Topology Optimization based on Monte Carlo Analysis

Dae Young Kim; Hyuk Chun Noh

doi:10.7734/COSEIK.2017.30.2.153

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2017 Vol.30, Issue 2 Preview Page Next Page

Topology Optimization based on Monte Carlo Analysis 몬테카를로 해석 기반 확률적 위상최적화

2017. pp. 153-158

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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-bo 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.

Keywords

topology optimization

compliance

probabilistic analysis

correlation distance

본 논문에서는 재료 탄성계수의 공간적 불확실성을 고려한 위상최적화 문제를 다루었다. 88줄로 작성된 MATLAB Code 를 사용하여 MBB(messerschmidt-bolkow-blohm) model에 대해 5,000개의 추계장 표본을 작성하여 해석에 사용하였다. 재 료탄성계수의 추계장 표본은 스펙트럼 모사법을 적용하여 작성하였고, 구조계영역 내에서 정규분포하는 것으로 가정하였다. 해석결과에 대한 통계처리를 통하여 형상최적화의 결과를 나타내는 체적률의 변화도를 추계장의 상관거리에 대하여 나타내 었다. 최적형상의 변화도는 상관거리가 작을 경우 크게 산정되었고, 상관거리가 큰 경우에는 적은 값을 나타내었다. 큰 상관 거리에서 변화도가 적은 것은 위상최적화가 선형해석에 따르기 때문이다. 따라서 위상최적화 시 구조재료 불확실성의 특성 에 따른 고려가 필요한 것으로 사료된다.

키워드

형상최적화

컴플라이언스

확률해석

상관거리

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Information

Publisher :Computational Structural Engineering Institute of Korea
Publisher(Ko) :한국전산구조공학회
Journal Title :Journal of the Computational Structural Engineering Institute of Korea
Journal Title(Ko) :한국전산구조공학회 논문집
Volume : 30
No :2
Pages :153-158
Received Date : 2017-02-01
Revised Date : 2017-02-02
Accepted Date : 2017-02-03
DOI :https://doi.org/10.7734/COSEIK.2017.30.2.153

Journal of the Computational Structural Engineering Institute of Korea ISSN:1229-3059(Print) 2287-2302(Online) 한국전산구조공학회 논문집

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