Journal of the Korean Society for Precision Engineering (한국정밀공학회지)

Korean Society for Precision Engineering (한국정밀공학회)
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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
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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

References

  1. Burczynski, T., 'Recent Advances in Boundary Element Approach to Design Sensitivity Analysis - a Survey,' In Design-Sensitivity Analysis (Edited by M. Kleiber and T. Hisada), Atianta Technology Publications, Atlanta, pp. 1-25, 1993
  2. Lee, B. Y., 'Direct Differentiation Formulation for Boundary Element Shape Sensitivity Analysis of Axisymmetric Elastic Solids,' Int. J. Solids Struct., Vol. 34, pp. 99-112, 1997 https://doi.org/10.1016/0020-7683(95)00290-1
  3. Choi, J. H., Lee, B. Y. & Han, J. S., 'Boundary Integral Method for Shape Optimization of Interface Problem and its Application to Implant Design in Dentistry,' Comp. Meth. Appl. Mech. Engng., Vol. 190, pp.6909-6926,2001 https://doi.org/10.1016/S0045-7825(01)00269-9
  4. Haug, E. J., Choi, K. K. & Komkov, V., Design Sensitivity Analysis of Structural Systems, Academic Press, New York, 1986
  5. Meric, R. A., Boundary Elements in Shape Design Sensitivity Analysis of Thermoelastic Solids, In Computer Aided Optimal Design: Structural and Mechanical Systems, (Edited by C.A. Mota Soares). Springer-Verlag, Berlin Heidelberg, pp. 7643-652, 1987
  6. Meric, R. A., 'Shape Design Sensitivity Analysis for Nonlinear Anisotropic Heat Conducting Solids and Shape Optimization by the BEM,' Int. J. Numer. Methods Engng., Vol. 26, pp. 109-120, 1988 https://doi.org/10.1002/nme.1620260108
  7. Meric, R. A., 'Differential and integral sensitivity formulations and shape optimization by BEM,' Engng. Anal. Boundary Elem., Vol. 15, pp. 181-188, 1995 https://doi.org/10.1016/0955-7997(95)00016-H
  8. Park, C. W. & Yoo, Y. M., 'Shape Design Sensitivity Analysis of a Two-Dimensional Heat Transfer System using the Boundary Element Method,' Comp. Struct., Vol. 28, pp. 543-550, 1988 https://doi.org/10.1016/0045-7949(88)90027-2
  9. Lee, B. Y. & Kwak, B. M., 'Shape Optimization of Two-Dimensional Thermoelastic Structures using Boundary Integral Equation Formulation,' Comp. Struct., Vol. 41, pp. 709-722,1991 https://doi.org/10.1016/0045-7949(91)90181-K
  10. Lee, B. Y. & Kwak, B. M., 'Axisymmetric Thermoelastic Shape Sensitivity Analysis and its Application to Turbine Disc Design,' Int. J. Numer. Methtods Engng., Vol. 33, pp. 2073-2089, 1992 https://doi.org/10.1002/nme.1620331006
  11. Lee, B. Y., Choi, J. H. & Kwak, B. M., 'Shape Optimization of Two-Dimensional Thermal Conducting Solid using Boundary Integral Equation Formulation,' Korean Soc. Mech. Engrs J., Vol. 6, pp. 114-121,1992
  12. Lee, B. Y., Choi, J. H. & Kwak, B. M., Direct Differentiation Method for Shape Design Sensitivity Analysis of Thermal Conducting Solids, In Design-Sensitivity Analysis, ed. M. Kleiber & T. Hisada, Atlanta Technology Publications, Atlanta, pp. 140-165,1993
  13. Lee, B. Y., 'Shape Sensitivity Formulation for Axisymmetric Thermal Conducting Solids,' Proc. Instn Mech. Engrs, Part C J. Mech. Engng. Sci., Vol. 207, pp. 209-216, 1993
  14. Aithal, R. & Saigal, S., 'Shape Sensitivity Analysis in Thermal Problems using BEM,' Engng. Anal. Boundary Elem., Vol. 15, pp. 115-120, 1995 https://doi.org/10.1016/0955-7997(95)00010-L
  15. Sluzalec, A. & Kleiber, M., 'Shape Sensitivity Analysis for Nonlinear Steady-State Heat Conduction Problems,' Int. J. Heat Mass Transfer, Vol. 12, pp. 2609-2613, 1996 https://doi.org/10.1016/0017-9310(95)00237-5
  16. Kane, J. H. & Wang, H., 'Boundary Element Shape Sensitivity Analysis Formulations for Thermal Problems with Nonlinear Boundary Conditions,' AIAA. J., Vol. 29, pp. 1978-1989, 1991 https://doi.org/10.2514/3.10828
  17. Kane, J. H. & Wang, H., 'Boundary Formulations for Shape Sensitivity of Temperature Dependent Conductivity Problems,' Int. J. Numer. Methtods Engng., Vol. 33, pp. 2073-2089, 1992 https://doi.org/10.1002/nme.1620331006
  18. Dems, K. & Mroz, Z., 'Sensitivity Analysis and Optimal Design of External Boundaries and Interfaces for Heat Conduction Systems,' J. Thermal Stresses, Vol. 21, pp. 461-488,1998 https://doi.org/10.1080/01495739808956156
  19. Mustoe, G. G. W., 'A Combination of the Finite Element Method and Boundary Integral Procedure for Continuum Problems,' Ph.D. Thesis, University of Wales, University College, Swansea, 1980
  20. Arora, J. S., An Algorithm for Optimum Structural Design without Line Search, In New Directions in Optimum Structural Design, ed. E. Atrek, Wiley, New York, pp. 429-441, 1984