A further work on directed rods

Journal of Elasticity - Tập 28 - Trang 123-142 - 1992
H. Cohen1, Q. -X. Sun
1Department of Applied Mathematics, University of Manitoba, Winnipeg, Canada

Tóm tắt

In this paper, we discuss the field equations of a rod with three deformable directors. We then deal with the rod subjected to internal constraints. Finally, we compare the theory of the constrained directed rod with that of an unconstrained rod with two deformable directors and with that of Cosserat rods.

Tài liệu tham khảo

J.L. Ericksen and C. Truesdell, Exact theory of stress and strain in rods and shells.Arch. Rat. Mech. Anal. 1 (1958) 295–323. H. Cohen, A non-linear theory of elastic directed curves.Int. J. Engg. Sci. 4 (1966) 511–524. C.N. DeSilva and A.B. Whitman, Thermodynamical theory of directed rods.J. Math. Phys. 12 (1971) 1603–1609. A.E. Green, P.M. Naghdi and M.L. Wenner, On the theory of rods II. Developments by direct approach.Roy. Soc. London A. 337 (1974) 485–507. S.S. Antman, The theory of rods. In: C. Truesdell (ed.),Handbuch der Physik VIa/2. Berlin: Springer Verlag (1972), pp. 641–703. P.M. Naghdi, Finite deformation of elastic rods and shells. In: D.E. Carlson and R.T. Shield (eds.),Proc. IUTAM Symp.-Finite Elasticity (Bethlehem, PA 1980). The Hague, Netherlands: Martinus Nijhoff Pub. (1982), pp. 47–103 G. Capriz, A contribution to the theory of rods.Riv. Mat. Univ. Parma 7 (1981) 489–506. G. Capriz and P. Podio-Guidugli, Formal structure and classification of theories of oriented materials.Annali Matematica pura et applicate (IV) CXV (1977) 17–39. H. Cohen and R.G. Muncaster,The Theory of Pseudo-Rigid Bodies. Berlin: Springer Verlag (1988). C. Truesdell,A First Course in Rational Continuum Mechanics 1. New York: Academic Press (1977). P.M. Naghdi and M.B. Rubin, Constrained theories of rods.J. Elasticity 14 (1984) 343–361. G. Capriz, Continua with latent microstructure.Arch. Rat. Mech. Anal. 90 (1985) 43–56. A.B. Whitman and C.N. DeSilva, A dynamic theory of elastic directed curves.J. Appl. Math. Phy. (ZAMP) 20 (1969) 200–212.