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Mathematical Proof for Structural Optimization with Equivalent Static Loads Transformed from Dynamic Loads

동하중에서 변환된 등가정하중에 의한 최적화 방법의 수학적 고찰

  • 박경진 (한양대학교 기계설계학과) ;
  • 강병수 (한양대학교 기계설계학과 대학원)
  • Published : 2003.02.01

Abstract

Generally, structural optimization is carried out based on external static loads. All forces have dynamic characteristics in the real world. Mathematical optimization with dynamic loads is extremely difficult in a large-scale problem due to the behaviors in the time domain. The dynamic loads are often transformed into static loads by dynamic factors, design codes, and etc. Therefore, the optimization results can give inaccurate solutions. Recently, a systematic transformation has been proposed as an engineering algorithm. Equivalent static loads are made to generate the same displacement field as the one from dynamic loads at each time step of dynamic analysis. Thus, many load cases are used as the multiple leading conditions which are not costly to include in modern structural optimization. In this research, it is mathematically proved that the solution of the algorithm satisfies the Karush-Kuhn-Tucker necessary condition. At first, the solution of the new algorithm is mathematically obtained. Using the termination criteria, it is proved that the solution satisfies the Karush-Kuhn-Tucker necessary condition of the original dynamic response optimization problem. The application of the algorithm is discussed.

Keywords

Dynamic Response Optimization;Equivalent Static Load;Karush-Kuhn-Tucker Necessary Condition;Structural Optimization

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