Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-28T05:15:58.026Z Has data issue: false hasContentIssue false
  • English
  • Français

On the linearised theory of buckling for a compressed viscoelastic rod

Published online by Cambridge University Press:  14 November 2011

David W. Reynolds
David W. Reynolds
Affiliation:
School of Mathematical Sciences, National Institute for Higher Education, Dublin 9, Republic of Ireland
Get access Rights & Permissions [Opens in a new window]

Synopsis

Results are obtained on the existence, multiplicity, blow-up and asymptotic behaviour of the solutions to the integro-differential equation

which arises in the linearised, quasi-static theory of buckling for a viscoelastic rod.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 99 , Issue 3-4 , 1985 , pp. 371 - 386
Copyright
Copyright © Royal Society of Edinburgh 1985

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Gurtin, M. E., Mizel, V. J. and Reynolds, D. W.. On nontrivial solutions for a compressed linear viscoelastic rod. J. Appl. Mech. 49 (1982), 245–246.Google Scholar
2Landau, L. D. and Lifshitz, E. M.. Theory of Elasticity, Second English Edition (Oxford: Pergamon, 1970).Google Scholar
3Antman, S. A. and Rosenfeld, G.. Global behaviour of nonlinearly elastic rods. SIAM Rev. 20 (1978), 513–566.Google Scholar
4Gurtin, M. E.. Some questions and open problems in continuum mechanics and population dynamics. J. Differential Equations 48 (1983), 293–312.CrossRefGoogle Scholar
5Mignot, F. and Puel, J. P.. Buckling of a viscoelastic rod. Arch. Rational Mech. Anal. 85 (1984), 251–277.CrossRefGoogle Scholar
6Moore, G.. The numerical buckling of a visco-elastic rod. Proceedings of Dortmund Conference on Numerical Methods for Bifurcation Problems (Basel: Birkhauser, 1984).Google Scholar
7Gurtin, M. E., Reynolds, D. W. and Spector, S. J.. On uniqueness and bifurcation in nonlinear viscoelasticity. Arch. Rational Mech. Anal. 72 (1980), 303–313.CrossRefGoogle Scholar
8Reynolds, D. W.. On linear singular Volterra equations of the second kind. J. Math. Anal. Appl. 103 (1984), 230–262.Google Scholar
9Paley, R. E. A.C. and Wiener, N.. Fourier Transforms in the Complex Domain. A.M.S. Colloquium Publications, Vol. XIX (New York: American Mathematical Society, 1934).Google Scholar
10Distéfano, J. N.. Sulla stabilità in regime visco-elastico a compartamento lineare I & II. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 72 (1959), 205–211& 356–361.Google Scholar
11Distéfano, J. N.. Creep buckling of slender columns. J.Struct. Div. Proc. A.S.C.E. 91 (1965), 127–150.CrossRefGoogle Scholar
12Goldengerschel, E. I.. Spectrum of a Volterra operator on a half-axis and Euler stability of viscoelastic rods. Soviet Phys. Dokl. 19 (1974), 549–550.Google Scholar
13Goldengerschel, E. I.. On the Euler stability of viscoelastic rod. J. Appl. Math. Mech. 38 (1974), 172–178.Google Scholar
14Goldengerschel, E. I.. New Euler stability criterion for a viscoelastic rod. J. Appl. Math. Mech. 40 (1976), 714–716.Google Scholar