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    Marohnić, Maroje and Velčić, Igor 2016. Non-periodic homogenization of bending–torsion theory for inextensible rods from 3D elasticity. Annali di Matematica Pura ed Applicata (1923 -), Vol. 195, Issue. 4, p. 1055.


    Davoli, Elisa 2014. Quasistatic evolution models for thin plates arising as low energy Γ-limits of finite plasticity. Mathematical Models and Methods in Applied Sciences, Vol. 24, Issue. 10, p. 2085.


    Romero, I. Urrecha, M. and Cyron, C.J. 2014. A torsion-free non-linear beam model. International Journal of Non-Linear Mechanics, Vol. 58, p. 1.


    Davoli, Elisa and Mora, Maria Giovanna 2013. A quasistatic evolution model for perfectly plastic plates derived by Γ-convergence. Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Vol. 30, Issue. 4, p. 615.


    FREDDI, LORENZO MORA, MARIA GIOVANNA and PARONI, ROBERTO 2013. NONLINEAR THIN-WALLED BEAMS WITH A RECTANGULAR CROSS-SECTION — PART II. Mathematical Models and Methods in Applied Sciences, Vol. 23, Issue. 04, p. 743.


    Bîrsan, M. Altenbach, H. Sadowski, T. Eremeyev, V.A. and Pietras, D. 2012. Deformation analysis of functionally graded beams by the direct approach. Composites Part B: Engineering, Vol. 43, Issue. 3, p. 1315.


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    Neukamm, Stefan 2012. Rigorous Derivation of a Homogenized Bending-Torsion Theory for Inextensible Rods from Three-Dimensional Elasticity. Archive for Rational Mechanics and Analysis, Vol. 206, Issue. 2, p. 645.


    Velčić, Igor 2012. Nonlinear Weakly Curved Rod by Γ-Convergence. Journal of Elasticity, Vol. 108, Issue. 2, p. 125.


    Gaudiello, Antonio and Zappale, Elvira 2011. A Model of Joined Beams as Limit of a 2D Plate. Journal of Elasticity, Vol. 103, Issue. 2, p. 205.


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  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 139, Issue 5
  • October 2009, pp. 1037-1070

Asymptotic models for curved rods derived from nonlinear elasticity by Γ-convergence

  • Lucia Scardia (a1)
  • DOI: http://dx.doi.org/10.1017/S0308210507000194
  • Published online: 01 September 2009
Abstract

We study the problem of the rigorous derivation of one-dimensional models for a thin curved beam starting from three-dimensional nonlinear elasticity. We describe the limiting models obtained for different scalings of the energy. In particular, we prove that the limit functional corresponding to higher scalings coincides with the one derived by dimension reduction starting from linearized elasticity.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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