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Shape Design Sensitivity Analysis of Two-Dimensional Thermal Conducting Solids with Multiple Domains Using the Boundary Element Method  

이부윤 (계명대학교 기계자동차공학부)
임문혁 (계명대학교 기계자동차공학부)
Publication Information
Journal of the Korean Society for Precision Engineering / v.20, no.8, 2003 , pp. 175-184 More about this Journal
Abstract
A method of the shape design sensitivity analysis based on the boundary integral equation formulation is presented for two-dimensional inhomogeneous thermal conducting solids with multiple domains. Shape variation of the external and interface boundary is considered. A sensitivity formula of a general performance functional is derived by taking the material derivative to the boundary integral identity and by introducing an adjoint system. In numerical analysis, state variables of the primal and adjoint systems are solved by the boundary element method using quadratic elements. Two numerical examples of a compound cylinder and a thermal diffuser are taken to show implementation of the shape design sensitivity analysis. Accuracy of the present method is verified by comparing analyzed sensitivities with those by the finite difference. As application to the shape optimization, an optimal shape of the thermal diffuser is found by incorporating the sensitivity analysis algorithm in an optimization program.
Keywords
Shape design sensitivity analysis; Boundary integral equation; Boundary element method; Thermal conduction; Inhomogeneous; Multiple domain;
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