Convergence of equilibria of thin elastic rods under physical growth conditions for the energy density
Elisa Davoli, Maria Giovanna Mora · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2012
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.