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Advances in Calculus of Variations

Managing Editor: Duzaar, Frank / Kinnunen, Juha

Editorial Board: Armstrong, Scott N. / Balogh, Zoltán / Cardiliaguet, Pierre / Dacorogna, Bernard / Dal Maso, Gianni / DiBenedetto, Emmanuele / Fonseca, Irene / Gianazza, Ugo / Ishii, Hitoshi / Kristensen, Jan / Manfredi, Juan / Martell, Jose Maria / Mingione, Giuseppe / Nystrom, Kaj / Riviére, Tristan / Schaetzle, Reiner / Shen, Zhongwei / Silvestre, Luis / Tonegawa, Yoshihiro / Touzi, Nizar / Wang, Guofang

IMPACT FACTOR 2017: 1.676

CiteScore 2017: 1.30

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Source Normalized Impact per Paper (SNIP) 2017: 1.138

Mathematical Citation Quotient (MCQ) 2017: 1.15

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Volume 6, Issue 1


Thin-walled beams with a cross-section of arbitrary geometry: Derivation of linear theories starting from 3D nonlinear elasticity

Elisa Davoli
Published Online: 2013-01-03 | DOI: https://doi.org/10.1515/acv-2011-0003


The subject of this paper is the rigorous derivation of lower dimensional models for a nonlinearly elastic thin-walled beam whose cross-section is given by a thin tubular neighbourhood of a smooth curve. Denoting by h and , respectively, the diameter and the thickness of the cross-section, we analyse the case where the scaling factor of the elastic energy is of order , with . Different linearized models are deduced according to the relative order of magnitude of with respect to h.

Keywords: Thin-walled beams; nonlinear elasticity; Γ-convergence; dimension reduction

About the article

Received: 2011-06-30

Accepted: 2011-11-28

Published Online: 2013-01-03

Published in Print: 2013-01-01

Citation Information: , Volume 6, Issue 1, Pages 33–91, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2011-0003.

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