Dynamics of linear anisotropic rods

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 accountflexure, extension, torsion and warping deformations, which are coupled due to the anisotropy ; if we assume that the sLv, .m... m~e~tr.~ v_ , _n~ro u.n~ ro _f~ t he material comprisin~e~ ~t.h~e ro~d. con~t~ai~ns.~ ~th~.e.~ ~r~e. f l~e~ct~io~n~s ..u~~nr~o_n ~ the cross-section, the one-dimensional equations of motion split into three independent groups concerned, respectively, with extension, fiexure and torsion-warpin,q deformations. This result generalizes the equations obtained by Green et al. [(1967) Arch. Ra&nal Mech. Analys. 25, 285-2981 and those originally proposed by Timoshenko [(1921) Phiios. Mug. 43, 125-1311 and Vlasov [(1961) Thin-walled Elastic Beams. Israel Program for Scientific Translation, Tel Aviv] in the isotropic case.