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X.—The Dynamic Stresses Produced in Elastic Bodies by Uneven Heating

Published online by Cambridge University Press:  14 February 2012

G. Eason  and
I. N. Sneddon
G. Eason
Affiliation:
King's College, Newcastle upon Tyne
I. N. Sneddon
Affiliation:
The University of Glasgow.
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Synopsis

The presence of a non-uniform distribution of temperature in an elastic solid gives rise to an additional term in the generalized Hooke's Law connecting the stress and strain tensors and to a term involving the time rate of change of the dilatation in the equation governing the conduction of heat in the solid. The present paper is concerned with the effects produced by these additional terms in two simple situations. In the first, the elastic solid is regarded as being of infinite extent and the distribution of temperature in the solid is produced by heat sources whose strength may vary with time. In the second, the solid is supposed to be semi-infinite and to be deformed by prescribed variations in the temperature of the bounding plane and by heat sources within itself.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 65 , Issue 2 , 1959 , pp. 143 - 176
Copyright
Copyright © Royal Society of Edinburgh 1959

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