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The determination of thermal stresses in dissimilar media

Published online by Cambridge University Press:  24 October 2008

K. Aderogba
K. Aderogba
Affiliation:
University of Lagos, Nigeria
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Abstract

It is shown that if, in an infinite homogeneous unbounded elastic heat-conducting solid, we are given the thermal stresses which arise when any arbitrarily shaped subregion of the upper half-space z > 0 is emitting any quantity of heat into the surrounding, then on introducing a different heat-conducting material into the half-space z < 0, the new thermal stresses in z >0 and in z < 0 are explicitly expressible in an invariant form in terms of the known thermal stresses in the homogeneous infinite solid. Specialization of the derived dependence shows that the physically interesting interfacial discontinuities inherent in the problem admit the representation

while the traction transmitted across the interface takes the form

where αi and βi are constants. An application is then made to the case when the region emitting heat into the surrounding is ellipsoidal, since this is a fundamental shape of practical importance. Applications can however be made to any shape of the region emitting heat, provided that the corresponding harmonic and biharmonic potentials are available.

The paper may be considered to have its origin in the half-space theorem of Lorentz in hydrodynamics.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 3 , May 1981 , pp. 533 - 542
Copyright
Copyright © Cambridge Philosophical Society 1981

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