Multiple bent cracks in an infinite orthotropic plate under an anti-plane shear stress
Authors:
B. M. Singh, J. Rokne and R. S. Dhaliwal
Journal:
Quart. Appl. Math. 64 (2006), 253-269
MSC (2000):
Primary 74B05, 44A15, 65R20
DOI:
https://doi.org/10.1090/S0033-569X-06-00990-6
Published electronically:
May 10, 2006
MathSciNet review:
2243862
Full-text PDF Free Access
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Abstract: The problem of bent cracks of finite length in an orthotropic plate subject to an arbitrary longitudinal shear is studied with the help of Mellin transforms. The case of constant shear stress is considered in detail. The final results of this paper are obtained in closed form, and the expressions for stress intensity factors and crack energy are obtained. The numerical results for stress intensity factors are given in tabular form.
Irwin58 G. R. Irwin, Fracture Mechanics. ONR First Symposium on Naval Structural Mechanics, Pergamon Press (1958).
- G. I. Barenblatt, The mathematical theory of equilibrium cracks in brittle fracture., Advances in Applied Mechanics, Vol. 7, Academic Press, New York, 1962, pp. 55–129. MR 0149728
Kitagawa75 H. Kitagawa, R. Yunki and T. Ohira, Crack-morphological aspects in fracture mechanics. Engineering Fracture Mechanics 7, 515-529 (1975).
Zhang89A Y. Zhang and X. S. Zhang, General solutions to an infinite plate weakened by a bent crack for the opening and sliding modes. Engineering Fracture Mechanics 34, 1023-1029 (1989).
Zhang89B X. S. Zhang and Y. Zhang, The general solution to an orthotropic infinite plate with a bent crack under an arbitrary anti-plane shear stress. Engineering Fracture Mechanics 34, 263-268 (1989).
- B. M. Singh, Quadruple integral equations involving inverse Mellin transforms, Z. Angew. Math. Mech. 54 (1974), 201–203. MR 358258, DOI https://doi.org/10.1002/zamm.19740540314
- Ian N. Sneddon, Mixed boundary value problems in potential theory, North-Holland Publishing Co., Amsterdam; Interscience Publishers John Wiley & Sons, Inc., New York, 1966. MR 0216018
Erdelyi54 A. Erdelyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Tables of Integral Transforms. Vol. 1, McGraw Hill, New York (1954).
- A. K. Nagar, L. S. Fu, and D. A. Mendelsohn, On quadruple integral equations related to a certain crack problem, J. Elasticity 16 (1986), no. 2, 163–177. MR 849670, DOI https://doi.org/10.1007/BF00043583
Irwin58 G. R. Irwin, Fracture Mechanics. ONR First Symposium on Naval Structural Mechanics, Pergamon Press (1958).
Barenblatt62 G. I. Barenblatt, Mathematical theory of equilibrium cracks of brittle fracture. In: Advances in Applied Mechanics, VII (ed. H. L. Dryden and Th. von Karman), Academic Press, New York, 55-129 (1962).
Kitagawa75 H. Kitagawa, R. Yunki and T. Ohira, Crack-morphological aspects in fracture mechanics. Engineering Fracture Mechanics 7, 515-529 (1975).
Zhang89A Y. Zhang and X. S. Zhang, General solutions to an infinite plate weakened by a bent crack for the opening and sliding modes. Engineering Fracture Mechanics 34, 1023-1029 (1989).
Zhang89B X. S. Zhang and Y. Zhang, The general solution to an orthotropic infinite plate with a bent crack under an arbitrary anti-plane shear stress. Engineering Fracture Mechanics 34, 263-268 (1989).
Singh74 B. M. Singh, Quadruple integral equations involving inverse Mellin transforms. Zeitschrift für Angew. Math. und Mech. (ZAMM) 54, 201-203 (1974).
Sneddon66 I. N. Sneddon, Mixed boundary value problems in potential theory, North-Holland, Amsterdam (1966).
Erdelyi54 A. Erdelyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Tables of Integral Transforms. Vol. 1, McGraw Hill, New York (1954).
Nagar86 A. K. Nagar, L. S. Fu and D. A. Mendelsohn, On quadruple integral equations related to a certain crack problem. Journal of Elasticity 16, 163-177 (1986).
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Additional Information
B. M. Singh
Affiliation:
Department of Computer Science, The University of Calgary, Calgary, Alberta, Canada T2N-1N4
J. Rokne
Affiliation:
Department of Computer Science, The University of Calgary, Calgary, Alberta, Canada T2N-1N4
Email:
rokne@cpsc.ucalgary.ca
R. S. Dhaliwal
Affiliation:
Department of Mathematics, The University of Calgary, Calgary, Alberta, Canada T2N-1N4
Email:
dhali.r@shaw.ca
Received by editor(s):
April 7, 2005
Published electronically:
May 10, 2006
Article copyright:
© Copyright 2006
Brown University
