Elasticity pp 347-361 | Cite as

Thermoelastic Displacement Potentials

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


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
$$2\mu u = \nabla \phi$$
The thermoelastic stress-strain relations (14.3, 14.4) can be solved to give
$$\sigma _{xx} = \lambda e + 2\mu e_{xx} - (3\lambda + 2\mu )\alpha T$$
$$\sigma _{xy} = 2\mu e_{xy} $$


Maximum Tensile Stress Circular Inclusion Airy Stress Function Quarter Plane Unperturbed Problem 
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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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