Abstract
The present study investigates a numerical algorithm for solving systems of Cauchy singular integral equations of the second kind such as those which often occur in the analysis of interface crack problems. The algorithm takes advantage of many standard subroutines for performing numerical integrations and can be easily applied to equations which are defined over different intervals of the dependent variable. The solution technique is illustrated by analyzing two homogeneous center cracked panels: one loaded in tension and the other loaded in shear and bending. In the second example problem, the presence of crack face friction strongly couples the underlying singular integral equations. The numerical results are compared to closed form elasticity solutions and are shown to be extremely accurate. In addition, the study also illustrates the feasibility of using various assumed forms of the undetermined functions. By assuming these slightly altered forms, many rather complex problems are either solved directly or reduced in complexity.
Similar content being viewed by others
References
N.I. Muskhelishvili, Singular Integral Equations, J.M. Radok (ed.), P. Noordhoff Ltd, Groningen, Netherlands (1953).
S.G. Mikhlin, Integral Equations, The Macmillan Company, New York (1964).
F. Erdogon, G. Gupta and T. Cook, Mechanics of Fracture Vol. I, Method of Analysis and Solutions of Crack Problems, George Sih (ed.), Noordhoff Publishers, Leyden, The Netherlands (1973) Chapter 7.
G.R. Miller and L.M. Keer, Quarterly of Applied Mathematics (1985) 455–465.
R.D. Kurtz, Analysis of Bimaterial Crack Problems in the Presence of Friction, Ph.D. thesis, Purdue University, W. Lafayette, submitted August 1993.
A. Gerasoulis, Computers and Mathematics with Applications 8 (1982) 15–22.
S.C. Chapra and R.P. Canale, Numerical Method for Engineers, McGraw-Hill Book Company, New York (1988).
W.H. Press et al., Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, New York (1986).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kurtz, R.D., Farris, T.N. & Sun, C.T. The numerical solution of Cauchy singular integral equations with application to fracture. Int J Fract 66, 139–154 (1994). https://doi.org/10.1007/BF00020079
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00020079