  15. S. Müller and M.R. Pakzad, Convergence of equilibria of thin elastic plates – the von Kármán case. Comm. Part. Differ. Equ. 33 (2008) 1018–1032. [CrossRef]
  16. M. Spivak, A Comprehensive Introduction to Differential Geometry, Vol. V. Second Edn., Publish or Perish Inc., Australia (1979).
  17. T. von Kármán, Festigkeitsprobleme im Maschinenbau, in Encyclopädie der Mathematischen Wissenschaften IV. B.G. Teubner, Leipzig, Germany (1910) 311–385.