Fundamental solutions for steady-state heat transfer in an exponentially graded anisotropic material

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 56, Issue 2, 2005, Pages 293-303

  Berger, J R ^a   Martin, P A ^a   Mantic V ^b   Gray, L J ^c  

^a Department of Geology and Geological Engineering   (United States)

^b UNIVERSIDAD DE SEVILLA   (Spain)

^c OAK RIDGE NATIONAL LABORATORY   (United States)

Author keywords

Functionally graded materials; Green's functions; Heat conduction

Indexed keywords

EID: 15544378407     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00033-004-1131-6     Document Type: Article

References (18)

1. G. Barton, Elements of Green's Functions and Propagation. Oxford Science Publications, Oxford, 1989.
2. M. Bonnet and M. Guiggiani, Comments about the paper 'A generalized boundary integral equation for isotropic heat conduction with spatially varying thermal conductivity'. Engng. Analysis with Boundary Elements 22 (1998), 235-240.
3. A. H. -D. Cheng, Darcy flow with variable permeability. Water Resources Research 20 (1984), 980-984.
4. D. L. Clements, Thermal stress in an anisotropic half-space. SIAM J. Appl. Math. 24 (1973), 332-337.
5. D. L. Clements, A boundary integral equation method for the numerical solution of a second order elliptic equation with variable coefficients. J. Austral. Math. Soc. B 22 (1980), 218-228.
6. D. L. Clements and W. S. Budhi, A boundary element method of the solution of a class of steady-state problems for anisotropic media. J. Heat Transfer 121 (1999), 462-465.
7. D. L. Clements and C. Rogers, A boundary integral equation of the solution of a class of problems in anisotropic inhomogeneous thermostatics and elastostatics. Q. Appl. Math. 41 (1984), 99-105.
8. T. A. Cruse, Boundary Element Analysis in Computational Fracture Mechanics, Martinus Nijhoff, New York, 1988.
9. L. J. Gray, T. Kaplan, J. D. Richardson and G. H. Paulino, Green's functions and boundary integral analysis for exponentially graded materials: heat conduction. J. Appl. Mech. 70 (2003), 543-549.
10. T. Hirai, Functionally Graded Materials. In Materials Science and Technology, Processing of Ceramics, Part 2, (ed. R. J. Brook), vol. 17B, VCH Verlagsgesellschaft mbH, Weinheim, pages 292-341, 1996.
11. A. Kassab and E. Divo, A generalized boundary integral equation for isotropic heat conduction with spatially varying thermal conductivity. Engng. Analysis with Boundary Elements 18 (1996), 273-286.
12. A. Kassab and E. Divo, Generalized boundary integral equation for heat conduction in non-homogeneous media: recent developments on the sifting property. Engng. Analysis with Boundary Elements 22 (1998), 221-234.
13. P. K. Kythe, Differential Operators and Applications. Birkhauser, Boston, 1996.
14. V. Mantič and F. Paris, On free terms and singular integrals in isotropic and anisotropic potential theory. In Computational Mechanics '95 (eds S. N. Atluri, G. Yagawa and T. A. Cruse), Springer, Berlin, pages 2806-2811, 1995.
15. Y. Miyamoto, W. A. Kaysser, B. H. Rabin, A. Kawasaki and R. G. Ford, Functionally Graded Materials: Design, Processing and Applications. Kluwer, Dordrecht, 1999.
16. R. Shaw, Steady state heat conduction with a separable position and temperature dependent conductivity. Boundary Elements Communications 10 (1999), 15-18.
17. R. Shaw and N. Makris, Green's functions for Helmholtz and Laplace equations in heterogeneous media. Engng. Analysis with Boundary Elements 10 (1992), 179-183.
18. S. Suresh and A. Mortensen, Fundamentals of Functionally Graded Materials. The Institute of Materials, IOM Communications Ltd., London, 1998.