Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Dynamical equations for the finite elastic bending, torsion, and stretching of rods


Author: D. F. Parker
Journal: Quart. Appl. Math. 45 (1987), 533-548
MSC: Primary 73K05
DOI: https://doi.org/10.1090/qam/910460
MathSciNet review: 910460
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  • [1] J. L. Ericksen, Bending a prism to helical form, Arch. Rat. Mech. Anal. 66, 1-18 (1977) MR 0459169
  • [2] J. L. Ericksen, On the Foundations of St.-Venant's Problem, Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, Vol. 1, pp. 158-186, London, Pitman, 1977 MR 0495524
  • [3] J. L. Ericksen, Special Topics in Elastostatics, Adv. Appl. Mech., Vol. 17, New York, Academic, 1977, pp. 189-244
  • [4] D. F. Parker, The role of Saint-Venant's solutions in rod and beam theories, ASME J. Appl. Mech. 46, 861-866 (1979) MR 552384
  • [5] D. F. Parker, On the derivation of nonlinear rod theories from three dimensional elasticity, Z.A.M.P. 35, 833-947 (1984)
  • [6] A. E. Green and N. Laws, A general theory of rods, Proc. Roy. Soc. A 293, 145-155 (1966)
  • [7] J. L. Ericksen, Periodic solutions for elastic prisms, Quart. Appl. Math. 37, 443-446 (1980) MR 564735
  • [8] J. C. Alexander and S. S. Antman, The ambiguous twist of Love, Quart. Appl. Math. 40, 83-91, 1982 MR 652052
  • [9] A. E. H. Love, The Mathematical Theory of Elasticity, New York, Dover, 1944 MR 0010851
  • [10] G. E. Hay, The finite displacement of thin rods, Trans. Amer. Math. Soc. 51, 65-99 (1942) MR 0006318
  • [11] A. Rigolot, Sur une théorie asymptotique des poutres, Jnl. de Méc. 11, 673-703 (1972) MR 0368552
  • [12] A. Rigolot, Déplacements finis et petites déformations des poutres droites: Analyse asymptotique de la solution à grande distance des bases, Jnl. de Méc. Appl. 1, 175-206 (1977) MR 0459148
  • [13] D. F. Parker, An asymptotic analysis of large deflections and rotations of elastic rods, Internat. J. Solids Structs. 15, 361-377 (1979) MR 529189
  • [14] S. S. Antman, The Theory of Rods, Handbuch der Physik VIa/2, Springer-Verlag (1972)
  • [15] R. G. Muncaster, Invariant manifolds in mechanics I: The general construction of coarse theories from fine theories, Arch. Rat. Mech. Anal. 84, 353-373 (1983) MR 721190

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DOI: https://doi.org/10.1090/qam/910460
Article copyright: © Copyright 1987 American Mathematical Society

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