Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



On Saint-Venant's principle in dynamic linear viscoelasticity

Author: Stan Chiriţa
Journal: Quart. Appl. Math. 55 (1997), 139-149
MSC: Primary 73F15; Secondary 73C10
DOI: https://doi.org/10.1090/qam/1433757
MathSciNet review: MR1433757
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] E. Sternberg and S. M. Al-Khozaie, On Green's functions and Saint-Venant's principle in the linear theory of viscoelasticity, Arch. Rational Mech. Anal. 15, 112-146 (1964)
  • [2] E. Sternberg, On Saint-Venant's principle, Quart. Appl. Math. 11, 393-402 (1954) MR 0058414
  • [3] R. A. Toupin, Saint-Venant's principle, Arch. Rational Mech. Anal. 18, 83-96 (1965) MR 0172506
  • [4] W. S. Edelstein, On Saint-Venant's principle in linear viscoelasticity, Arch. Rational Mech. Anal. 36, 366-380 (1970) MR 0260246
  • [5] R. E. Neapolitan and W. S. Edelstein, Further study of Saint-Venant's principle in linear viscoelasticity, Z. Angew. Math. Phys. 24, 823-837 (1973) MR 0363087
  • [6] S. Rionero and S. Chiriţa, On the asymptotic behaviour of quasi-static solutions in a semi-infinite viscoelastic cylinder, Rend. Accad. Sci. Fis. Mat. Serie IV, vol. LIX, 147-165 (1992) MR 1244040
  • [7] C. O. Horgan and J. K. Knowles, Recent developments concerning Saint-Venant's principle, Adv. Appl. Mech. (T. Y. Wu and J. W. Hutchinson, eds.), vol. 23, Academic Press, New York, 1983, pp. 179-269 MR 889288
  • [8] C. O. Horgan, Recent developments concerning Saint-Venant's principle: An update, Appl. Mech. Rev. 42, 295-303 (1989) MR 1021553
  • [9] S. Chiriţa, Saint-Venant's principle in elastodynamics, submitted.
  • [10] J. N. Flavin and R. J. Knops, Some spatial decay estimates in continuum dynamics, J. Elasticity 17, 249-264 (1987) MR 888318
  • [11] J. N. Flavin, R. J. Knops, and L. E. Payne, Decay estimates for the constrained elastic cylinder of variable cross section, Quart. Appl. Math. 47, 325-350 (1989) MR 998106
  • [12] J. N. Flavin, R. J. Knops, and L. E. Payne, Energy bounds in dynamical problems for a semi-infinite elastic beam, Elasticity, Mathematical Methods and Applications (G. Eason and R. W. Ogden, eds.), Ellis-Horwood, Chichester, 1990, pp. 101-111
  • [13] M. J. Leitman and G. M. C. Fisher, The linear theory of viscoelasticity, Handbuch der Physik, vol. VIa/2 (C. Truesdell, ed.), Springer, Berlin, 1972
  • [14] C. M. Dafermos, Asymptotic stability in viscoelasticity, Arch. Rational Mech. Anal. 37, 297-308 (1970) MR 0281400
  • [15] V. L. Berdichevskii, On the proof of the Saint- Venant principle for bodies of arbitrary shape, Prikl. Mat. Mekh. 38, 851-864 (1974); J. Appl. Math. Mech. 37, 140-156 (1975) MR 0373425
  • [16] R. J. Knops, A Phragmén-Lindelof theorem for the free elastic cylinder, Rendiconti di Matematica, Serie VII 10, 601-622 (1990) MR 1080316

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73F15, 73C10

Retrieve articles in all journals with MSC: 73F15, 73C10

Additional Information

DOI: https://doi.org/10.1090/qam/1433757
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society