Abstract
An infinite cylinder, of isotropic and linearly
elastic material, with an internal ring shaped crack and two penny shaped rigid
inclusions was considered in this study. The considered cylinder was subjected
to axial tensile forces from its two ends. The complex problem of the axially
loaded infinite cylinder was solved by using the superposition of two problems
including: (i) an infinite cylinder, without any cracks or inclusions, loaded
at infinity and (ii) an infinite cylinder with an internal ring shaped crack
and two penny shaped inclusions and free of loading. Associated Navier
equations are solved with Fourier and Hankel transforms to obtain general expressions
for the considered problem. Then, the considered problem is reduced to three
singular integral equations and numerically solved by using Gauss-Lobatto
integration formula with associated system of linear algebraic equations.
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.
- Cook, T.S., Erdogan, F.(1972) Stresses in bonded materials with a crack perpendicular to the interface. International Journal of Engineering Sciences, 10: 677-697.
- Durucan, A.R. (2010). Axisymmetric finite cylinder with rigid ends and a circumferential edge crack. M.S. thesis. Middle East Technical University, Ankara, Turkey.
- Erdol, R., Erdogan, F. (1978). Thick-walled cylinder with an axisymmetric internal or edge crack. Journal of Applied Mechanics, Transactions, ASME, 45: 281-286.
- Gecit, M.R., Turgut, A. (1988). Extension of a finite strip bonded to a rigid support. Computational Mechanics, 3: 398-410.
- Gecit, M.R., (1987). Analysis of tensile test for a cracked adhesive layer pulled by rigid cylinders. International Journal of Fracture, 32: 241-256.
- Gecit, M.R., (1984). Antiplane shear in adhesively bonded semi-infinite media with transverse cracks. International Journal of Fracture, 24: 163-178.
- Gupta, G.D. (1973). An integral equation approach to the semi-infinite strip problem. Journal of Applied Mechanics, Transactions, ASME, 40: 948-954.
- Gupta, G.D.(1974). The analysis of the semi-infinite cylinder problem. International Journal of Solids and Structures, 10: 137-148.
- 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. (2007). An axisymmetric infinite cylinder with two cracks and a rigid inclusion, Turkish J Eng Env Sci, 31: 29-52.
- Krenk, S. (1978). Quadrature formulae of closed type for solution of singular integral equations. IMA Journal of Applied Mathematics,22: 99-107.
- 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.
- Muskhelishvili, N.I. (1953). Singular integral equations. Gröningen: P.Noordhoff.
- 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.
- Williams, M.L.(1958). Stress singularities resulting from various boundary conditions in angular corners of plates in extension. Journal of Applied Mechanics, 19: 526-528.
- Yetmez, M., Gecit, M.R.(2005). Finite strip with a central crack under tension. International Journal of Engineering Sciences, 43: 472-493.
Abstract
Bu çalışmada elastik
ve izotropik malzemeden imal edilmiş, halka şeklinde bir iç çatlak ve daire
şeklinde iki adet rijit enklüzyon içeren sonsuz bir silindir incelenmiştir.
İncelenen silidir iki ucundan eksenel yüke tabi tutulmuştur. Eksenel yüklenmiş
sonsuz silindiri içeren karmaşık problem iki problemin süperpoze edilmesiyle
çözülmüştür. Bu problemler: (i) çatlak veya enklüzyon içermeyen sonsuzda
yüklenmiş bir sonsuz silindir, (ii) yükleme
altında olmayan, halka şeklinde bir iç çatlak ve iki daire şekilli enklüzyon
içeren sonsuz silindirdir. İlgili Navier eşitlikleri, Hankel ve Fourier
dönüşümleri kullanılarak çözülerek, ilgilenilen probleme yönelik genel ifadeler
elde edilmiştir. Sonra, problem üç adet tekil integral denklemine indirgenmiş
ve ilgili doğrusal cebrik denklem takımı Gauss- Lobatto integrasyon formülleri
kullanılarak sayısal yöntemlerle çözülmüştür.
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.
- Cook, T.S., Erdogan, F.(1972) Stresses in bonded materials with a crack perpendicular to the interface. International Journal of Engineering Sciences, 10: 677-697.
- Durucan, A.R. (2010). Axisymmetric finite cylinder with rigid ends and a circumferential edge crack. M.S. thesis. Middle East Technical University, Ankara, Turkey.
- Erdol, R., Erdogan, F. (1978). Thick-walled cylinder with an axisymmetric internal or edge crack. Journal of Applied Mechanics, Transactions, ASME, 45: 281-286.
- Gecit, M.R., Turgut, A. (1988). Extension of a finite strip bonded to a rigid support. Computational Mechanics, 3: 398-410.
- Gecit, M.R., (1987). Analysis of tensile test for a cracked adhesive layer pulled by rigid cylinders. International Journal of Fracture, 32: 241-256.
- Gecit, M.R., (1984). Antiplane shear in adhesively bonded semi-infinite media with transverse cracks. International Journal of Fracture, 24: 163-178.
- Gupta, G.D. (1973). An integral equation approach to the semi-infinite strip problem. Journal of Applied Mechanics, Transactions, ASME, 40: 948-954.
- Gupta, G.D.(1974). The analysis of the semi-infinite cylinder problem. International Journal of Solids and Structures, 10: 137-148.
- 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. (2007). An axisymmetric infinite cylinder with two cracks and a rigid inclusion, Turkish J Eng Env Sci, 31: 29-52.
- Krenk, S. (1978). Quadrature formulae of closed type for solution of singular integral equations. IMA Journal of Applied Mathematics,22: 99-107.
- 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.
- Muskhelishvili, N.I. (1953). Singular integral equations. Gröningen: P.Noordhoff.
- 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.
- Williams, M.L.(1958). Stress singularities resulting from various boundary conditions in angular corners of plates in extension. Journal of Applied Mechanics, 19: 526-528.
- Yetmez, M., Gecit, M.R.(2005). Finite strip with a central crack under tension. International Journal of Engineering Sciences, 43: 472-493.
Details
| Primary Language | English |
|---|---|
| Subjects | Civil Engineering |
| Journal Section | Civil Engineering |
| Authors | |
| Publication Date | March 30, 2018 |
| Submission Date | December 1, 2017 |
| Published in Issue | Year 2018 |