ABSTRACT
This chapter presents the basic treatment of plane thermoelastic problems. The special cases of plane strain and plane stress are introduced along with derivations of the associated governing equations. Three techniques are introduced: the thermal stress function method, which is the analogue of the Airy stress function method for isothermal problems; the complex variable method; and the potential method. The thermal stress function technique is a powerful tool for plane problems. The stresses are defined by partial differentiation of the thermal stress function, whereas the displacement components are expressed in terms of the thermal stress function and an additional plane function. The complex representation for both simply-connected and multiply-connected bodies is discussed. Moreover, the method of conformal mapping is presented in order to treat bodies with complex boundary contours. Finally, the plane counterpart of the 3D Navier's solution is considered.
