Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-10T20:35:49.915Z Has data issue: false hasContentIssue false
  • English
  • Français

I.—On the Use of Stress Functions for Solving Problems in Linear Viscoelasticity Theory that Involve Moving Boundaries*

Published online by Cambridge University Press:  14 February 2012

G. A. C. Graham
G. A. C. Graham
Affiliation:
Department of Mathematics, University of Glasgow.
Get access Rights & Permissions [Opens in a new window]

Synopsis

The traditional method of solution to problems in linear viscoelasticity theory involves the direct application of the Laplace transform to the relevant field equations and boundary conditions. If the shape of the body under consideration or the type of boundary condition specified at a point or both vary with time then this method no longer works. In this paper we investigate the applicability of stress function solutions to this situation. It is shown that for time-dependent ablating regions a generalization of the Papkovich Neuber stress function solution of elasticity holds. As an example the stress and displacement fields are calculated for the problem of an infinite viscoelastic body with a spherical ablating stress free cavity and prescribed time-dependent stresses at infinity.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 67 , Issue 1 , 1965 , pp. 1 - 8
Copyright
Copyright © Royal Society of Edinburgh 1963

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

References to Literature

Al-Khozaie, Said M., and Lee, E. H., 1962. “Influence of Material Compressibility in the Viscoelastic Contact Problem”. (Report prepared for the Armstrong Cork Company, Div. Appi. Math., Brown Univ.).Google Scholar
Corneliussen, A. H., Kamowitz, E. F., Lee, E. H., and Radok, J. R. M., 1961. “Viscoelastic Stress Analysis of a Spinning Hollow Circular Cylinder with an Ablating Pressurised Cavity”, Trans. Soc. Rheol., 7, 357.CrossRefGoogle Scholar
Green, A. E., and Zerna, W., 1954. Theoretical Elasticity, 172. Oxford: Clarendon Press.Google Scholar
Gurtin, M. E., and Sternberg, Eli, 1962. “On the Linear Theory of Visco-elasticity”, Arch. Rational Mech. Analysis, II, 291.CrossRefGoogle Scholar
Hunter, S. C., 1960 a. “The Hertz Problem for a Rigid Spherical Indentor and a Viscoelastic Half-space”, J. Mech. Phys. Solids, 8, 219.CrossRefGoogle Scholar
Hunter, S. C., 1960 b. “The Rolling Contact of a Rigid Cylinder with a Viscoelastic Half-Space”, J. Appi. Mech., 28, 611.CrossRefGoogle Scholar
Lamb, H., 1902. “On Boussinesq's Problem”, Proc. Lond. Math. Soc, 34, 276.Google Scholar
Lee, E. H., 1955. “Stress Analysis in Viscoelastic Bodies“, Quart. Appi. Math., 13, 183.CrossRefGoogle Scholar
Lee, E. H., 1960. “Viscoelastic Stress Analysis”, Proc. First Symp. Nav. Struct. Mech. Pergamon Press.Google Scholar
Lee, E. H., and Radok, J. R. M., 1960. “The Contact Problem for Viscoelastic Bodies”, J. Appi. Mech., 27, 438.CrossRefGoogle Scholar
Lee, E. H., Radok, J. R. M., and Woodward, W. B., 1959. “Stress Analysis for Linear Viscoelastic Materials”, Trans. Soc. Rheol., 3, 41.CrossRefGoogle Scholar
Lee, E. H., and Rogers, T. G., 1962. “Non-linear Effects of Temperature Variation in Stress Analysis of Isothermally Linear Viscoelastic Materials”. (Tech. Rep. No. 3, Contract Nonr 562(30), Brown Univ.).Google Scholar
Radok, J. R. M., 1957. “Viscoelastic Stress Analysis”, Quart. Appi. Math., 15, 198.CrossRefGoogle Scholar
Rogers, T. G., and Lee, E. H., 1962. “Thermo-viscoelastic Stresses in a Sphere with an Ablating Cavity”, Progr. Appi. Mech., Prager Anniversary Volume, 355. Macmillan.Google Scholar