Elasticity pp 347-361 | Cite as

# Thermoelastic Displacement Potentials

Chapter

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## 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
etc.

$$\sigma _{xx} = \lambda e + 2\mu e_{xx} - (3\lambda + 2\mu )\alpha T$$

(22.2)

$$\sigma _{xy} = 2\mu e_{xy} $$

(22.3)

## 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