Osobliwe Równania Całkowe Termosprężystości - Ignaczak, J.; Nowacki, W. (Engineering Transactions, 1965)
The present paper contains a derivation of the integral representation of the general solution of coupled linear elasticity. It is assumed that the material and thermal constants are independent of the temperature and that the vibration is harmonic. The integral relations are obtained by means of two sets of singular solutions of which the first determines the symmetric second order displacement tensor and the temperature both corresponding to the action, in an infinite body of a concentrated force, and the setond the potential displacement vector and the temperature produced in an infinite thermoelastic body by the action of a concentrated source of heat. These sets of singular solutions are used to define the thermoelastic potential of a single, double and mixed layer and to obtain singular integral equations for the fundamental boundary-value problems. These equations have the form of coupled singular Fredholm equations of the second kind, the integrals involved being understood in the sense of principal values. In the last section of the paper the integral representation of the solution is made use of to obtain an approximate solution of three-dimensional problems of thermoelasticity using the canonical functional equations.