Numerical solution of random singular integral equation appearing in crack problemsThe solution of several elasticity problems, and particularly crack problems, can be reduced to the solution of one-dimensional singular integral equations with a Cauchy-type kernel or to a system of uncoupled singular integral equations. Here a method for the numerical solution of random singular integral equations of Cauchy type is presented. The solution technique involves a Chebyshev series approximation, the coefficients of which are the solutions of a system of random linear equations. This method is applied to the problem of periodic array of straight cracks inside an infinite isotropic elastic medium and subjected to a nonuniform pressure distribution along the crack edges. The statistical properties of the random solution are evaluated numerically, and the random solution is used to determine the values of the stress-intensity factors at the crack tips. The error, expressed as the difference between the mean of the random solution and the deterministic solution, is established. Values of stress-intensity factors at the crack tip for different random input functions are presented.
Document ID
19870028481
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Sambandham, M. (Atlanta Univ. GA, United States)
Srivatsan, T. S. (Atlanta Univ. GA, United States)
Bharucha-Reid, A. T. (Atlanta University GA, United States)