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Boundary-Based Shape Design Sensitivity Analysis of Elastostatics Problems

정탄성학 문제에서 경계 기반 형상설계 민감도 해석

  • 원준호 (한국항공대학교 대학원 항공우주 및 기계공학과) ;
  • 최주호 (한국항공대학교 항공우주 및 기계공학과)
  • Published : 2006.02.01

Abstract

A boundary-based design sensitivity analysis(DSA) technique is proposed for addressing shape optimization issues in the elastostatics problems. Sensitivity formula is derived based on the continuum formulation in a boundary integral form, which consists of the boundary solutions and shape variation vectors. Though the boundary element method(BEM) has been mainly used to obtain the boundary solution, the FEM is used in this paper because this is much more popular, and has greatly improved meshing and computing power recently. The advantage of the boundary DSA is that the shape variation vectors, which are also known as design velocity fields, are needed only on the boundary. Then, the step for determining the design velocity field over the whole domain, which was necessary in the domain-based DSA, is eliminated, making the process easy to implement and efficient. Problem of fillet design is chosen to illustrate the efficiency of the proposed method. Accuracy of the sensitivity is good with this method even by employing the free mesh for the FE analysis.

References

  1. Haftka, R. T. and Grandhi, R. V.. 1986, 'Structural shape optimization - a survey,' Computer Methods in Applied Mechanics and Engineering, Vol. 57, pp. 91-106 https://doi.org/10.1016/0045-7825(86)90072-1
  2. Kwak, B. M., 1994, 'A Review on Shape Optimal Design and Sensitivity Analysis,' Journal of Structural Mechanics and Earthquake Engineering, JSCE, Vol. 10, pp. 1595 -1745
  3. Zolesio, J.P., 1981, 'The Material Derivative (or Speed) Method for Shape Optimization,' in Haug EJ and Cea J (eds.), Optimization of Distributed Parameters Structures, Sijthoff-Noordhoff, Alphen aan den Rijn, The Netherlands, pp. 1152 -1194
  4. Rousselet, B. and Haug E. J., 1981, 'Design Sensitivity Analysis of Shape Variation,' in Haug EJ and Cea J, (eds.), Optimization of Distributed Parameter Structures, Sijthoff-Noordhoff, Alphen aan den Rijn, The Netherlands, pp. 1397 -1442
  5. Choi, K. K. and Haug, E. J., 1983, 'Shape Design Sensitivity Analysis of Elastic Structures,' Journal of Structural Mechanics, Vol. 11, No.2, pp. 231-269 https://doi.org/10.1080/03601218308907443
  6. Dems, K. and Mroz, Z., 1984, 'Variational Approach by Means of Adjoint Systems to Structural Optimization and Sensitivity Analysis-II,' Structure Shape Variation. International Journal of Solids and Structures, Vol. 20, No.6, pp. 527 - 552 https://doi.org/10.1016/0020-7683(84)90026-X
  7. Yang, R.J. and Choi, K. K., 1985, 'Accuracy of Finite Element Based Shape Design Sensitivity Analysis,' Journal of Structural Mechanics, Vol. 13,No.2, pp. 223-239 https://doi.org/10.1080/03601218508907498
  8. Choi, K. K. and Seong, H. G., 1986, 'Domain Method for Shape Design Sensitivity Analysis of Built-up Structures,' Computer Methods in Applied Mechanics and Engineering, Vol. 57, No.1, pp. 1-15 https://doi.org/10.1016/0045-7825(86)90066-6
  9. Yang, R. J. and Botkin, M. E., 1987, 'Accuracy of the Domain Material Derivative Approach to Shape Design Sensitivities,' AIAA Journal, Vol. 25, No. 12, pp. 1606-1610 https://doi.org/10.2514/3.9831
  10. Yao, T. M. and Choi, K. K., 1989, '3-D Shape Optimal Design and Automatic Finite Element Regridding,' International Journal for Numerical Methods in Engineering, Vol. 28, pp. 369 - 384 https://doi.org/10.1002/nme.1620280209
  11. Chang, K. H., Choi, K. K., Tsai, C. S., Chen, C. J., Choi, B. S. and Yu, X., 1995, 'Design Sensitivity Analysis and Optimization Tool (DSO) for Shape Design Applications,' Computing Systems in Engineering, Vol. 6, No.2, pp. 151-175 https://doi.org/10.1016/0956-0521(95)00006-L
  12. Hardee, E., Chang, K. H., Tu, J., Choi, K. K., Grindeanu, I. and Yu, X., 1999, 'A CAD-Based Design Parameterization for Shape Optimization of Elastic Solids,' Advances in Engineering Software, Vol. 30, pp 185-199 https://doi.org/10.1016/S0965-9978(98)00065-9
  13. Rodenas, J. J., Fuenmayor, F. J. and Tarancon, J. E. 2004, 'A Numerical Methodology to Assess the Quality of the Design Velocity Field Computation Methods in Shape Sensitivity Analysis,' International Journal for Numerical Methods in Engineering, Vol. 59,pp.1725-1747 https://doi.org/10.1002/nme.933
  14. Burczyski, T. and Adamczyk, T., 1985, 'The Boundary Element Formulation for Multiparameter Structural Shape Optimization,' Applied Mathematical Modelling, Vol. 9, No.3, pp. 195 - 200 https://doi.org/10.1016/0307-904X(85)90007-1
  15. Choi, J. H. and Kwak, B. M., 1988, 'Boundary Integral Equation Method for Shape Optimization of Elastic Structures,' International Journal for Numerical Methods in Engineering, Vol. 26, pp. 1579 -1595 https://doi.org/10.1002/nme.1620260709
  16. Park, C. W., Yoo, Y. M. and Kwon K. H., 1989, 'Shape Design Sensitivity Analysis of an Axisymmetric Turbine Disk Using the Boundary Element Method,' Computers & Structures, Vol. 33, No.1, pp.7-16 https://doi.org/10.1016/0045-7949(89)90123-5
  17. Meric, R. A., 1995, 'Differential and Integral Sensitivity Formulations and Shape Optimization by BEM,' Engineering Analysis with Boundary Elements, Vol. 15,pp. 181-188 https://doi.org/10.1016/0955-7997(95)00016-H
  18. Repalle, J., Grandhi, R. V. and Choi, J. H., 'Boundary Integral Shape Design Sensitivity Analysis of Metal Forming Process - Application to Steady-State Extrusion,' Submitted to
  19. Haug, E. J., Choi, K. K. and Komkov, V., 1985, 'Design Sensitivity Analysis of Structural Systems,' Academic press, New York