The linked crack solved by Mellin transform
type: Item
instance of: scholarly article
title: The linked crack solved by Mellin transform
zbMATH Open document ID: 0602.73100
DOI: 10.1007/BF00041764
author: G. N. Makrakis
author: Pericles S. Theocaris
published in: Journal of Elasticity
publication date: 1986-01-01T00:00:00Z
review text: The problem of the evaluation of the stress intensity factors (SIF) at a kinked crack-tip is treated by the use of the most appropriate tool for this problem, the Mellin transform technique. The advantage of this technique lies on the validity of the solution everywhere in the stress field and for every length of the branched crack. Since in the limiting case of the kinked crack, numerical difficulties appear in the evaluation of the kernel functions of the corresponding Fredholm integral-equation system, an asymptotic development, with respect to the length of the kinked crack, is constructed for these functions and therefore for the SIFs at the kinked tip. This analysis yields the interesting result that the SIFs at the crack tip tend to vanish as the kinked crack reduces in length, a result which is similar to the already established behavior of the SIFs at an interfacial tip.
Mathematics Subject Classification ID: 74R05
Mathematics Subject Classification ID: 74G70
Mathematics Subject Classification ID: 45B05
zbMATH DE Number: 3972384
zbMATH Keywords: reduction to system of four coupled Fredholm integral equations of the second kind
zbMATH Keywords: second order polynomial approximation
zbMATH Keywords: Filon's method
zbMATH Keywords: reduction of line integrals to real integrals
zbMATH Keywords: stress intensity factors
zbMATH Keywords: kinked crack-tip
zbMATH Keywords: Mellin transform technique
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00041764
OpenAlex ID: W2081619497
description: scientific article; zbMATH DE number 3972384