KSCE Journal of Civil and Environmental Engineering Research (대한토목학회논문집)

Korean Society of Civil Engeneers (대한토목학회)
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Stress Intensity Factor of Cracked Plates with Bonded Composite Patch by p-Convergence Based Laminated Plate Theory

p-수렴 적층 평판이론에 의한 균열판의 팻취보강후 응력확대계수 산정

  • 우광성 (영남대학교 건설시스템공학과) ;
  • 한상현 (롯데건설(주) 토목공사팀) ;
  • 양승호 (영남대학교 건설시스템공학과)
  • Received : 2008.01.22
  • Accepted : 2008.06.30
  • Published : 2008.09.30
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Abstract

The enhancement of the service life of damaged or cracked structures is a major issue for researchers and engineers. The hierarchic void element based on the integrals of Legendre polynomials is used to characterize the fracture behaviour of unpatched crack as well as repaired crack with bonded composite patches by computing the stress intensity factors and stress contours at the crack tip. Since the equivalent single layer approach is adopted in this study, the proposed element is necessary to represent a discontinuous crack part as a continuum body with zero stiffness. Thus the aspect ratio of this element to represent the crack should be extremely slender. The sensitivity of numerical solution with respect to energy release rate, displacement and stress has been tested to show the robustness of zero stiffness element as the aspect ratio is increased up to 2000. The stiffness derivative method and displacement extrapolation method have been applied to calculate the stress intensity factors of Mode I problem. It is noted that the proposed hierarchical void element can be one of alternatives to analyze the patched crack problems.

손상 또는 균열된 구조물의 내구성을 향상시키려는 과제는 연구자들과 엔지니어들에게 중요한 과제로 떠오르고 있다. 팻취로 보강되지 않은 균열판과 팻취보강된 균열판의 응력확대계수 및 응력등고선의 산정 및 비교에 의한 균열선단에서의 파괴거동의 특성을 적분형 르장드르 다항식에 기초를 둔 계층적 무강성요소를 사용하여 표현하고자 한다. 이 연구에서는 등가단층이론이 채택되므로, 제안된 무강성요소는 불연속 균열부를 강성이 0인 연속체로 간주된다. 그러므로 균열을 모델링하는 무강성요소의 변장비는 매우 커질 수밖에 없다. 제안된 요소의 강건성을 보이기 위해 형상비 변화에 따른 에너지방출률, 변위 및 응력값에 대한 유한요소해의 민감도는 변장비를 2000까지 증가시켜 가면서 평가되었다. 한편, 강성도미분법과 변위외삽법이 인장모우드가 발생되는 문제의 응력확대계수를 예측하는데 사용된다. 제안된 계층적 무강성요소는 팻취보강된 균열문제를 해석할 수 있는 대안중의 하나라 평가된다.

Keywords

References

  1. 최창근(2002) 유한요소법, 테크노프레스
  2. 홍종현, 박진환, 우광성(2002) 기하 및 재료비선형을 갖는 적층 평판의 p-Version 유한요소해석. 한국전산구조공학회 논문집, 한국전산구조공학회, 제15권, 제3호(통권 53호), pp. 491-499
  3. Robinson, J. (1976) A single element test. Comput. Meth. Appl. Mech. Eng. 7, pp. 191-200 https://doi.org/10.1016/0045-7825(76)90012-8
  4. Reddy, J.N. (1997) Mechanics of Laminated Composite Plates: Theory and Analysis, CRC Press
  5. Hinton, E. and Owen, D.R.J. (1984) Finite Element Software for Plates and Shells, Pineridge Press, Swansea, U.K
  6. Park, D.M. (1974) A stiffness derivative finite element technique of crack tip stress intensity factors for determination. International Journal of Fracture, Vol. 10, pp. 487-520 https://doi.org/10.1007/BF00155252
  7. Zienkiewicz, O.C., De, J. P., Gago, S.R., and Kelly, D.W. (1983) The Hierarchic Concept in Finite Element Analysis. Computer & Structures, Vol. 16, pp. 51-65
  8. Woo, K.S. (1993) Robustness of hierarchical elements formulated by integrals of Legendre polynomials. Computers & Structures, Vol. 49, No. 3, pp. 421-426 https://doi.org/10.1016/0045-7949(93)90043-D
  9. Ellyin, F., Ozah, F., and Xia, Z. (2007) 3-D modelling of cyclically loaded composite patch repair of a cracked plate. Composite Structures, Vol. 78, pp. 486-494 https://doi.org/10.1016/j.compstruct.2005.11.010
  10. Ahmad, S., Irons, B.M., and Zienkiewicz, O.C. (1970) Analysis of thick and thin shell structures by curved finite elements. Numer. Meth. Engng, Vol. 2, pp. 419-451 https://doi.org/10.1002/nme.1620020310
  11. Ayatollahi, M.R. and Hashemi, R. (2007) Computation of stress intensity factor ($K_r$,$K_{II}$) and T-stress for cracks reinforced by composite patching. Composite Structures, Vol. 78, pp. 602-609 https://doi.org/10.1016/j.compstruct.2005.11.024
  12. Woo, K.S., Park, J.H., and Hong, C.H.(2004) A new hierarchic degenerated shell element for geometrically non-linear analysis of composite laminated square and skew plates. Structural Engineering & Mechanics, Vol. 17, No. 6, pp. 751-766 https://doi.org/10.12989/sem.2004.17.6.751