Integral equations with hypersingular kernels - Theory and applications to fracture mechanics

Youn Sha Chan, Albert C. Fannjiang, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

107 Scopus citations


Hypersingular integrals were investigated for general integers α (positive) and m (nonnegative). The integrals were evaluated to calculate the stress intensity factors. Examples involving crack problems were given and discussed with emphasis on the linkage between mathematics and mechanics of fracture. Analysis shows that as material property variation in space and higher order graded continuum theories are considered, the formulation of the crack problem and the associated kernels becomes quite involved.

Original languageEnglish (US)
Pages (from-to)683-720
Number of pages38
JournalInternational Journal of Engineering Science
Issue number7
StatePublished - Apr 2003
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • General Engineering
  • Mechanical Engineering
  • General Materials Science


  • Asymptotic analysis
  • Chebyshev polynomials
  • Collocation method
  • Fredholm integral equation
  • Functionally graded materials
  • Hypersingular integrals
  • Integral equation method
  • Mode I crack
  • Mode III crack
  • Stress intensity factors


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