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Elasticity pp 347-361 | Cite as

Thermoelastic Displacement Potentials

  • J. R. Barber
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 172)

Abstract

As in the two-dimensional case (Chapter 14), three-dimensional problems of thermoelasticity are conveniently treated by finding a particular solution — i.e. a solution which satisfies the field equations without regard to bound ary conditions — and completing the general solution by superposition of an appropriate representation for the general isothermal problem, such as the Papkovich-Neuber solution.

In this section, we shall show that a particular solution can always be obtained in the form of a strain potential — i.e. by writing
$$2\mu u = \nabla \phi$$
(22.1)
The thermoelastic stress-strain relations (14.3, 14.4) can be solved to give
$$\sigma _{xx} = \lambda e + 2\mu e_{xx} - (3\lambda + 2\mu )\alpha T$$
(22.2)
$$\sigma _{xy} = 2\mu e_{xy} $$
(22.3)
etc.

Keywords

Maximum Tensile Stress Circular Inclusion Airy Stress Function Quarter Plane Unperturbed Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Mechanical Engineering and Applied MechanicsUniversity of MichiganAnn ArborUSA

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