Analysis of Dynamic Crack Propagation using MLSDifference Method

윤 영철; Yoon Young-Cheol; 김 경환; Kim Kyeong-Hwan; 이 상호; Lee Sang-Ho

doi:10.7734/COSEIK.2014.27.1.17

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2014 Vol.27, Issue 1 Preview Page Next Page

Analysis of Dynamic Crack Propagation using MLSDifference Method

2014. pp. 17-26

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Abstract

본 논문은 MLS(Moving Least Squares) 차분법을 바탕으로 동적균열전파 해석을 수행하기 위한 알고리즘을 제시한다. MLS 차분법은 절점만으로 이루어진 수치모델을 사용하며, 이동최소제곱법을 이용하여 전개한 Taylor 다항식을 기초로 미분근사식을 유도하기 때문에, 요소망의 제약에서 완벽하게 벗어난 절점해석이 가능하다. 시간항을 포함하는 동적 평형방정식은 Newmark 방법으로 시간적분 하였다. 동적하중을 받는 균열이 전파할 때, 매 시간단계마다 절점모델을 재구성하지 않고 균열선단 주변에서 국부적인 수정을 통해 해석이 가능하다. 동적균열을 묘사하기 위해 가시한계법(visibility criterion)을 적용하였고, 동적 에너지해방률을 산정하여 균열의 진전유무와 그에 상응하는 진전방향을 결정하였다. 모드Ⅰ 상태와 혼합모드 상태에서 균열이 진전하는 현상을 모사하였고, 이론해와 Element-Free Galerkin법으로 계산한 결과와의 비교를 통해 개발된 알고리즘의 정확성과 안정성을 검증하였다.

키워드

dynamic crack propagation, MLS difference method, newmark method, visibility criterion, dynamic energy release rate

동적균열전파해석, MLS 차분법, Newmark 방법, 가시한계법, 동적 에너지해방률

This paper presents a dynamic crack propagation algorithm based on the Moving Least Squares(MLS) difference method. The derivative approximation for the MLS difference method is derived by Taylor expansion and moving least squares procedure. The method can analyze dynamic crack problems using only node model, which is completely free from the constraint of grid or mesh structure. The dynamic equilibrium equation is integrated by the Newmark method. When a crack propagates, the MLS difference method does not need the reconstruction of mode model at every time step, instead, partial revision of nodal arrangement near the new crack tip is carried out. A crack is modeled by the visibility criterion and dynamic energy release rate is evaluated to decide the onset of crack growth together with the corresponding growth angle. Mode I and mixed mode crack propagation problems are numerically simulated and the accuracy and stability of the proposed algorithm are successfully verified through the comparison with the analytical solutions and the Element-Free Galerkin method results.

키워드

dynamic crack propagation, MLS difference method, newmark method, visibility criterion, dynamic energy release rate

동적균열전파해석, MLS 차분법, Newmark 방법, 가시한계법, 동적 에너지해방률

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Information

Publisher :Computational Structural Engineering Institute of Korea
Publisher(Ko) :한국전산구조공학회
Journal Title :Journal of the Computational Structural Engineering Institute of Korea
Journal Title(Ko) :한국전산구조공학회 논문집
Volume : 27
No :1
Pages :17-26
Received Date : 2013-09-03
Revised Date : 2013-11-19
Accepted Date : 2013-11-20
DOI :https://doi.org/10.7734/COSEIK.2014.27.1.17

Journal of the Computational Structural Engineering Institute of Korea ISSN:1229-3059(Print) 2287-2302(Online) 한국전산구조공학회 논문집

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