Journal of the Computational Structural Engineering Institute of Korea (한국전산구조공학회논문집)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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Isogeometric Shape Design Optimization of Power Flow Problems at High Frequencies

고주파수 파워흐름 문제의 아이소-지오메트릭 형상 최적설계

  • Yoon, Minho (National Creative Research Initiatives(NCRI) Center for Isogeometric Optimal Design, Department of Naval Architecture and Ocean Engineering, Seoul National University) ;
  • Ha, Seung-Hyun (Department of Civil Engineering, Johns Hopkins University) ;
  • Cho, Seonho (National Creative Research Initiatives(NCRI) Center for Isogeometric Optimal Design, Department of Naval Architecture and Ocean Engineering, Seoul National University)
  • 윤민호 (서울대학교 아이소-지오메트릭 최적설계 창의연구단) ;
  • 하승현 (존스홉킨스대학교 토목공학과) ;
  • 조선호 (서울대학교 아이소-지오메트릭 최적설계 창의연구단)
  • Received : 2014.03.17
  • Accepted : 2014.05.17
  • Published : 2014.06.30
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Abstract

Using an isogeometric approach, a continuum-based shape design optimization method is developed for steady state power flow problems at high frequencies. In case the isogeometric method is employed to the shape design optimization, the NURBS basis functions used in CAD geometric modeling are directly utilized to embed the exact geometry into the computational framework so that the design parameterization for shape optimization is much easier than that in the finite element method and consequently provides the enhanced smoothness of design perturbations. Thus, exact geometric models can be used in both the response and the shape sensitivity analyses, where normal vector and curvature are continuous over the whole design space so that enhanced shape sensitivity can be expected. Through numerical examples, the developed isogeometric sensitivity is compared with finite difference one to provide excellent agreement. Also, it turns out that the proposed method works very well in the shape optimization problems.

본 논문에서는 아이소-지오메트릭 해석법을 이용하여 고주파수를 가지는 파워흐름 문제에 대하여 연속체 기반 형상 최적 설계를 수행하였다. 아이소-지오메트릭 기법을 형상 최적설계에 적용하면, CAD 기하 모델링에서 쓰이던 NURBS 기저 함수가 직접 쓸 수 있기에 정확한 기하학 정보가 수치계산에서 고려되고, 이에 따라 형상 최적설계 관점에서 볼 때, 전통적인 유한요소법에 비해 향상되고 부드러운 설계 섭동량을 가지는 설계 매개화가 가능하게 된다. 즉, 정확한 기하 모델이 응답 해석과 설계민감도 해석에 쓰이게 되고, 이에 따라 설계영역 전체에서 법선 벡터와 곡률이 연속적으로 되게 된다. 결과적으로 정밀한 민감도 해석이 가능하게 된다. 몇 가지 수치예제를 통하여 개발된 아이소-지오메트릭 설계민감도가 유한차분 설계민감도와 비교하여 정확성을 확인할 수 있었으며, 형상 최적설계 문제를 통해서 본 방법론을 적용하여 검증하였다.

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References

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