Shape Sensitivities and Optimal Configurations for Heat Diffusion Problems: a BEM Approach

[+] Author and Article Information
S. Saigal

Department of Civil Engineering, Carnegie Institute of Technology, Carnegie Mellon University, Pittsburgh, PA 15213

A. Chandra

Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721

J. Heat Transfer 113(2), 287-295 (May 01, 1991) (9 pages) doi:10.1115/1.2910559 History: Received October 17, 1989; Revised June 04, 1990; Online May 23, 2008


Design sensitivity analysis, along with the shape optimization of heat diffusion problems using the boundary element method (BEM), is presented in this paper. The present approach utilizes the implicit differentiation of discretized boundary integral equations with respect to the design variables to yield the sensitivity equations. A technique based on the response of an object to a constant boundary temperature is presented for the evaluation of singular terms in the thermal sensitivity kernels. A procedure for the design sensitivity analysis of a reduced system of equations obtained via substructuring and condensation is also presented. The BEM formulations are implemented for both two-dimensional and axisymmetric objects. A number of sample problems are solved to demonstrate the accuracy of the present sensitivity formulation and to obtain optimal configurations of some mechanical components of practical interest, which are subjected to different thermal environments.

Copyright © 1991 by The American Society of Mechanical Engineers
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