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

Published online by Cambridge University Press:  21 September 2009

Lucia Scardia
Lucia Scardia
Affiliation:
SISSA, Via Beirut 2–4, 34014 Trieste, Italy ([email protected])
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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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 5 , October 2009 , pp. 1037 - 1070
Copyright
Copyright © Royal Society of Edinburgh 2009

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