ASME Journal of Applied Mechanics,Vol. 70, No.4, pp.543-549, 2003
L. J. Gray,
T. Kaplan and J. D Richardson
Computer Science & Mathematics Division, Oak Ridge
National Laboratory, Oak Ridge, TN 37831-6367.
G.H. Paulino,
Department of Civil and Environmental Engineering, University of Illinois
at Urbana-Champaign, Newmark
Laboratory, 205 North Mathews Avenue, IL
61801-2352
Abstract
Free space Green's functions are derived for graded materials in which the thermal conductivity varies exponentially in one coordinate. Closed form expressions are obtained for the time independent (steady state) diffusion equation, in two and three dimensions. The corresponding boundary integral equation formulations for these problems are derived, and the three dimensional steady state case has
been solved numerically using a Galerkin approximation. The results of test calculations are in excellent agreement with exact solutions and finite element simulations.
Key words: Green's functions, functionally graded materials, diffusion, boundary integral analysis, Galerkin approximation.