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Level Set Based Shape Optimization of Linear Structures using Topological Derivatives

위상민감도를 이용한 선형구조물의 레벨셋 기반 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) ;
  • Kim, Min-Geun (WTG development team, Samsung Heavy Industries) ;
  • 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) ;
  • 김민근 (삼성중공업 풍력발전사업부) ;
  • 조선호 (서울대학교 아이소-지오메트릭 최적설계 창의연구단)
  • Received : 2013.07.01
  • Accepted : 2014.01.28
  • Published : 2014.02.28

Abstract

Using a level set method and topological derivatives, a topological shape optimization method that is independent of an initial design is developed for linearly elastic structures. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set function, which facilitates to handle complicated topological shape changes. The "Hamilton-Jacobi(H-J)" equation and computationally robust numerical technique of "up-wind scheme" lead the initial implicit boundary to an optimal one according to the normal velocity field while minimizing the objective function of compliance and satisfying the constraint of allowable volume. Based on the asymptotic regularization concept, the topological derivative is considered as the limit of shape derivative as the radius of hole approaches to zero. The required velocity field to update the H-J equation is determined from the descent direction of Lagrangian derived from optimality conditions. It turns out that the initial holes are not required to get the optimal result since the developed method can create holes whenever and wherever necessary using indicators obtained from the topological derivatives. It is demonstrated that the proper choice of control parameters for nucleation is crucial for efficient optimization process.

Acknowledgement

Supported by : 한국연구재단

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