Thermoelastic Equilibrium of Some Semi-Infinite Domains Subjected to the Action of a Heat Source

Abstract

By using the integral representations for main thermoelastic Green's functions (MTGFs) we prove a theorem about new structural formulas for MTGFs for a whole class of boundary value problems (BVPs) of thermoelasticity for some semi-infinite Cartesian domains. According to these new structural formulas many MTGFs for a plane, a half-plane, a quadrant, a space, a quarter-space and an octant may be obtained by changing the respective well-known GFPE and their regular parts. The crucial moment of our investigation consists of elaboration of a new technique for calculating some generalized integrals containing products of two different GFPEs. Also, the types of boundary conditions for volume dilatation considered and GFPE for temperature differ on a single boundary only. As example of application of the obtained new structural formulas, the new MTGFs for a concrete BVP of thermoelaesticity for an octant are derived in elementary functions. The MTGFs obtained are validated on a known example for a BVP for half-space. Graphical computer evaluation of the derived in elementary functions new MTGFs is included.

Keywords:

• Elasticity
• Green's functions
• Heat conduction
• Thermoelastic Green's functions
• Thermoelasticity
• Volume dilatation

ACKNOWLEDGMENTS

This article was written during a research visit of Professor Victor Şeremet to the Department of Engineering Mechanics at Henan University of Technology. He is very grateful to Professor Hui Wang for his invitation and for fruitful collaboration in the field of constructing Green's functions for thermoelastic BVPs.

Notes

Color versions for one or more of the figures in the article can be found online at www.tandfonline.com/uths.