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On the status of the uncoupled approximation within quasistatic thermoelasticity

Published online by Cambridge University Press:  26 February 2010

W. A. Day
W. A. Day
Affiliation:
Hertford College, Oxford.
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We consider a body which occupies the open, bounded, regular region B, whose boundary is ∂B and whose closure is . We denote by da the element of surface area, by dυ the element of volume, and by n the outward unit normal. We suppose the behaviour of the body to be described by the equations of the quasi-static theory of homogeneous and isotropic thermoelasticity. These equations, which are obtained from the equations of the dynamical theory (see, for example, Carlson [1], Chadwick [2] or Boley and Weiner [3]) by omitting the inertial term pű from the right-hand side of the equation of motion (4), are:

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Type
Research Article
Information
Mathematika , Volume 28 , Issue 2 , December 1981 , pp. 286 - 294
Copyright
Copyright © University College London 1981

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References

1.Carlson, D. E.. “Linear Thermoelasticity”, The Encyclopedia of Physics, Vol. VIa/2 (Springer, 1972).Google Scholar
2.Chadwick, P.. “Thermoelasticity. The Dynamical Theory”, Progress in Solid Mechanics, Vol. 1 (North-Holland, 1960).Google Scholar
3.Boley, B. A. and Weiner, J. H.. Theory of Thermal Stresses (Wiley, 1960).Google Scholar
4.Day, W. A.. “Justification of the uncoupled and quasi-static approximations in a problem of dynamic thermoelasticity”, Arch. Rational Mech. Anal., to appear.Google Scholar
5.Day, W. A.. “Further justification of the uncoupled and quasi-static approximations in thermoelasticity”, Arch. Rational Mech. Anal, to appear.Google Scholar
6.Sigillito, V. G.. Explicit A Priori Inequalities with Applications to Boundary Value Problems (Pitman, 1977).Google Scholar