Integral form of the general solution of equations of steady-state Thermoelasticity

Abstract

A new integral formula is obtained for solving the equation of steady-state thermoelasticity in a three-dimensional region, differing from the well-known formula /1/ in containing no volume integral. A similar formula is encountered in the case of a two-dimensional region, and its use in constructing the integral equation for boundary value problems is suggested. The fact that there are no volume integrals in the integral equations facilitates their numerical solution. If the temperature is represented by Green's formula in terms of the Newtonian potentials of the single and double layer, and the mass force is conservative, then, as shown below, the volume integrals will also be transformed into surface integrals over the boundary surface. The resulting formula however is less suitable for the numerical solution of boundary value problems as it contains a large number of integrals with different kernels.