Dynamics of linear anisotropic rods

We obtain a one-dimensional model for the dynamics of a rod-like body as an exact consequence of three-dimensional linear anisotropic elasticity, by means of the internal constraint of indeformability of the cross-section in its plane. The model takes into account flexure, extension, torsion and warping deformations, which are coupled due to the anisotropy; if we assume that the symmetry group of the material comprising the rod contains the reflections upon the cross-section, the one-dimensional equations of motion split into three independent groups concerned, respectively, with extension, flexure and torsion-warping deformations. This result generalizes the equations obtained by Green et al. [(1967) Arch. Rational Mech. Analys. 25, 285-298] and those originally proposed by Timoshenko [(1921) Philos. Mag. 43, 125-131] and Vlasov [(1961) Thin-walled Elastic Beams. Israel Program for Scientific Translation, Tel Aviv] in the isotropic case.