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

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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A Gridless Finite Difference Method for Elastic Crack Analysis

탄성균열해석을 위한 그리드 없는 유한차분법

  • 윤영철 (명지전문대학 토목과) ;
  • 김동조 (연세대학교 사회환경시스템공학부) ;
  • 이상호 (연세대학교 사회환경시스템공학부)
  • Published : 2007.06.30
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Abstract

This study presents a new gridless finite difference method for solving elastic crack problems. The method constructs the Taylor expansion based on the MLS(Moving Least Squares) method and effectively calculates the approximation and its derivatives without differentiation process. Since no connectivity between nodes is required, the modeling of discontinuity embedded in the domain is very convenient and discontinuity effect due to crack is naturally implemented in the construction of difference equations. Direct discretization of the governing partial differential equations makes solution process faster than other numerical schemes using numerical integration. Numerical results for mode I and II crack problems demonstrates that the proposed method accurately and efficiently evaluates the stress intensity factors.

본 연구는 탄성균열문제를 신속하고 정확하게 해석할 수 있는 새로운 개념의 그리드(grid) 없는 유한차분법을 제시한다. 이동최소제곱법을 이용한 Taylor 전개식 구성을 통해 직접적인 미분계산 없이 근사함수와 그 미분을 손쉽게 계산한다. 그리드로 인한 절점 간의 종속성이 없어 해석영역 내의 불연속면 모델링이 용이하여 차분식 구성시 균열로 인한 불연속 효과를 고려하는 과정도 자연스럽다. 유한차분법에 근간을 두고 있어 지배 미분방정식을 직접 이산화하기 때문에 수치적분이 필요한 수치기법에 비해 계산속도도 빠르다. 모드 I과 모드 II 균열문제 해석을 통해 본 해석기법이 정확하고 효율적으로 응력확대계수를 계산할 수 있음을 보였다.

Keywords

References

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