Exact Elementary Green’s Functions and Integral Formulas in Thermoelasticity for a Half-Wedge
Publication: Journal of Engineering Mechanics
Volume 138, Issue 7
Abstract
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 -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 and, also, in calculating a volume integral of the product of function 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 , 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.
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Acknowledgments
The writer is grateful to the University Paris-Est, Marne-la-Vallee, Laboratory MSME UMAR 8208 CNRS, France, and to the Weierstrass Institute for Applied Analysis and Stochastic, Berlin, Germany, for their support through research visits. The writer expresses many thanks to the reviewers of this paper, whose comments have contributed substantially to its improvement.
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Information
Published In
Journal of Engineering Mechanics
Volume 138 • Issue 7 • July 2012
Pages: 721 - 737
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Jan 7, 2010
Accepted: Dec 13, 2011
Published online: Jun 15, 2012
Published in print: Jul 1, 2012
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