Journal of Elasticity

, Volume 86, Issue 3, pp 263–296 | Cite as

Thin-walled Beams: A Derivation of Vlassov Theory via Γ-Convergence



This paper deals with the asymptotic analysis of the three-dimensional problem for a linearly elastic cantilever having an open cross-section which is the union of rectangles with sides of order ε and ε 2, as ε goes to zero. Under suitable assumptions on the given loads and for homogeneous and isotropic material, we show that the three-dimensional problem Γ-converges to the classical one-dimensional Vlassov model for thin-walled beams.

Key words

thin-walled cross-section beams linear elasticity Γ-convergence dimension reduction 

Mathematics Subject Classifications (2000)

74K20 74B10 49J45 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Lorenzo Freddi
    • 1
  • Antonino Morassi
    • 2
  • Roberto Paroni
    • 3
  1. 1.Dipartimento di Matematica e InformaticaUniversità di UdineUdineItaly
  2. 2.Dipartimento di Georisorse e TerritorioUniversità di UdineUdineItaly
  3. 3.Dipartimento di Architettura e PianificazioneUniversità degli Studi di SassariAlgheroItaly

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