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Axisymmetric finite cylinder with rigid ends and a circumferential edge crack

Year 2018, Volume 21, Issue 2, 121 - 130, 30.06.2018
https://doi.org/10.17780/ksujes.360635

Abstract

An axisymmetric linearly elastic and isotropic finite cylinder with rigid ends and a circumferential edge crack subjected to axial tension is considered. Finite cylinder problem is obtained from an infinite cylinder containing an internal ring-shaped crack and two penny-shaped rigid inclusions. Navier equations are solved by using Fourier and Hankel transforms. Formulation is reduced to three singular integral equations which are converted to a system of linear algebraic equations with the aid of Gauss-Lobatto and Gauss-Jacobi integration formulas. Stress intensity factors at the edges of crack and around the corner of the cylinder are calculated.

References

  • Artem, H., Gecit. M.R. (2002). An elastic hollow cylinder under axial tension containing a crack and two rigid inclusions of ring shape. Computers & Structures, 80, 2277-2287.
  • Chang, S.S. (1985). The general solution of a finite cylinder with a concentric penny-shaped crack under torsion. Engng Fract Mech, 22: 571-578.
  • Durucan, A.R. (2010). Axisymmetric finite cylinder with rigid ends and a circumferential edge crack. M.S. thesis. Middle East Technical University, Ankara, Turkey.
  • Erdogan, F., Gupta, G.D., Cook, T.S. (1973). Numerical solution of singular integral equations. In: Sih GC, editor. Methods of analysis and solutions of crack problems. Leyden: Noordhoff International Publishing, 368-425.
  • Erdol, R., Erdogan, F. (1978). Thick-walled cylinder with an axisymmetric internal or edge crack. Journal of Applied Mechanics, Transactions, ASME, 45: 281-286.
  • Gupta, G.D. (1973). An integral equation approach to the semi-infinite strip problem. Journal of Applied Mechanics, Transactions, ASME, 40: 948-954.
  • Kadioglu, F.S.(2005) Edge cracks in a transversely isotropic hollow cylinder. Engineering Fracture Mechanics,72: 2159-2173.
  • Kaman, M.O., Gecit, M.R. (2006). Cracked semi-infinite cylinder and finite cylinder problems. International Journal of Engineering Sciences,44: 1534–1555.
  • Kaman, M.O., Gecit, M.R. (2008). Axisymmetric finite cylinder with one end clamped and the other under uniform tension containing a penny-shaped crack. Engineering Fracture Mechanics, 75: 3909-3923.
  • Lee, D.S. (2002). A long circular cylinder with a circumferential edge crack subjected to a uniform shearing stress. Int J Solids Struct, 39, 2613-2628.
  • Lee, D.S. (2003). Tension of a long circular cylinder having a spherical cavity with a peripheral edge crack. International Journal of Solids and Structures, 40: 2659-2671.
  • Liang, B., Zhang, X.S. (1992). The problem of a concentric penny-shaped crack of mode III in a nonhomogeneous finite cylinder. Engng Fract Mech, 42, 79-85.
  • Meshii, T., Watanabe, K. (2001). Stress intensity factor for a circumferential crack in a finite-length thin to thick-walled cylinder under an arbitrary biquadratic stress distribution on the crack surface. Engng Fract Mech, 68, 975-986.
  • Nied, H.F., Erdogan, F.(1983). The elasticity problem for a thick-walled cylinder containing a circumferential crack. International Journal of Fracture, 22: 277-301.
  • Toygar, M.E., Gecit, M.R. (2006). Cracked infinite cylinder with two rigid inclusions under axisymmetric tension. International Journal of Solids and Structures, 43: 4777-4794.
  • Zhang, X.S. (1988). Off-plane concentric penny-shaped crack in a finite cylinder under arbitrary torsion. Theor Appl Fract Mech, 9, 263-270.

Çevresel kenar çatlağı içeren rijit uçlu eksenel simetrik sonlu silindir

Year 2018, Volume 21, Issue 2, 121 - 130, 30.06.2018
https://doi.org/10.17780/ksujes.360635

Abstract

Bu çalışmada doğrusal elastik ve izotropik malzemeden imal edilmiş, çevresel bir kenar çatlağı içeren rijit uçlu sonlu uzunlukta eksenel simetrik bir silindir incelenmiştir. Sonlu silindir problemine ulaşmak için, halka şeklinde iç çatlak ve iki dairesel şekilli enklüzyon içeren sonsuz bir silindirden yola çıkılmıştır. Navier denklemleri Fourier ve Hankel dönüşümleri kullanılarak çözülmüştür. Formülasyon tekil integral denklemlerine indirgenmiş ve Gauss-Lobatto ve Gauss-Jakobi integrasyon formülleri ile doğrusal cebrik denklem takımlarına dönüştürülmüştür. Çatlağın kenarlarındaki ve silindirin çevresi etrafındaki gerilme yığılma faktörleri hesaplanmıştır.

References

  • Artem, H., Gecit. M.R. (2002). An elastic hollow cylinder under axial tension containing a crack and two rigid inclusions of ring shape. Computers & Structures, 80, 2277-2287.
  • Chang, S.S. (1985). The general solution of a finite cylinder with a concentric penny-shaped crack under torsion. Engng Fract Mech, 22: 571-578.
  • Durucan, A.R. (2010). Axisymmetric finite cylinder with rigid ends and a circumferential edge crack. M.S. thesis. Middle East Technical University, Ankara, Turkey.
  • Erdogan, F., Gupta, G.D., Cook, T.S. (1973). Numerical solution of singular integral equations. In: Sih GC, editor. Methods of analysis and solutions of crack problems. Leyden: Noordhoff International Publishing, 368-425.
  • Erdol, R., Erdogan, F. (1978). Thick-walled cylinder with an axisymmetric internal or edge crack. Journal of Applied Mechanics, Transactions, ASME, 45: 281-286.
  • Gupta, G.D. (1973). An integral equation approach to the semi-infinite strip problem. Journal of Applied Mechanics, Transactions, ASME, 40: 948-954.
  • Kadioglu, F.S.(2005) Edge cracks in a transversely isotropic hollow cylinder. Engineering Fracture Mechanics,72: 2159-2173.
  • Kaman, M.O., Gecit, M.R. (2006). Cracked semi-infinite cylinder and finite cylinder problems. International Journal of Engineering Sciences,44: 1534–1555.
  • Kaman, M.O., Gecit, M.R. (2008). Axisymmetric finite cylinder with one end clamped and the other under uniform tension containing a penny-shaped crack. Engineering Fracture Mechanics, 75: 3909-3923.
  • Lee, D.S. (2002). A long circular cylinder with a circumferential edge crack subjected to a uniform shearing stress. Int J Solids Struct, 39, 2613-2628.
  • Lee, D.S. (2003). Tension of a long circular cylinder having a spherical cavity with a peripheral edge crack. International Journal of Solids and Structures, 40: 2659-2671.
  • Liang, B., Zhang, X.S. (1992). The problem of a concentric penny-shaped crack of mode III in a nonhomogeneous finite cylinder. Engng Fract Mech, 42, 79-85.
  • Meshii, T., Watanabe, K. (2001). Stress intensity factor for a circumferential crack in a finite-length thin to thick-walled cylinder under an arbitrary biquadratic stress distribution on the crack surface. Engng Fract Mech, 68, 975-986.
  • Nied, H.F., Erdogan, F.(1983). The elasticity problem for a thick-walled cylinder containing a circumferential crack. International Journal of Fracture, 22: 277-301.
  • Toygar, M.E., Gecit, M.R. (2006). Cracked infinite cylinder with two rigid inclusions under axisymmetric tension. International Journal of Solids and Structures, 43: 4777-4794.
  • Zhang, X.S. (1988). Off-plane concentric penny-shaped crack in a finite cylinder under arbitrary torsion. Theor Appl Fract Mech, 9, 263-270.

Details

Primary Language English
Subjects Civil Engineering
Journal Section Civil Engineering
Authors

Ayşe Ruşen DURUCAN (Primary Author)
FIRAT ÜNİVERSİTESİ
Türkiye

Publication Date June 30, 2018
Application Date December 2, 2017
Acceptance Date December 20, 2017
Published in Issue Year 2018, Volume 21, Issue 2

Cite

APA Durucan, A. R. (2018). Axisymmetric finite cylinder with rigid ends and a circumferential edge crack . Kahramanmaraş Sütçü İmam Üniversitesi Mühendislik Bilimleri Dergisi , 21 (2) , 121-130 . DOI: 10.17780/ksujes.360635