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Shape Design Optimization of Crack Propagation Problems Using Meshfree Methods

무요소법을 이용한 균열진전 문제의 형상 최적설계

  • Kim, Jae-Hyun (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 Ocean Engineering, Korea Maritime and Ocean University) ;
  • Cho, Seonho (National Creative Research Initiatives(NCRI) Center for Isogeometric Optimal Design, Department of Naval Architecture and Ocean Engineering, Seoul National University)
  • 김재현 (서울대학교 아이소-지오메트릭 최적설계 창의연구단) ;
  • 하승현 (한국해양대학교 해양공학과) ;
  • 조선호 (서울대학교 아이소-지오메트릭 최적설계 창의연구단)
  • Received : 2014.03.04
  • Accepted : 2014.09.24
  • Published : 2014.10.31

Abstract

This paper presents a continuum-based shape design sensitivity analysis(DSA) method for crack propagation problems using a reproducing kernel method(RKM), which facilitates the remeshing problem required for finite element analysis(FEA) and provides the higher order shape functions by increasing the continuity of the kernel functions. A linear elasticity is considered to obtain the required stress field around the crack tip for the evaluation of J-integral. The sensitivity of displacement field and stress intensity factor(SIF) with respect to shape design variables are derived using a material derivative approach. For efficient computation of design sensitivity, an adjoint variable method is employed tather than the direct differentiation method. Through numerical examples, The mesh-free and the DSA methods show excellent agreement with finite difference results. The DSA results are further extended to a shape optimization of crack propagation problems to control the propagation path.

Acknowledgement

Supported by : 한국연구재단

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