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Detailed Solution of a System of Singular Integral Equations for Mixed Mode Fracture in Functionally Graded Materials

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Listed:
  • Youn-Sha Chan
  • Edward Athaide
  • Kathryn Belcher
  • Ryan Kelly

Abstract

A mixed mode crack problem in functionally graded materials is formulated to a system of Cauchy singular Fredholm integral equations, then the system is solved by the singular integral equation method (SIEM). This specific crack problem has already been solved by N. Konda and F. Erdogan (Konda & Erdogan 1994). However, many mathematical details have been left out. In this paper we provide a detailed derivation, both analytical and numerical, on the formulation as well as the solution to the system of singular Fredholm integral equations. The research results include crack displacement profiles and stress intensity factors for both mode I and mode II, and the outcomes are consistent with the paper by Konda & Erdogan (Konda & Erdogan 1994).

Suggested Citation

  • 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.
    • Handle: RePEc:ibn:jmrjnl:v:12:y:2020:i:1:p:43
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    References listed on IDEAS

    as
    1. 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.
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    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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