Regularly and singularly perturbed cracks

Author:
Chien H. Wu

Journal:
Quart. Appl. Math. **52** (1994), 529-543

MSC:
Primary 73M25; Secondary 73V35

DOI:
https://doi.org/10.1090/qam/1292203

MathSciNet review:
MR1292203

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Abstract | References | Similar Articles | Additional Information

Abstract: In a nondimensionalized rectangular Cartesian coordinate system let denote the upper and lower surfaces of a hole where and is a small parameter. As tends to zero, the hole degenerates into a crack of length 2. The functions , together with their derivatives, are continuous and . For not equal to zero, the hole is called a regularly (singularly) perturbed crack if . Regular perturbation procedures are applied to obtain the stress intensity factors existing at the tips of regularly perturbed cracks. It is shown that the second term of a two-term expansion is not always of the order of . The notch-tip singularity associated with a singularly perturbed crack is obtained by the method of matched asymptotic expansions.

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Additional Information

DOI:
https://doi.org/10.1090/qam/1292203

Article copyright:
© Copyright 1994
American Mathematical Society