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Convergence of equilibria of thin elastic rods under physical growth conditions for the energy density

Published online by Cambridge University Press:  07 June 2012

Elisa Davoli  and
Maria Giovanna Mora
Elisa Davoli
Affiliation:
Scuola Internazionale Superiore di Studi Avanzati, via Bonomea 265, 34136 Trieste, Italy (davoli@sissa.it; mora@sissa.it)
Maria Giovanna Mora
Affiliation:
Scuola Internazionale Superiore di Studi Avanzati, via Bonomea 265, 34136 Trieste, Italy (davoli@sissa.it; mora@sissa.it)
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Abstract

We study the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod as the diameter of the cross-section tends to zero. Convergence results are established assuming physical growth conditions for the elastic energy density and suitable scalings of the applied loads that correspond at the limit to different rod models: the constrained linear theory, the analogue of the von Kármán plate theory for rods, and the linear theory.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 3 , June 2012 , pp. 501 - 524
Copyright
Copyright © Royal Society of Edinburgh 2012

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