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Exact elementary green’s functions and integral formulas in thermoelasticity for a half - wedge / Victor Seremet in Journal of engineering mechanics, Vol. 138 N° 7 (Juillet 2012) 

Public ISBD [article]  in Journal of engineering mechanics > Vol. 138 N° 7 (Juillet 2012) . - pp.721–737. Titre : Exact elementary green’s functions and integral formulas in thermoelasticity for a half - wedge Type de document : texte imprimé Auteurs : Victor Seremet, Auteur Année de publication : 2012 Article en page(s) : pp.721–737. Note générale : Mécanique appliquée Langues : Anglais (eng) Mots-clés : Green’s  functions  Thermoelasticity  Heat  conduction  Elasticity  Thermoelastic  influence  functions  Volume  dilatation Résumé : In this study new exact Green’s functions and a new exact Poisson-type integral formula for a boundary-value problem (BVP) in thermoelasticity for a half-wedge with mixed homogeneous mechanical boundary conditions are derived, in which the boundary angle is rigidly fixed and the normal displacements and tangential stresses or the normal stresses and tangential displacements are prescribed on the boundary quarter-planes. The thermoelastic displacements are subjected to a heat source applied to the inner points of the half-wedge and to mixed nonhomogeneous boundary heat conditions, in which the temperature is prescribed to the boundary angle or to one boundary quarter-plane and the heat flux is given on the other boundary quarter-plane. When the thermoelastic Green’s function is derived, the thermoelastic displacements are generated by an inner unit point heat source, described by the δ-Dirac function. All results are obtained in elementary functions that are formulated in a special theorem. Analogous results for an octant and for a quarter-space as particular cases of the angle of the thermoelastic half-wedge are also obtained. The main difficulties in obtaining these results are in deriving the functions of the influence of a unit concentrated force onto elastic volume dilatation Θ(q) and, also, in calculating a volume integral of the product of function Θ(q) and the Green’s function in heat conduction. Exact solutions in elementary functions for two particular BVPs of thermoelasticity for a half-wedge, using the derived Poisson-type integral formula and the influence functions Θ(q), also are included. The proposed approach may be extended not only to many various BVPs for half-wedges but also to many canonical cylindrical and other orthogonal domains. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0000382 [article] Exact elementary green’s functions and integral formulas in thermoelasticity for a half - wedge [texte imprimé] / Victor Seremet, Auteur . - 2012 . - pp.721–737. Mécanique appliquée Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 138 N° 7 (Juillet 2012) . - pp.721–737. Mots-clés : Green’s  functions  Thermoelasticity  Heat  conduction  Elasticity  Thermoelastic  influence  functions  Volume  dilatation Résumé : In this study new exact Green’s functions and a new exact Poisson-type integral formula for a boundary-value problem (BVP) in thermoelasticity for a half-wedge with mixed homogeneous mechanical boundary conditions are derived, in which the boundary angle is rigidly fixed and the normal displacements and tangential stresses or the normal stresses and tangential displacements are prescribed on the boundary quarter-planes. The thermoelastic displacements are subjected to a heat source applied to the inner points of the half-wedge and to mixed nonhomogeneous boundary heat conditions, in which the temperature is prescribed to the boundary angle or to one boundary quarter-plane and the heat flux is given on the other boundary quarter-plane. When the thermoelastic Green’s function is derived, the thermoelastic displacements are generated by an inner unit point heat source, described by the δ-Dirac function. All results are obtained in elementary functions that are formulated in a special theorem. Analogous results for an octant and for a quarter-space as particular cases of the angle of the thermoelastic half-wedge are also obtained. The main difficulties in obtaining these results are in deriving the functions of the influence of a unit concentrated force onto elastic volume dilatation Θ(q) and, also, in calculating a volume integral of the product of function Θ(q) and the Green’s function in heat conduction. Exact solutions in elementary functions for two particular BVPs of thermoelasticity for a half-wedge, using the derived Poisson-type integral formula and the influence functions Θ(q), also are included. The proposed approach may be extended not only to many various BVPs for half-wedges but also to many canonical cylindrical and other orthogonal domains. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0000382