New Poisson's integral formulas for thermoelastic half-space and other canonical domains

Abstract

In this paper the functions of influence of unit point heat source onto displacements and Poisson-type integral formula for a boundary value problem (BVP) in thermoelastic half-space, free of loadings on the boundary plane are presented in closed form. The thermoelastic displacements are generated by heat source applied at the inner point of the half-space and by heat flux, prescribed on its boundary. All these results are formulated in a special theorem. Furthermore, the advantages and usefulness of the obtained results are also discussed. The main difficulties to obtain such kind of results are to derive the functions of influence of a unit concentrated force onto elastic volume dilatation Θ ( k) and Green's functions in heat conduction G. For canonical Cartesian domains, these difficulties were addressed successfully, and the above-mentioned functions were derived and published earlier. Thus, it can be presumed that for the Cartesian domains, this paper will open a great possibility to derive new thermoelastic influence functions and Poisson's integral formulas in closed form. Moreover, the technique proposed here will also work for any orthogonal canonical domain, as soon as the lists of functions G and Θ ( k) are completed.