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
Full-text PDF Free Access
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Additional Information
- J. L. Ericksen, Bending a prism to helical form, Arch. Rational. Mech. Anal. 66 (1977), no. 1, 1–18. MR 0459169, DOI https://doi.org/10.1007/BF00250848
- J. L. Ericksen, On the formulation of St.-Venant’s problem, Nonlinear analysis and mechanics: Heriot-Watt Symposium (Edinburgh, 1976), Vol. I, Pitman, London, 1977, pp. 158–186. Res. Notes in Math., No. 17. MR 0495524
J. L. Ericksen, Special Topics in Elastostatics, Adv. Appl. Mech., Vol. 17, New York, Academic, 1977, pp. 189–244
- D. F. Parker, The role of Saint-Venant’s solutions in rod and beam theories, Trans. ASME Ser. E. J. Appl. Mech. 46 (1979), no. 4, 861–866. MR 552384
D. F. Parker, On the derivation of nonlinear rod theories from three dimensional elasticity, Z.A.M.P. 35, 833–947 (1984)
A. E. Green and N. Laws, A general theory of rods, Proc. Roy. Soc. A 293, 145–155 (1966)
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- J. C. Alexander and Stuart S. Antman, The ambiguous twist of Love, Quart. Appl. Math. 40 (1982/83), no. 1, 83–92. MR 652052, DOI https://doi.org/10.1090/S0033-569X-1982-0652052-8
- A. E. H. Love, A treatise on the Mathematical Theory of Elasticity, Dover Publications, New York, 1944. Fourth Ed. MR 0010851
- G. E. Hay, The finite displacement of thin rods, Trans. Amer. Math. Soc. 51 (1942), 65–102. MR 6318, DOI https://doi.org/10.1090/S0002-9947-1942-0006318-7
- Alain Rigolot, Sur une théorie asymptotique des poutres, J. Mécanique 11 (1972), 673–703 (French, with English summary). MR 368552
- Alain Rigolot, Déplacements finis et petites déformations des poutres droites: analyse asymptotique de la solution à grande distance des bases, J. Méc. Appl. 1 (1977), no. 2, 175–206 (French, with English summary). MR 459148
- D. F. Parker, An asymptotic analysis of large deflections and rotations of elastic rods, Internat. J. Solids Structures 15 (1979), no. 5, 361–377. MR 529189, DOI https://doi.org/10.1016/0020-7683%2879%2990059-3
S. S. Antman, The Theory of Rods, Handbuch der Physik VIa/2, Springer-Verlag (1972)
- R. G. Muncaster, Invariant manifolds in mechanics. I. The general construction of coarse theories from fine theories, Arch. Rational Mech. Anal. 84 (1983/84), no. 4, 353–373. MR 721190, DOI https://doi.org/10.1007/BF00250587
J. L. Ericksen, Bending a prism to helical form, Arch. Rat. Mech. Anal. 66, 1–18 (1977)
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
J. L. Ericksen, Special Topics in Elastostatics, Adv. Appl. Mech., Vol. 17, New York, Academic, 1977, pp. 189–244
D. F. Parker, The role of Saint-Venant’s solutions in rod and beam theories, ASME J. Appl. Mech. 46, 861–866 (1979)
D. F. Parker, On the derivation of nonlinear rod theories from three dimensional elasticity, Z.A.M.P. 35, 833–947 (1984)
A. E. Green and N. Laws, A general theory of rods, Proc. Roy. Soc. A 293, 145–155 (1966)
J. L. Ericksen, Periodic solutions for elastic prisms, Quart. Appl. Math. 37, 443–446 (1980)
J. C. Alexander and S. S. Antman, The ambiguous twist of Love, Quart. Appl. Math. 40, 83–91, 1982
A. E. H. Love, The Mathematical Theory of Elasticity, New York, Dover, 1944
G. E. Hay, The finite displacement of thin rods, Trans. Amer. Math. Soc. 51, 65–99 (1942)
A. Rigolot, Sur une théorie asymptotique des poutres, Jnl. de Méc. 11, 673–703 (1972)
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)
D. F. Parker, An asymptotic analysis of large deflections and rotations of elastic rods, Internat. J. Solids Structs. 15, 361–377 (1979)
S. S. Antman, The Theory of Rods, Handbuch der Physik VIa/2, Springer-Verlag (1972)
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)
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Article copyright:
© Copyright 1987
American Mathematical Society