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Consistent Displacement Load Method for Nonlinear Semi-Analytical Design Sensitivity Analysis

준해석적 비선형 설계민감도를 위한 보정변위하중법

  • 이민욱 (한양대학교 대학원 기계설계학과) ;
  • 유정훈 (한양대학교 대학원 기계설계학과) ;
  • 이태희 (한양대학교 기계공학부)
  • Published : 2005.09.01

Abstract

Three methods for design sensitivity such as numerical differentiation, analytical method and semi-analytical method have been developed for the last three decades. Although analytical design sensitivity analysis is exact, it is hard to implement for practical design problems. Therefore, numerical method such as finite difference method is widely used to simply obtain the design sensitivity in most cases. The numerical differentiation is sufficiently accurate and reliable for most linear problems. However, it turns out that the numerical differentiation is inefficient and inaccurate because its computational cost depends on the number of design variables and large numerical errors can be included especially in nonlinear design sensitivity analysis. Thus semi-analytical method is more suitable for complicated design problems. Moreover semi-analytical method is easy to be performed in design procedure, which can be coupled with an analysis solver such as commercial finite element package. In this paper, implementation procedure for the semi-analytical design sensitivity analysis outside of the commercial finite element package is studied and computational technique is proposed, which evaluates the pseudo-load for design sensitivity analysis easily by using the design variation of corresponding internal nodal forces. Errors in semi-analytical design sensitivity analysis are examined and numerical examples are illustrated to confirm the reduction of numerical error considerably.

References

  1. Haftka, R. T. and Adelman, H. M., 1986, 'Sensitivity Analysis for Discrete Structural Systems,' AIAA J, Vol. 24, pp. 823-832 https://doi.org/10.2514/3.48671
  2. Haftka, R. T. and Adelman, H. M., 1989,' Recent Developments ifn Structural Sensitivity Analysis,' Structural Optimization, pp.137-151 https://doi.org/10.1007/BF01637334
  3. Van Keulen, F, Haftka, R. T. and Qu, W-Y, 2000, 'Review of Optionfor Structural Sensitivity Calculations, AIAA-000-1351, pp.11-14
  4. Ryu, Y. S., Hapipian, M., Wu, C. C. and Arora, J. S., 1985, 'Structural Design Sensitivity Analysis of Nonlinear Response, 'Computers & Structures, Vol. 25, No. 1/2, pp.245-255 https://doi.org/10.1016/0045-7949(85)90247-0
  5. Wu, C.C. and Arora, J. S., 1987, 'Design Sensitivity Analysis and Optimizaiton of Nonlinear Structural Response using Incremental Procedure,' AIAA J. Vol. 25, No.8. pp.1118-1125 https://doi.org/10.2514/3.9752
  6. Van Keulen, F. and de Boer, H., 1998, 'Rigorous Improvement of Semi-Analytical Design Sensitivities By Exact Differentiation of Rigid Body Motion,'International Journal for Mumerical Methods in Engineering, Vol. 42, pp.71-91 https://doi.org/10.1002/(SICI)1097-0207(19980515)42:1<71::AID-NME350>3.0.CO;2-C
  7. Van Keulen, F. and De Noer, H., 2000,'Refine Semi-analytical Design Sensitivities,' Int. J. Solids and Structures Vol. 37. No. 6961-6980 https://doi.org/10.1016/S0020-7683(99)00322-4
  8. Kim, H. and Cho, M., 20010, 'A Refined Semi-Analytic Sensitivity Study Based on the Node Decomposition and Neumann Series Expansion (I),' Trans. of the KSME A, Vol.27, No. pp.585-592 https://doi.org/10.3795/KSME-A.2003.27.4.585
  9. Choi, K.K., Santos, J.T.L. and Frederick, M.C., 1987, Implementation of Design Sensitivity Analysis with Exlsting Finite Element Codes,' ASME Journal of Mechanism, transmissions, Automaiton if Design, Vol. 109, pp.385-391 https://doi.org/10.1115/1.3258807
  10. Arora, J. S. and Cardoso, J.E.B.,1989, 'A Design Sensitivity Analysis Principle and Its Implementation into ADINA,'Computers & Structures, Vol. 32. pp 691-705 https://doi.org/10.1016/0045-7949(89)90357-X
  11. Zhang, W.H. and Domaszewski, M., 1998, 'Recent Developments of sizing Optimization with ABAUS Code, 'AIAA-98-4710, pp. 190-197
  12. Lee, T., Yoo, J. and Kim, H., 2004, 'Refined Semi-analytical Design Sensitivity Analysis with Commercial Finite Element Packagem 'AIAA-2004-4534
  13. Lee, T., Yoo, J. and Kim, H., 2004, 'Displacement-Load method for Semi-Analytical Design Sensitivity Anslysis,' Trans. of the KSME A. Vol. 28, No. 10, pp.1590-1597 https://doi.org/10.3795/KSME-A.2004.28.10.1590