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 steady-state diffusion equation, in two and three dimensions. The corresponding boundary integral equation formulations for these problems are derived, and the three-dimensional case is solved numerically using a Galerkin approximation. The results of test calculations are in excellent agreement with exact solutions and finite element simulations.
Green’s Functions and Boundary Integral Analysis for Exponentially Graded Materials: Heat Conduction
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Dec. 14, 2000; final revision, Oct. 30, 2001. Associate Editor: M.-J. Pindera. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Department of Mechanical and Environmental Engineering University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
Gray , L. J., Kaplan, T., Richardson, J. D., and Paulino, G. H. (August 25, 2003). "Green’s Functions and Boundary Integral Analysis for Exponentially Graded Materials: Heat Conduction ." ASME. J. Appl. Mech. July 2003; 70(4): 543–549. https://doi.org/10.1115/1.1485753
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