Skip to main content

Mathematical Justifications of Plate Models

  • Living reference work entry
  • First Online:
Book cover Encyclopedia of Continuum Mechanics
  • 251 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

References

  • Anzellotti G, Baldo S, Percivale D (1994) Dimension reduction in variational problems, asymptotic developments in Γ-convergence and thin structures in elasticity. Asymptot Anal 9:61–100

    MathSciNet  MATH  Google Scholar 

  • Bourquin F, Ciarlet PG, Geymonat G, Raoult A (1992) Γ-convergence et analyse asymptotique des plaques minces, Comptes rendus de l’Acadžmie des sciences. Sžrie 1, Mathžmatique 315(9):1017–1024

    MATH  Google Scholar 

  • Ciarlet PG, Destuynder P (1979a) A justification of the two-dimensional linear plate model. J Mécanique 18:315–344

    MathSciNet  MATH  Google Scholar 

  • Ciarlet PG, Destuynder P (1979b) A justification of a nonlinear model in plate theory. Comput Methods Appl Mech Eng 17/18:227–258

    Article  MATH  Google Scholar 

  • Figueiredo IN, Trabucho L (1992) A Galerkin approximation for linear elastic shallow shells. Comput Mech 10(2):107–119

    Article  MathSciNet  MATH  Google Scholar 

  • Fox DD, Raoult A, Simo JC (1993) A justification of nonlinear properly invariant plate theories. Arch Ration Mech Anal 124:157–199

    Article  MathSciNet  MATH  Google Scholar 

  • Lods V, Miara B (1998) Nonlinearly elastic shell models: a formal asymptotic approach II. The flexural model. Arch Ration Mech Anal 142:355–374

    Article  MathSciNet  MATH  Google Scholar 

  • Miara B (1989) Optimal spectral approximation in linearized plate theory. Appl Anal 87:291–307

    Article  MathSciNet  MATH  Google Scholar 

  • Miara B (1994) Justification of the asymptotic analysis of elastic plates, II. The non-linear case. Asymptot Anal 9:119–134

    MathSciNet  MATH  Google Scholar 

  • Miara B, Trabucho L (1992) A Galerkin spectral approximation in linearized beam theory. ESAIM Math Model Numer Anal 26(3):425–446

    Article  MathSciNet  MATH  Google Scholar 

  • Mielke A (1995) On the justification of plate theories in linear elasticity theory using exponential decay estimates. J Elast 38(2):165–208

    Article  MathSciNet  MATH  Google Scholar 

  • Paroni R, Tomassetti G, Podio-Guidugli P (2007) A justification of the Reissner-Mindlin plate theory through variational convergence. Anal Appl 5(2):165–182

    Article  MathSciNet  MATH  Google Scholar 

  • Paumier J-C (1991) Existence and convergence of the expansion in the asymptotic theory of elastic thin plates. Math Model Numer Anal 25(3):371–391

    Article  MathSciNet  MATH  Google Scholar 

  • Schwab C (1993) The Fourier approach to the asymptotic analysis of plate models. Mathematics Research Report, pp 93–04. University of Maryland in Baltimore Country

    Google Scholar 

  • Trabucho L, Viano JM (1996) Mathematical modelling of rods. In: Handbook of numerical analysis, vol 4. North-Holland, Amsterdam. MR 1422507 — Zbl 0873.7304

    Google Scholar 

  • Veiga MF (1994) A Galerkin approximation for homogeneous anisotropic elastic beams. Appl Anal 53(1): 67–84

    Article  MathSciNet  MATH  Google Scholar 

  • Vogelius M, Babuska I (1981) On a dimensional reduction method. The optimal selection of basis functions. Math Comput 37(155):31–46

    MathSciNet  MATH  Google Scholar 

  • Xiao LM (1998) Asymptotic analysis of dynamic problems for linearly elastic shell justification of equation for dynamic membrane shell. Asymptot Anal 17:121–134

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bernadette Miara .

Editor information

Editors and Affiliations

Section Editor information

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer-Verlag GmbH Germany

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Miara, B. (2018). Mathematical Justifications of Plate Models. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_138-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-53605-6_138-1

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics