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