Integral form of the general solution of equations of steady-state thermoelasticity
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 [\textit{V. D. Kupradze}, \textit{T. G. Gegelia}, \textit{M. O. Basheleishvili} and \textit{T. V. Burchuladze}, Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity. Amsterdam, etc.: North-Holland (1979; Zbl 0406.73001)] 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 problem as it contains a large number of integrals with different kernels.
equation of steady-state thermoelasticity
integral equation for boundary value problems
large number of integrals with different kernels
scientific article; zbMATH DE number 3917793