Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-23T22:55:40.826Z Has data issue: false hasContentIssue false
  • English
  • Français

A pair of arbitrarily-oriented coplanar cracks in an anisotropic elastic slab

Published online by Cambridge University Press:  17 February 2009

W. T. Ang
W. T. Ang
Affiliation:
Engineering Mathematics Section, Universiti Sains Malaysia, Perak, Malaysia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The problem of an anisotropic elastic slab containing two arbitrarily-oriented coplanar cracks in its interior is considered. Using a Fourier integral transform technique, we reduce the problem to a system of simultaneous finite-part singular integral equations which can be solved numerically. Once the integral equations are solved, relevant quantities such as the crack energy can be readily computed. Numerical results for specific examples are obtained.

Type
Research Article
Information
The ANZIAM Journal , Volume 32 , Issue 3 , January 1991 , pp. 284 - 295
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Abramowitz, M. and Stegun, I. A. (eds), Handbook of Mathematical Functions (Dover, New York, 1970).Google Scholar
[2]Ang, W. T., “A cracked anisotropic elastic slab”, Int. J. Engng. Sc. 26 (1988) 277–283.CrossRefGoogle Scholar
[3]Ang, W. T., “An arbitrarily-oriented plane crack in an anisotropic elastic slab”, Engng. Fract. Mech. 32 (1989) 965–972.CrossRefGoogle Scholar
[4]Ang, W. T., “Transient response of a crack in an anisotropic strip”, Acta Mechanica 70 (1987) 97–109.CrossRefGoogle Scholar
[5]Clements, D. L., “A crack in an anisotropic elastic slab”, Quart. Appl. Maths 34 (1977) 437–443.CrossRefGoogle Scholar
[6]Clements, D. L. and Tauchert, T. R., “Deformation of an anisotropic slab containing a crack”, Acta Mechanica 32 (1979) 55–61.CrossRefGoogle Scholar
[7]Dhaliwal, R. S., “Two coplanar cracks in an infinitely long orthotropic slab”, Utilitas Mathematica 4 (1973) 115–128.Google Scholar
[8]Gradshtein, I. S. and Ryzhik, I. M., Table of Integrals, Series and Products (Academic Press, San Diego, 1980).Google Scholar
[9]Hill, D. L. and Clements, D. L., “On deformations of cracked anisotropic slabs”, J. Elast. 14 (1984) 403–413.CrossRefGoogle Scholar
[10]Loakimidis, N. I., “A new singular integral equation for the classical crack problem in plane and antiplane elasticity”, Int. J. Fract. 21 (1983) 115–122.CrossRefGoogle Scholar
[11]Kaya, A. C. and Erdogan, F., “On the solution of integral equations with strongly singular kernels”, Quart. Appl. Math. 45 (1987) 105–122.CrossRefGoogle Scholar
[12]Konishi, Y., “Two coplanar cracks in an infinite transversely isotropic medium”, Int. J. Engng. Sc. 10 (1972) 917–923.CrossRefGoogle Scholar
[13]Krenk, S., “The stress distribution in an infinite plate with co-linear cracks”, Int. J. Solids Structures 11 (1975) 449–460.CrossRefGoogle Scholar
[14]Sneddon, I. N., Fourier Transforms (McGraw-Hill, New York, 1951).Google Scholar
[15]Spencer, A. J. M., Deformations of fibre-reinforced materials (Oxford University Press, 1972).Google Scholar
[16]Stroh, A. N., “Dislocations and cracks in anisotropic elasticity”, Phil. Mag. 3 (1958) 625–646.CrossRefGoogle Scholar