Mathematical Details on Singular Integral Equation Method for Solving Crack Problems

Youn-Sha Chan and Sergiy Koshkin

Journal of Mathematics Research, 2019, vol. 11, issue 1, 102-117

Abstract: This article provides a detail derivation of a singular Fredholm integral equation for the solution of a mixed mode crack problem in a nonhomogeneous medium. The integral equation derived here has already been addressed by F. Delale and F. Erdogan (Delale & Erdogan 1983), one of the most cited and pioneer papers in fracture mechanics that uses singulalr integral equation method (SIEM) to solve crack problems. However, probably due to its limit of paper length, some mathematical details are not provided to bring this powerful method, SIEM, to its full strength. In this paper we fill in the mathematical gaps, and both analytical and numerical parts are addressed in details. Some discussions from the view point of differential equations are given, and new numerical outcomes under different loading functions are provided.

Keywords: crack-tip singularity; singular integral equation; functionally graded materials (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:11:y:2019:i:1:p:102

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