New closed-form thermoelastostatic Green function and Poisson-type integral formula for a quarter-plane

• Published in: Mathematical and computer modelling Vol. 53; no. 1; pp. 347 - 358
• Main Authors: Şeremet, Victor, Bonnet, Guy
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.01.2011; Elsevier
• Subjects: Elasticity; Engineering Sciences; Exact sciences and technology; Green’s functions; heat; Heat conduction; Mathematical analysis; Mathematics; Mechanics; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis; Numerical analysis. Scientific computation; Ordinary differential equations; Partial differential equations, boundary value problems; Physics; Poisson-type integral formula; Sciences and techniques of general use; Solid mechanics; temperature; Thermoelastic influence functions; Thermoelastostatics; Volume dilatation; Heat conduction; Volume dilatation; Green’s functions; Poisson-type integral formula; Elasticity; Thermoelastostatics; Thermoelastic influence functions; Elementary function; Green's functions; Boundary condition; Green function; Partial differential equation; Numerical analysis; Boundary value problem; Applied mathematics; Poisson integral; Mathematical model; Computer aided analysis
• ISSN: 0895-7177; 1872-9479
• DOI: 10.1016/j.mcm.2010.09.001

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.