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SM ISO690:2012 ŞEREMET, Victor, BONNET, Guy. New closed-form thermoelastostatic Green function and Poisson-type integral formula for a quarter-plane. In: Mathematical and Computer Modelling, 2011, vol. 53, pp. 347-358. ISSN 0895-7177. DOI: https://doi.org/10.1016/j.mcm.2010.09.001 |
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Mathematical and Computer Modelling | ||||||
Volumul 53 / 2011 / ISSN 0895-7177 | ||||||
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DOI:https://doi.org/10.1016/j.mcm.2010.09.001 | ||||||
Pag. 347-358 | ||||||
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A new Green's function and a new Poisson-type integral formula for a boundary value problem (BVP) in thermoelastostatics for a quarter-plane subject by mixed homogeneous mechanical boundary conditions are derived in this paper. The thermoelastic displacements are generated by a heat source, applied in the inner points of the quarter-plane and by temperature, prescribed on its boundary semi-straight-lines. All results, obtained in terms of elementary functions, are formulated in a special theorem. The first difficulty to obtain these results is in deriving the functions of influence of a unit concentrated force onto elastic volume dilatation Θ(k). The second difficulty is in calculating a volume integral of the product of function Θ(k) and Green's function G in heat conduction. A closed-form solution for a particular BVP of thermoelastostatics for a quarter-plane also is included. Using the proposed approach, it is possible to extend the obtained results not only for any canonical Cartesian domain, but also for any canonical orthogonal one. |
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Cuvinte-cheie elasticity, Green's functions, Heat conduction, Poisson-type integral formula, thermoelastic influence functions, Thermoelastostatics, volume dilatation |
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