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

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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Adaptive Element-free Galerkin Procedures by Delaunay Triangulation

Delaunay 삼각화를 이용한 적응적 Element-free Galerkin 해석

  • 이계희 (시설안전기술공단 진단1본부,) ;
  • 정흥진 (전주대학교 토목환경공학과) ;
  • 최창근 (한국과학기술원 토목공학과, 석좌교수)
  • Published : 2001.12.01
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Abstract

In this paper, a new adaptive analysis scheme for element-free Galerkin method(EFGM) is proposed. The novel point of this scheme is that the triangular cell structure based on the Delaunay triangulation is used in the numerical integration and the node adding/removing process. In adaptive analysis with this scheme, there is no need to divide the integration cell and the memory cell structure. For the adaptive analysis of crack propagation, the reconstruction of cell structure by adding and removing the nodes on integration cells based the estimated error should be carried out at every iteration step by the Delaunay triangulation technique. This feature provides more convenient user interface that is closer to the real mesh-free nature of EFGM. The analysis error is obtained basically by calculating the difference between the values of the projected stresses and the original EFG stresses. To evaluate the performance of proposed adaptive procedure, the crack propagation behavior is investigated for several examples.

본 연구에서는 무요소법의 일종인 element-free Galerkin 방법(EFGM)을 이용한 새로운 적응적 해석법을 제안하였다. 이 방법의 핵심은 Delaunay 삼각화에 기초를 둔 적분 격자를 기초로 수치적분과 적응적인 절점의 추가 및 소거를 수행하는 것이다. 이러한 적응적 해석법은 적분격자의 분할이나 이를 위한 추가적인 정보에 대한 관리가 필요 없이 간편하게 적응적 해석을 수행할 수 있다. 또한 균열의 진전과 같은 다단계 적응적 해석에 있어서도 매 해석단계별로 평가된 오차에 기초를 둔 최적 해석모델이 Delaunay 삼각화에 의해 구성되도록 하였다. 이러한 특성은 요소의 구성으로부터 자유로운 무요소법의 장점을 최대한 활용하여 해석모델의 구축을 보다 원활하게 수행할 수 있다. 적응적 해석에 기초가 되는 해석 후 오차평가는 계산된 응력과 투영응력과의 차이를 오차로 추정하는 투영응력법을 이용하였다. 균열진전을 포함하는 2차원예제의 해석을 수행한 결과 제안된 해석법의 타당성과 적용성을 입증할 수 있었다.

Keywords

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