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

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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Topology Optimization based on Monte Carlo Analysis

몬테카를로 해석 기반 확률적 위상최적화

  • Kim, Dae Young (Department of Civil and Environmental Engineering, Sejong Univ.) ;
  • Noh, Hyuk Chun (Department of Civil and Environmental Engineering, Sejong Univ.)
  • 김대영 (세종대학교 건설환경공학과) ;
  • 노혁천 (세종대학교 건설환경공학과)
  • Received : 2017.02.01
  • Accepted : 2017.02.03
  • Published : 2017.04.28
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Abstract

In this paper, we take into account topology optimization problems considering spatial randomness in the material property of elastic modulus. Based on 88 lines MATLAB Code, Monte Carlo analysis has been performed for MBB(messerschmidt-$b{\ddot{o}}lkow$-blohm) model using 5,000 random sample fields which are generated by using the spectral representation scheme. The random elastic modulus is assumed to be Gaussian in the spatial domain of the structure. The variability of the volume fraction of the material, which affects the optimum topology of the given problem, is given in terms of correlation distance of the random material. When the correlation distance is small, the randomness in the topology is high and vice versa. As the correlation distance increases, the variability of the volume fraction of the material decreases, which comply with the feature of the linear static analysis. As a consequence, it is suggested that the randomness in the material property is need to be considered in the topology optimization.

본 논문에서는 재료 탄성계수의 공간적 불확실성을 고려한 위상최적화 문제를 다루었다. 88줄로 작성된 MATLAB Code를 사용하여 MBB(messerschmidt-$b{\ddot{o}}lkow$-blohm) model에 대해 5,000개의 추계장 표본을 작성하여 해석에 사용하였다. 재료탄성계수의 추계장 표본은 스펙트럼 모사법을 적용하여 작성하였고, 구조계영역 내에서 정규분포하는 것으로 가정하였다. 해석결과에 대한 통계처리를 통하여 형상최적화의 결과를 나타내는 체적률의 변화도를 추계장의 상관거리에 대하여 나타내었다. 최적형상의 변화도는 상관거리가 작을 경우 크게 산정되었고, 상관거리가 큰 경우에는 적은 값을 나타내었다. 큰 상관거리에서 변화도가 적은 것은 위상최적화가 선형해석에 따르기 때문이다. 따라서 위상최적화 시 구조재료 불확실성의 특성에 따른 고려가 필요한 것으로 사료된다.

Keywords

References

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