A local BIEM for analysis of transient heat conduction with nonlinear source terms in FGMs

Engineering Analysis with Boundary Elements

Volumn 28, Issue 1, 2004, Pages 1-11

  Sladek, Jan ^a   Sladek, Vladimir ^a   Zhang, Ch ^b  

^a INSTITUTE OF CONSTRUCTION AND ARCHITECTURE   (Slovakia)

^b UNIVERSITY OF APPLIED SCIENCES ZITTAU GÖRLITZ   (Germany)

Author keywords

Absorbtivity; Functionally graded materials; Hot spots; Laplace transform; Local boundary integral equations; Moving least square approximation; Transient heat conduction analysis

Indexed keywords

APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; DIFFUSION; FINITE ELEMENT METHOD; FUNCTIONALLY GRADED MATERIALS; GREEN'S FUNCTION; HEAT FLUX; INTEGRAL EQUATIONS; LAPLACE TRANSFORMS; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; NONLINEAR SYSTEMS;

LOCAL BOUNDARY INTEGRAL EQUATIONS (LBIE); NONLINEAR SOURCES;

HEAT CONDUCTION;

EID: 0347526066     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0955-7997(03)00093-6     Document Type: Article

References (17)

1. Zhu S., Zhang Y., Marchant T.R. A DRBEM model for microwave heating problems. Appl Math Modelling. 19:1995;287-297.
2. Miyamoto Y., Kaysser W.A., Rabin B.H., Kawasaki A., Ford R.G. Functionally graded materials: design processing and applications. 1999;Kluwer Academic Publishers, Dordrecht.
3. Suresh S., Mortensen A. Fundamentals of functionally graded materials. 1998;Institute of Materials, London.
4. Butterfield R. An application of the boundary element method to potential flow problems in generally inhomogeneous bodies. Brebbia C.A. Recent advances in boundary element method. 1978;Pentech Press, London.
5. Sutradhar A., Paulino G.H., Gray L.J. Transient heat conduction in homogeneous and non-homogeneous materials by the Laplace transform Galerkin boundary element method. Engng Anal Bound Elem. 26:2002;119-132.
6. Zhu T., Zhang J.D., Atluri S.N. A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approach. Comput Mech. 21:1998;223-235.
7. De S., Bathe K.J. The method of finite spheres. Comput Mech. 25:2000;329-345.
8. Sladek J., Sladek V., Atluri S.N. Local boundary integral equation (LBIE) method for solving problems of elasticity with nonhomogeneous material properties. Comput Mech. 24:2000;456-462.
9. Sladek J, Sladek V, Zhang Ch. Transient heat conduction analysis in functionally graded materials by the meshless local boundary integral equation method. Submitted for publication; 2002.
10. Belytschko T., Krongauz Y., Organ D., Fleming M., Krysl P. Meshless methods: an overview and recent developments. Comput Meth Appl Mech Engng. 139:1996;3-47.
11. Chen H.T., Lin J.Y. Application of Laplace transform to nonlinear transient problems. Appl Math Modelling. 15:1992;144-151.
12. Ramachandran P.A. Application of the boundary element method to nonlinear diffusion with reaction problems. Int J Numer Meth Engng. 29:1990;1021-1031.
13. Sladek V., Sladek J., Atluri S.N., Van Keer R. Numerical integration of singularities in meshless implementation of local boundary integral equations. Comput Mech. 25:2000;394-403.
14. Chati M.K., Paulino G.H., Mukherjee S. The meshless standard and hypersingular boundary node methods: applications to error estimation and adaptivity in three-dimensional problems. Int J Numer Meth Engng. 50:2001;2233-2269.
15. Stehfest H. Algorithm 368: numerical inversion of Laplace transform. Comm Assoc Comput Mach. 13:1970;47-49.
16. Zhu S., Satravaha P. An efficient computational method for modelling transient heat conduction with nonlinear source terms. Appl Math Modelling. 20:1996;513-522.
17. Frank-Kamenetskii D.A. Diffusion and heat exchange in chemical kinetics. 1955;Princeton University Press, Princeton.