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Mathematical Details on Singular Integral Equation Method for Solving Crack Problems

Author

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  • Youn-Sha Chan
  • Sergiy Koshkin

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.

Suggested Citation

  • Youn-Sha Chan & Sergiy Koshkin, 2019. "Mathematical Details on Singular Integral Equation Method for Solving Crack Problems," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(1), pages 102-117, February.
    • Handle: RePEc:ibn:jmrjnl:v:11:y:2019:i:1:p:102
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    Citations

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    Cited by:

    1. Liudmila Nickelson & Raimondas Pomarnacki & Tomyslav Sledevič & Darius Plonis, 2021. "Method of Singular Integral Equations for Analysis of Strip Structures and Experimental Confirmation," Mathematics, MDPI, vol. 9(2), pages 1-14, January.
    2. Youn-Sha Chan & Edward Athaide & Kathryn Belcher & Ryan Kelly, 2020. "Detailed Solution of a System of Singular Integral Equations for Mixed Mode Fracture in Functionally Graded Materials," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 12(1), pages 1-43, February.

    More about this item

    Keywords

    crack-tip singularity; singular integral equation; functionally graded materials;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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