Nonlinear Response Structural Optimization of a Spacer Grid Spring for a Nuclear Fuel Rod Using the Equivalent Loads

등가하중을 이용한 원자로 핵연료봉 지지격자 스프링의 비선형 응답 구조 최적설계

  • 김도원 (한양대학교 대학원 기계공학과) ;
  • 이현아 (한양대학교 대학원 기계공학과) ;
  • 송기남 (한국원자력연구소) ;
  • 김용일 (한양대학교 대학원 기계공학과) ;
  • 박경진 (한양대학교 기계정보경영학부)
  • Published : 2007.12.01


The spacer grid set is a part of a nuclear fuel assembly. The set has a spring and the spring supports the fuel rods safely. Although material nonlinearity is involved in the deformation of the spring, nonlinearity has not been considered in design of the spring. Recently a nonlinear response structural optimization method has been developed using equivalent loads. It is called nonlinear response optimization equivalent loads (NROEL). 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. Shape optimization of the spring is carried out based on EL. The objective function is defined by minimizing the maximum stress in the spring while mass is limited and the support force of the spring is larger than a certain value. The results are verified by nonlinear response analysis. ABAQUS is used for nonlinear response analysis and GENESIS is employed for linear response optimization.


Spacer Grid;Shape Optimization;Nonlinear Response Optimization;Equivalent Load(EL)


  1. Park, G J., Park, K J. and Lee, J. N., 2001, 'Impact Analysis of the Spacer Grid Assembly and Shape Optimization of the Attached Spring,' KAERI/CM-509/2001, pp. 1-73
  2. Park, G. J., Park, K. J., Kwon, Y. D. and Lee, J. J., 2006, 'Impact Analysis of the Spacer Grid Assembly and Axiomatic Design based Shape Optimization of the Attached Spring,' KAERI/CM-911/2005, pp. 7-43
  3. Park, G.J., Lee, H. A., Kim, C. K., and Song, K. N., 2007, 'Development of the High Performance Spacer Grid,' KAERI/ CM-949/2006, pp. 7-43
  4. im, Y. J., Lee, H. A. and Park, G. J., 2006, 'Case Studies of Nonlinear Response Structural Optimization using Equivalent Loads,' The Fourth China-Japan-Korea Joint Symposium on Optimization Of Structural and Mechanical Systems, CJK-OSM4, Kunming, China, pp. 83-88
  5. 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, Vol. 196, Issues 4-6, 1, pp. 1154-1167
  6. 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
  7. GENESIS Version 7.5, User's Manual, 2001, Vanderplaats Research and Development, Inc., Colorado Springs, CO
  8. ABAQUS/Standard Version 6.4-1, User's Manual, 2004, Hibbit, Karlson and Sorensen, Inc., Pawtucket, RI
  9. Vanderplaats, G.N., 1984, Numerical Optimization Techniques for Engineering Design, McGraw-Hill Book Company, New York, USA
  10. Taylor, J. E. and Bendsoe, M. P., 1984, 'An Interpretation for Min-Max Structural Design Problems Including a Method for Relaxing Constraints,' International Journal of Solids Structures, Vol. 20, No. 4, pp. 301-314
  11. Arora, J.S., 2004, Introduction to Optimum Design, Elsevier Academic Press, CA
  12. Stephen Prata and Lee. D. H., 1999, 'C++ Basic Plus,' Sungandang, Korea
  13. 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
  14. Lee, H. A., Kim, C. K., Song, K. N. and Park, G. J., 2007, 'Optimization of a Nuclear Fuel Spacer Grid Using Considering Impact and Wear with Homology Constraints,' Computational Structural Engineering Institute of Korea Annual Conference, Seoul, Korea

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