Skip to main content

On the Variational Derivation of the Kinematics for Thin-Walled Closed Section Beams

  • Conference paper
IUTAM Symposium on Relations of Shell Plate Beam and 3D Models

Part of the book series: IUTAM Bookseries ((IUTAMBOOK,volume 9))

  • 533 Accesses

Abstract

The kinematics of thin-walled closed cross section beams is studied by comparing the behavior of a closed section with an open section which differs from the former by a “cut” on one side.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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.

    MATH  MathSciNet  Google Scholar 

  2. G. Anzellotti, S. Baldo, and D. Percivale, Dimension reduction in variational problems, asymptotic development in Γ-convergence and thin structures in elasticity, Asymptot. Anal. 9(1) (1994), 61–100.

    MATH  MathSciNet  Google Scholar 

  3. F. Bourquin, P.G. Ciarlet, G. Geymonat, and A. Raoult, Gamma-convergence et analyse asymptotique des plaques minces, C.R. Acad. Sci. Paris, t. 315, Sćrie I, (1992), 1017–1024.

    MATH  MathSciNet  Google Scholar 

  4. A. Braides, Γ-convergence for beginners, Oxford Lecture Series in Mathematics and its Applications, 22. Oxford University Press, Oxford, 2002.

    Google Scholar 

  5. G. Dal Maso, An introduction to Γ-convergence, Birkhäuser, Boston, 1993.

    Google Scholar 

  6. E. De Giorgi and T. Franzoni, Su un tipo di convergenza variazionale, Rend. Sem. Mat. Brescia 3 (1979), 63–101.

    Google Scholar 

  7. L. Freddi, A. Morassi, and R. Paroni, Thin-walled beams: the case of the rectangular cross-section, J. Elasticity 76 (2004), 45–66.

    Article  MATH  MathSciNet  Google Scholar 

  8. L. Freddi, A. Morassi and R. Paroni, Thin-walled beams: a derivation of Vlassov theory via Γ–convergence, J. Elasticity 86 (2007), 263–296.

    Article  MATH  MathSciNet  Google Scholar 

  9. 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.

    MATH  MathSciNet  Google Scholar 

  10. M.G. Mora and S. Müller, A nonlinear model for inextensible rods as a low energy Γ-limit of three-dimensional nonlinear elasticity, Ann. I. H. Poincaré, 21, (2004), 271–293.

    Article  MATH  Google Scholar 

  11. A. Morassi, Torsion of thin tubes: a justification of some classical results, J. Elasticity 39 (1995), 213–227.

    Article  MATH  MathSciNet  Google Scholar 

  12. A. Morassi, Torsion of thin tubes with multicell cross-section, Meccanica 34 (1999), 115–132.

    Article  MATH  MathSciNet  Google Scholar 

  13. A. Morassi, An asymptotic analysis of the flexure problem for thin tubes, Math. Mech. Solids 4 (1999), 357–390.

    Article  MATH  MathSciNet  Google Scholar 

  14. D. Percivale, Thin elastic beams: the variational approach to St. Venant’s problem, Asymptot. Anal. 20 (1999), 39–59.

    MATH  MathSciNet  Google Scholar 

  15. J.M. Rodríguez and J.M. Viaño, Asymptotic derivation of a general linear model for thin-walled elastic rods, Comput. Methods Appl. Mech. Engrg. 147 (1997), 287–321.

    Article  MATH  MathSciNet  Google Scholar 

  16. J.M. Rodríguez and J.M. Viaño, Asymptotic analysis of Poisson’s equation in a thin domain and its application to thin-walled elastic beams and tubes, Math. Methods Appl. Sci. 21 (1998), 187–226.

    Article  MATH  MathSciNet  Google Scholar 

  17. B.Z. Vlassov, Pièces Longues en Voiles Minces, Éditions Eyrolles, Paris, 1962.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer Science+Business Media B.V.

About this paper

Cite this paper

Freddi, L., Morassi, A., Paroni, R. (2008). On the Variational Derivation of the Kinematics for Thin-Walled Closed Section Beams. In: Jaiani, G., Podio-Guidugli, P. (eds) IUTAM Symposium on Relations of Shell Plate Beam and 3D Models. IUTAM Bookseries, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8774-5_9

Download citation

  • DOI: https://doi.org/10.1007/978-1-4020-8774-5_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-8773-8

  • Online ISBN: 978-1-4020-8774-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics