Summary
This paper gives a treatment of Saint-Venant's problem for viscoelastic cylinders by reformulating the quasi-static equilibrium equations as a formal integro-differential operator over the cross section of the cylinder, with the axial variable playing the role of a parameter. Then, the conditions are established that the solution of Saint-Venant's problem may be treated as a generalized plane strain problem. Further, two classes of semi-inverse solutions to Saint-Venant's problem are described. These classes are used in order to obtain a solution for the relaxed Saint-Venant's problem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ieşan, D.: On Saint-Venant's problem. Arch. Rat. Mech. Anal.91, 363–373 (1986).
Ieşan, D.: Saint-Venant's Problem. In: Lecture notes in mathematics, vol. 1279 (Dold, A., Eckmann, B., eds.) Berlin/Heidelberg/New York/Tokyo: Springer 1987.
Fichera, G.: Existence theorems in elasticity. In: Handbuch der Physik, Bd. VIa/2 (Truesdell, C. A., ed.) Berlin/Heidelberg/New York: Springer 1972.
Leitman, M. J., Fisher, G. M. C.: The linear theory of viscoelasticity. In: Handbuch der Physik, Bd. VIa/3 (Truesdell, C. A., ed.). Berlin/Heidelberg/New York: Springer 1973.
Corduneanu, C.: Integral equations and applications. Cambridge/New York/Melbourne: Cambridge University Press 1991.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chiriţâ, S. Saint-Venant's problem and semi-inverse solutions in linear viscoelasticity. Acta Mechanica 94, 221–232 (1992). https://doi.org/10.1007/BF01176651
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01176651