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


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.


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



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.


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Copyright information

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

Authors and Affiliations

  1. 1.Hanyang UniversityAnsanRepublic of Korea

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