New Thermoelastic Green’s Functions by Using a New Integral Representation of Beltrami–Michel Equations
Publication: Journal of Engineering Mechanics
Volume 141, Issue 11
Abstract
New integral representations for thermal stresses in Beltrami–Michel equations are proposed in this paper. Using these representations, the author derived thermoelastic volume dilatation (TVD) on the boundary and inside a generalized octant. Then, applying the integral representations for the main thermoelastic Green’s functions (MTGFs) for Lame’s equations, there have been derived new structural formulas for MTGFs. These results are formulated in two theorems. According to structural formulas, many MTGFs for 22 boundary value problems (BVPs) of thermoelasticity may be obtained in terms of elementary functions by changing the respective well-known Green’s functions for Poisson’s equation (GFPE), its regular parts, and calculating some simple integrals. As an example of the application of structural formulas, new MTGFs for a particular BVP for an octant are derived in elementary functions that are very important for their numerical implementation, especially for the elaboration of new boundary elements. Validation of the obtained MTGFs is confirmed on the known MTGFs for a half-space. Graphical and numerical computer evaluation of the derived MTGFs using Maple 15 software is also included. Using the proposed integral representation and technique, it is possible to extend all the obtained results onto any domain of a Cartesian system of coordinates.
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Acknowledgments
The author expresses many thanks to the editor and reviewers of this paper, whose efforts and comments have contributed substantially to its improvement.
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Published In
Journal of Engineering Mechanics
Volume 141 • Issue 11 • November 2015
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Sep 4, 2014
Accepted: Jan 26, 2015
Published online: May 13, 2015
Discussion open until: Oct 13, 2015
Published in print: Nov 1, 2015
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