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Journal of Elasticity

, Volume 76, Issue 1, pp 45–66 | Cite as

Thin-Walled Beams: the Case of the Rectangular Cross-Section

  • Lorenzo Freddi
  • Antonino Morassi
  • Roberto Paroni
Article

Abstract

In this paper we present an asymptotic analysis of the three-dimensional problem for a thin linearly elastic cantilever Ωɛɛ×(0,l) with rectangular cross-section ωɛ of sides ɛ and ɛ2, as ɛ goes to zero. Under suitable assumptions on the given loads, we show that the three-dimensional problem converges in a variational sense to the classical one-dimensional model for extension, flexure and torsion of thin-walled beams.

Keywords

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

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Copyright information

© Springer 2005

Authors and Affiliations

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

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