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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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References

References to Literature

Biot, M. A., 1956. “Thermoelasticity and Irreversible Thermodynamics”, J. Appl. Phys., 27, 240.CrossRefGoogle Scholar
Brillouin, L., 1938. Tenseurs en Mécanique et en Élasticité. Paris: Masson et Cie.Google Scholar
Bullen, K. E., 1947. An Introduction to the Theory of Seismology. Cambridge University Press.Google Scholar
Carslaw, H. S., and Jaeger, J. C., 1947. The Conduction of Heat in Solids. Oxford University Press.Google Scholar
Chadwick, P., and Sneddon, I. N., 1958. “Plane Waves in an Elastic Solid Conducting Heat”, J. Mech. Phys. Solids, 6, 223.CrossRefGoogle Scholar
Duhamel, J. M. C., 1837. “Second Mémoirs sur les Phénomènes Thermo-Mécanique”, J. Éc. Polyt. Paris, 15, 1.Google Scholar
Eason, G., 1954. Ph.D. Thesis, University of Birmingham.Google Scholar
Eason, G., Fulton, J., and Sneddon, I. N., 1956. “The Generation of Waves in an Infinite Elastic Solid by Variable Body Forces”, Phil. Trans., A., 248, 575.Google Scholar
Erdélyi, A. (Edit.), 1954. Tables of Integral Transforms. Vol. 1. New York: McGraw-Hill Book Co.Google Scholar
Jeffreys, H., 1930. “The Thermodynamics of an Elastic Solid,” Proc. Camb. Phil. Soc., 26, 101.CrossRefGoogle Scholar
Lamb, H., 1904. “On the Propagation of Tremors over the Surface of an Elastic Solid”, Phil. Trans., A., 203, 1.Google Scholar
Lessen, M., 1956. “Thermoelasticity and Thermal Shock”, J. Mech. Phys. Solids, 5, 57.CrossRefGoogle Scholar
Lessen, M., 1957. “The Motion of a Thermoelastic Solid”, Quart. Appl. Math., 15, 105.CrossRefGoogle Scholar
Neumann, F. E., 1885. Vorlesung über die Theorie der Elasticität der Festen Körper. Leipzig:Google Scholar
Sokolnikoff, I. S., 1956. The Mathematical Theory of Elasticity. New York: McGraw-Hill Book Co.Google Scholar
Sneddon, I. N., 1951. Fourier Transforms. New York: McGraw-Hill Book Co.Google Scholar
Sneddon, I. N., 1958. “The Propagation of Thermal Stresses in Thin Metallic Rods”, Proc. Roy. Soc. Edin., A., 65, 121.Google Scholar
Sneddon, I. N., and Berry, D. S., 1958. “The Classical Theory of Elasticity”, Handb. Phys., 6, 1–124.Google Scholar
Voigt, W., 1910. Lehrbuch der Kristallphysik. Berlin: Teubner-Verlag.Google Scholar
Watson, G. N., 1944. A Treatise on the Theory of Bessel Functions. 2nd ed. Cambridge University Press.Google Scholar
Weiner, J. H., 1957. “A Uniqueness Theorem for the Coupled Thermoelastic Problem”, Quart. Appl. Math., 15, 102.CrossRefGoogle Scholar