Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
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Case Studies of Nonlinear Response Structural Optimization Using Equivalent Loads

등가하중법을 이용한 비선형 반응 구조최적설계 사례연구

  • 김용일 (한양대학교 대학원 기계공학과) ;
  • 박경진 (한양대학교 기계정보경영공학부)
  • Published : 2007.11.01
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Abstract

Nonlinear response structural optimization is performed using equivalent loads (NROEL). Nonlinear response optimization is extremely cost because many nonlinear analyses are required. In NROEL, the external loads are transformed to the equivalent loads (EL) for linear static analysis and linear response optimization is carried out based on the EL in a cyclic manner until the convergence criteria are satisfied. EL is the load set which generates the same response field of linear analysis as that of nonlinear analysis. The primitive from of theory has been published. In this research, the theory is investigated with large scale example problems. Four examples are solved by using NROEL. Conventional optimization with sensitivity analysis using the finite difference method (FDM) is also applied to the same examples. Moreover, response surface optimization method is applied to the last two examples. The results of the optimizations are compared. In nonlinear response optimization of large scale problems, hundreds (or even thousands) of nonlinear analyses are expected to satisfy the convergence criteria. However, in nonlinear response optimization using equivalent loads, only tens of nonlinear analyses are required. The results are discussed and the usefulness of NROEL is presented.

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References

  1. Reddy, J. N., 2004, An Introduction to Nonlinear Finite Element Analysis, Oxford University Press Inc., New York, U.S.A
  2. Bathe, K. J., 1996, Finite Element Procedures, Prentice-Hall, Inc., New Jersey, U.S.A
  3. Robert, D. C., David, S. M., Michael, E. P., Robert, J. W, 2002, Concepts and Applications of Finite Element Analysis, John Wiley & Sons. Inc., New York, U.S.A
  4. Ryu, Y. S., Haririan, M., Wu, C. C. and Arora, J. S., 1985, 'Structural design sensitivity analysis of nonlinear response,' Computers and Structures, Vol. 21, 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 optimization of nonlinear structural response using incremental procedure,' AIAA Journal, Vol. 25, No. 8, pp. 1118-1125 https://doi.org/10.2514/3.9752
  6. Park, G. J., 2007, Analytic Methods in Design Practice, Springer-Verlag., Germany. (will be published)
  7. Haftka, R. T. and Guerdal, Z., 1992, Elements of Structural Optimization, Kluwer Academic Publishers, Netherlands
  8. Arora, J. S., 2004, Introduction to Optimum Design, Elsevier Inc., U.S.A
  9. Thomas, H., 1996, 'Optimization of structures designed using nonlinear FEM analysis,' Proceedings of the 37th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf., AIAA-96-1385-CP, pp. 604-608
  10. Suleman, A. and Sedaghati, R., 2005, 'Benchmark case studies in optimization of geometric nonlinear structures,' Structural and Multidisciplinary Optimization, Vol. 30, pp. 273-296 https://doi.org/10.1007/s00158-005-0524-2
  11. Raymond, H. M. and Douglas, C. M., 2002, Response Surface Methodology, John Wiley & Sons. Inc., New York, U.S.A
  12. Park, K. J. and Park, G. J., 2004, 'Structural optimization of truss with nonlinear response using equivalent linear loads,' Transactions of the KSME (A), Vol. 28, No. 4, pp. 467-474
  13. Park, K. J. and Park, G. J., 2005, 'Structural optimization for nonlinear behavior using equivalent static loads (I),' Transactions of the KSME (A), Vol. 29, No. 8, pp. 1051-1060 https://doi.org/10.3795/KSME-A.2005.29.8.1051
  14. Park, K. J. and Park, G. J., 2005, 'Structural optimization for nonlinear behavior using equivalent static loads (II),' Transactions of the KSME (A), Vol. 29, No. 8, pp. 1061-1069 https://doi.org/10.3795/KSME-A.2005.29.8.1061
  15. Shin, M. K., Park, K. J. and Park, G. J., 2007, 'Optimization of structures with nonlinear behavior using equivalent loads,' Computer Methods in Applied Mechanics and Engineering. (will be published)
  16. ABAQUS/Standard Version 6.4, User's Manual, 2004, Hibbitt, Karlsson and Sorensen, Inc., Pawtucket, RI, U.S.A
  17. Optistruct Version 7.0, User's Manual, 2004, Altair Engineering, Inc., U.S.A
  18. DOT Version 5.x User's Manual, 2001, Vanderplaats Research & Development, Inc., Colorado Springs, U.S.A
  19. Visual DOC Manuals, http://www.vrand.com, 2004, Vanderplaats Research & Development, Inc., Colorado Springs, U.S.A
  20. Stroustrup, B, 2000, The C++ programming language, Addison Wesley, U.S.A

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