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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.
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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

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References

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