Goursat functions for an infinite plate with a generalized curvilinear hole in ζ-plane

M. A. Abdou*, S. A. Aseeri

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We used a rational mapping function with complex constants to derive exact and close expressions of Goursat functions for the first and second fundamental problems (plane elasticity problems) of an infinite plate weakened by a hole having arbitrary shape. Notable, the area outside the hole is conformally mapped outside a unit circle by means of the rational mapping. The complex variable method has been applied in the procedure and it transforms the fundamental problems to the integro-differential equations that can be solved by using Cauchy type integrals. The hole takes different famous shapes which can be found throughout the nature like tunnels, caves, excavation in soil or rock, etc. Many previous works have been considered as special cases of this work. Also many new cases can be derived from the problem.

Original languageEnglish (US)
Pages (from-to)23-36
Number of pages14
JournalApplied Mathematics and Computation
Issue number1
StatePublished - Jun 1 2009


  • Complex variable method
  • Conformal mapping
  • Curvilinear hole
  • Plane elasticity

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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