

Preprint 28/2008
Asymptotic models for curved rods derived from nonlinear elasticity by Gamma-convergence
Lucia Scardia
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Submission date: 31. Mar. 2008
Pages: 27
published in: Proceedings of the Royal Society of Edinburgh / A, 139 (2009) 5, p. 1037-1070
DOI number (of the published article): 10.1017/S0308210507000194
Bibtex
MSC-Numbers: 74K10, 49J45
Keywords and phrases: dimension reduction, curved beams, nonlinear elasticity
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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.