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

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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A Study on the Analysis Parameter Used in Improved EFG Crack Analysis Technique Based on Error Estimate

오차분석을 통한 개선된 EFG 균열해석기법의 해석계수 영향평가

  • Published : 2002.12.01
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Abstract

Recently, an improved EFG(Element-Free Galerkin) crack analysis technique, which includes a discontinuous approximation and a singular basis function on the auxiliary supports, was developed. The technique is able to accurately analyze the crack propagation problem without any modification of the analysis model; however, it shows some dependency on the analysis parameters used. In this study, the effect of analysis parameters such as the size of compact support, dilation parameter, the smoothness of shape function around the crack tip, and the number of node using auxiliary supports on the accuracy of solution has been investigated. Through a patch test with a crack, relative L₂ error norm of stresses and the stress intensity factor were computed and compared for various analysis parameters and the results were presented as guidelines for adequate choice of analysis parameters.

최근에 불연속 근사변위함수와 보조받침을 이용한 특이기저함수를 도입하여 균열의 불연속성과 특이성을 구현한 개선된 EFG(Element-Free Galerkin) 균열해석기법이 제안되었다. 개선된 EFG 균열해석기법은 균열의 성장에 따른 해석모형의 수정 없이도 높은 정확도로 균열전파해석을 수행할 수 있지만, 다른 무요소법과 마찬가지로 해석결과가 사용되는 해석계수에 의존하게 된다. 본 연구에서는 개선된 EFG 균열해석기법에서 사용하는 해석계수 즉, compact 받침 크기, 팽창계수, 선단주변에서의 형상함수의 평활화, 보조받침을 사용하는 절점개수가 수치해석 결과에 미치는 영향을 분석하였다. 균열문제에 대한 patch 시험을 통해 응력에 대한 L₂오차노름과 응력확대계수를 산정하여 해석계수의 영향을 분석하였으며, 그 결과는 해석계수의 선택에 대한 지침으로 제시된다.

Keywords

References

  1. Belytschko, T., Lu, Y. Y. and Gu, L., 'Element-free Galerkin methods,' International Journal of Numerical Methods in Engineering, Vol. 37, 1994, pp.229-256 https://doi.org/10.1002/nme.1620370205
  2. Belytschko, T., Lu, Y. Y., Gu, L. and Tabbara, M., 'Element-free Galerkin methods for static and dynamic fracture,' International Journal of Solids and Structures, Vol. 32, 1995, pp.2547-2570 https://doi.org/10.1016/0020-7683(94)00282-2
  3. Belytschko, T. and Tabbara, M., 'Dynamic fracture using element-free Galerkin methods,' International Journal for Numerical Methods in Engineering, Vol. 39, 1996, pp.923-938 https://doi.org/10.1002/(SICI)1097-0207(19960330)39:6<923::AID-NME887>3.0.CO;2-W
  4. Fleming, M., Chu, Y. A., Moran, B. and Belytschko, T., 'Enrichment element-free Galerkin methods for crack tip fields,' International Journal for Numerical Methods in Engineering, Vol. 40, 1997, pp.1483-1504 https://doi.org/10.1002/(SICI)1097-0207(19970430)40:8<1483::AID-NME123>3.0.CO;2-6
  5. Organ, D. J., Fleming, M., Terry, T. and Belytschko, T., 'Continuous meshless approxi- mations for nonconvex bodies by diffraction and transparency,' Computational Mechanics, Vol. 18, 1996, pp.225-235 https://doi.org/10.1007/BF00369940
  6. Belytschko, T. and Fleming, M., 'Smoothing, enrichment and contact in the element-free Galerkin method,'Computer and Structures, Vol. 71, 1999, pp.173-195 https://doi.org/10.1016/S0045-7949(98)00205-3
  7. Belytschko, T. and Black, T., 'Elastic crack growth in finite elements with minimal re- meshing,'International Journal for Numerical Methods in Engineering, Vol. 45, 1999, pp. 601-620 https://doi.org/10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S
  8. Moes, N., Dolbow, J. and Belytschko, T., 'A finite element method for crack growth without remeshing,' International Journal for Numerical Methods in Engineering, Vol. 46, 1999, pp.131-150 https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J
  9. Melenk, J. M. and Babul ka, I., 'The partition of unity finite element method: Basic theory and applications,'Computer Methods in Applied Mechanics and Engineering, Vol. 139, 1996, pp.289-314 https://doi.org/10.1016/S0045-7825(96)01087-0
  10. Belytschko, T. Krongauz, Y. Dolbow, J. and Gerlach, C., On the completeness of meshfree particle methods,'International Journal for Numerical Methods in Engineering, Vol. 43, 1998, pp.785-819 https://doi.org/10.1002/(SICI)1097-0207(19981115)43:5<785::AID-NME420>3.0.CO;2-9
  11. Moran, B. and Shih C. F., 'Crack tip and associated domain integrals from momentum and energy balance'Engineering Fracture Mechanics, Vol. 27, 1987, pp.615-641 https://doi.org/10.1016/0013-7944(87)90155-X
  12. Lee, S-H and Yoon, Y-C., 'An improved crack analysis technique by element-free Galerkin method with auxiliary supports', International Journal for Numerical Methods in Engineering, accepted for publication, 2002
  13. 이상호, 윤영철, 'Element-Free Galerkin법을 이용한 혼합모드상태 균열의 균열진전해석', 한국전산구조공학회 논문집, 제12권, 제3호, 1999, pp.485-494
  14. 이상호, 윤영철, 'EFG법을 이용한 다수균열 함유 강부재의 피로균열 성장거동 해석', 한국전산구조공학회 논문집, 제12권, 제4호, 1999, pp.691-700
  15. 이상호, 윤영철, 'Mesh-Free법을 이용한 강부재 절취부 발생 피로균열의 성장해석,' 대한토목학회 논문집, 제22권, 제4-A호, 2002, pp.739-749
  16. 이상호, 윤영철, '특이기저함수를 이용하여 개선한 Mesh-Free 균열해석기법,' 한국전산구조공학회 논문집, 제14권, 제3호, 2001, pp.381-390
  17. '균열선단의 특이성을 반영한 개선된 EFG 해석기법들의 비교,'2002년도 한국전산구조공학회 봄 학술발표회 논문집, 제15권, 제1집, pp.69-76