Inserted: 5 oct 2010
Last Updated: 9 jul 2012
Journal: Proc. Roy. Soc. Edinburgh Sect. A
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.
Keywords: nonlinear elasticity, equilibrium configurations, stationary points, rod theories