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

경계요소법을 이용한 2 차원 복수 영역 열전도 고체의 형상 설계 민감도 해석

  • 이부윤 (계명대학교 기계자동차공학부) ;
  • 임문혁 (계명대학교 기계자동차공학부)
  • Published : 2003.08.01


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.


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