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Structural and Multidisciplinary Optimization

, Volume 59, Issue 1, pp 311–316 | Cite as

Discussion on the optimality condition of the equivalent static loads method for linear dynamic response structural optimization

  • Gyung-Jin ParkEmail author
  • Youngmyung Lee
BRIEF NOTE
  • 182 Downloads

Abstract

The equivalent static loads method (ESLM) is a structural optimization method that can consider an analysis method other than linear static analysis. This method defines two separate domains: the analysis domain and design domain. Analysis is performed in the analysis domain, equivalent static loads (ESLs) sets are generated, linear static response optimization is carried out in the design domain using the ESLs and the process iterates until the stopping criteria are satisfied. This method is quite popular and some commercial systems have installed the method. Theoretical foundation of ESLM was validated for linear dynamic response optimization by Park and Kang (J Optim Theory Appl 18:191‑200, 2003). They claimed that when the ESLM process terminates, the optimum solution satisfies the Karush-Kuhn-Tucker (KKT) necessary condition. Some critical issues were raised by Stolpe (Struct Multidiscip Optim 50:921‑926, 2014). He showed that the theoretical results in Park and Kang are not valid. In this paper, the validation process of Park and Kang is amended according to the Stolpe’s corrections. It is shown that the original claim for the KKT condition is valid by adding some mathematical aspects.

Keywords

Equivalent static loads method Structural optimization Karush-Kuhn-Tucker necessary condition 

Notes

Acknowledgments

This work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MEST) (No. 2017R1A2B4004480). The authors are thankful to Mrs. MiSun Park for the English correction of the manuscript.

References

  1. Choi WS, Park GJ (2002) Structural optimization using equivalent static loads at all time intervals. Comput Methods Appl Mech Eng 191(19):2105–2122CrossRefGoogle Scholar
  2. GENESIS user's manual version 13.1 design reference (2014) Vanderplaats Research and Development, Inc., Colorado Springs, CO, USAGoogle Scholar
  3. Haftka RT, Gürdal Z (2012) Elements of structural optimization. Springer Science & Business Media, GermanyzbMATHGoogle Scholar
  4. Kim E, Kim H, Baek S, Cho M (2014) Effective structural optimization based on equivalent static loads combined with system reduction method. Struct Multidiscip Optim 50(5):775–786CrossRefGoogle Scholar
  5. Kim YI, Park GJ (2010) Nonlinear dynamic response structural optimization using equivalent static loads. Comput Methods Appl Mech Eng 199(9):660–676CrossRefGoogle Scholar
  6. Lee JJ, Park GJ (2014) Optimization of the structural and process parameters in the sheet metal forming process. J Mech Sci Technol 28(2):605–619CrossRefGoogle Scholar
  7. Lee Y, Park GJ (2017) Non-linear dynamic response structural optimization for frontal-impact and side-impact crash tests. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 231(5):600–614Google Scholar
  8. NASTRAN user's guide (2013) MSC Software Co., CA, USAGoogle Scholar
  9. Altair OptiStruct user’s manual version 13.0 (2014) Altair Engineering, Inc., MI, USAGoogle Scholar
  10. Park GJ (2007) Analytic methods for design practice. Springer Science & Business Media, GermanyzbMATHGoogle Scholar
  11. Park GJ (2011) Technical overview of the equivalent static loads method for non-linear static response structural optimization. Struct Multidiscip Optim 43(3):319–337CrossRefGoogle Scholar
  12. Park GJ, Kang BS (2003) Validation of a structural optimization algorithm transforming dynamic loads into equivalent static loads. J Optim Theory Appl 118(1):191–200MathSciNetCrossRefGoogle Scholar
  13. Schmit LA (1981) Structural synthesis-its genesis and development. AIAA J 19(10):1249–1263CrossRefGoogle Scholar
  14. Shin MK, Park KJ, Park GJ (2007) Optimization of structures with nonlinear behavior using equivalent loads. Comput Methods Appl Mech Eng 196(4):1154–1167CrossRefGoogle Scholar
  15. Stolpe M (2014) On the equivalent static loads approach for dynamic response structural optimization. Struct Multidiscip Optim 50(6):921–926MathSciNetCrossRefGoogle Scholar
  16. Yi SI, Lee HA, Park GJ (2011) Optimization of a structure with contact conditions using equivalent loads. J Mech Sci Technol 25(3):773–782CrossRefGoogle Scholar
  17. Yoo JT, Yoon JH, Lee HS, Youn SK (2014) Blank optimization for free bulging of Inconel 718 to maximize bulged height at high temperatures. J Mech Sci Technol 28(8):3095–3102CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Hanyang UniversityAnsanRepublic of Korea

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