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Level Set Based Topological Shape Optimization Combined with Meshfree Method

레벨셋과 무요소법을 결합한 위상 및 형상 최적설계

  • Ahn, Seung-Ho (National Creative Research Initiatives(NCRI) Center for Isogeometric Optimal Design, Department of Naval Architecture and Ocean Engineering, Seoul National University) ;
  • Ha, Seung-Hyun (National Creative Research Initiatives(NCRI) Center for Isogeometric Optimal Design, Department of Naval Architecture and Ocean Engineering, Seoul National University) ;
  • Cho, Seonho (National Creative Research Initiatives(NCRI) Center for Isogeometric Optimal Design, Department of Naval Architecture and Ocean Engineering, Seoul National University)
  • 안승호 (서울대학교 조선해양공학과 아이소-지오메트릭 최적설계 창의연구단) ;
  • 하승현 (서울대학교 조선해양공학과 아이소-지오메트릭 최적설계 창의연구단) ;
  • 조선호 (서울대학교 조선해양공학과 아이소-지오메트릭 최적설계 창의연구단)
  • Received : 2013.07.01
  • Accepted : 2014.02.02
  • Published : 2014.02.28

Abstract

Using the level set and the meshfree methods, we develop a topological shape optimization method applied to linear elasticity problems. Design gradients are computed using an efficient adjoint design sensitivity analysis(DSA) method. The boundaries are represented by an implicit moving boundary(IMB) embedded in the level set function obtainable from the "Hamilton-Jacobi type" equation with the "Up-wind scheme". Then, using the implicit function, explicit boundaries are generated to obtain the response and sensitivity of the structures. Global nodal shape function derived on a basis of the reproducing kernel(RK) method is employed to discretize the displacement field in the governing continuum equation. Thus, the material points can be located everywhere in the continuum domain, which enables to generate the explicit boundaries and leads to a precise design result. The developed method defines a Lagrangian functional for the constrained optimization. It minimizes the compliance, satisfying the constraint of allowable volume through the variations of boundary. During the optimization, the velocity to integrate the Hamilton-Jacobi equation is obtained from the optimality condition for the Lagrangian functional. Compared with the conventional shape optimization method, the developed one can easily represent the topological shape variations.

Acknowledgement

Supported by : 한국연구재단

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