Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 284380, 18 pages
New Poisson's Type Integral Formula for Thermoelastic Half-Space
1Department of Mathematics and Engineering, Agrarian State University of Moldova, Mircesti Street 44, 2049 Chisinau, Moldova
2Laboratoire de Modélisation et Simulation Multi-Echelle FRE 3160 CNRS, Université Paris Est, 5 boulevard Descartes, 77454 Marne la Vallée Cedex, France
3Department of Mathematics, Agrarian State University of Moldova, Mircesti Street 44, 2049 Chisinau, Moldova
Received 5 January 2009; Revised 23 April 2009; Accepted 7 May 2009
Academic Editor: Saad A. Ragab
Copyright © 2009 Victor Seremet et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A new Green's function and a new Poisson's type integral formula for a boundary value problem (BVP) in thermoelasticity for a half-space with mixed boundary conditions are derived. The thermoelastic displacements are generated by a heat source, applied in the inner points of the half-space and by temperature, and prescribed on its boundary. All results are obtained in closed forms that are formulated in a special theorem. A closed form solution for a particular BVP of thermoelasticity for a half-space also is included. The main difficulties to obtain these results are in deriving of functions of influence of a unit concentrated force onto elastic volume dilatation and, also, in calculating of a volume integral of the product of function and Green's function in heat conduction. Using the proposed approach, it is possible to extend the obtained results not only for any canonical Cartesian domain, but also for any orthogonal one.