On Saint-Venant’s principle in dynamic linear viscoelasticity
Author:
Stan Chiriţǎ
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
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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)
- E. Sternberg, On Saint-Venant’s principle, Quart. Appl. Math. 11 (1954), 393–402. MR 58414, DOI https://doi.org/10.1090/S0033-569X-1954-58414-7
- R. A. Toupin, Saint-Venant’s principle, Arch. Rational Mech. Anal. 18 (1965), 83–96. MR 172506, DOI https://doi.org/10.1007/BF00282253
- Warren S. Edelstein, On Saint-Venant’s principle in linear viscoelasticity, Arch. Rational Mech. Anal. 36 (1970), 366–380. MR 260246, DOI https://doi.org/10.1007/BF00282273
- Richard E. Neapolitan and Warren S. Edelstein, Further study of Saint-Venant’s principle in linear viscoelasticity, Z. Angew. Math. Phys. 24 (1973), 823–837 (English, with German summary). MR 363087, DOI https://doi.org/10.1007/BF01590792
- S. Rionero and S. Chiriţă, On the asymptotic behaviour of quasi-static solutions in a semi-infinite viscoelastic cylinder, Rend. Accad. Sci. Fis. Mat. Napoli (4) 59 (1992), 147–166 (1993) (English, with English and Italian summaries). MR 1244040
- Cornelius O. Horgan and James K. Knowles, Recent developments concerning Saint-Venant’s principle, Adv. in Appl. Mech. 23 (1983), 179–269. MR 889288
- Cornelius O. Horgan, Recent developments concerning Saint-Venant’s principle: an update, AMR 42 (1989), no. 11, 295–303. MR 1021553, DOI https://doi.org/10.1115/1.3152414
S. Chiriţǎ, Saint-Venant’s principle in elastodynamics, submitted.
- J. N. Flavin and R. J. Knops, Some spatial decay estimates in continuum dynamics, J. Elasticity 17 (1987), no. 3, 249–264. MR 888318, DOI https://doi.org/10.1007/BF00049455
- 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 (1989), no. 2, 325–350. MR 998106, DOI https://doi.org/10.1090/S0033-569X-1989-0998106-1
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
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
- Constantine M. Dafermos, Asymptotic stability in viscoelasticity, Arch. Rational Mech. Anal. 37 (1970), 297–308. MR 281400, DOI https://doi.org/10.1007/BF00251609
- V. L. Berdichevskii, On the proof of the Saint-Venant principle for bodies of arbitrary shape, Prikl. Mat. Meh. 38 (1974), 851–864 (Russian); English transl., J. Appl. Math. Mech. 38 (1974), 799–813 (1975). MR 0373425, DOI https://doi.org/10.1016/0021-8928%2874%2990122-1
- R. J. Knops, A Phragmén-Lindelöf theorem for the free elastic cylinder, Rend. Mat. Appl. (7) 10 (1990), no. 3, 601–622 (English, with Italian summary). MR 1080316
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)
E. Sternberg, On Saint-Venant’s principle, Quart. Appl. Math. 11, 393–402 (1954)
R. A. Toupin, Saint-Venant’s principle, Arch. Rational Mech. Anal. 18, 83–96 (1965)
W. S. Edelstein, On Saint-Venant’s principle in linear viscoelasticity, Arch. Rational Mech. Anal. 36, 366–380 (1970)
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)
S. Rionero and S. Chiriţǎ, 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)
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
C. O. Horgan, Recent developments concerning Saint-Venant’s principle: An update, Appl. Mech. Rev. 42, 295–303 (1989)
S. Chiriţǎ, Saint-Venant’s principle in elastodynamics, submitted.
J. N. Flavin and R. J. Knops, Some spatial decay estimates in continuum dynamics, J. Elasticity 17, 249–264 (1987)
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)
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
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
C. M. Dafermos, Asymptotic stability in viscoelasticity, Arch. Rational Mech. Anal. 37, 297–308 (1970)
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)
R. J. Knops, A Phragmén-Lindelof theorem for the free elastic cylinder, Rendiconti di Matematica, Serie VII 10, 601–622 (1990)
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© Copyright 1997
American Mathematical Society
