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

2010/10/04 by Elisa Davoli, Maria Giovanna Mora, Davoli, Elisa +1 · 1 citation
Mathematics · #74B20 #74G10 #74K10 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:74B20 #msc:74G10 #msc:74K10

paper · pdf · doi:10.48550/arxiv.1010.0492

arxiv created 2010/10/04 · arxiv updated 2010/10/05

Abstract

The subject of this paper is the study of 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 analogous of von Kármán plate theory for rods, and the linear theory.

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• Dimension reduction for time-dependent von Kármán rods

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