Fundamental problems for a weakened infinite plate by a curvilinear hole in a half-plane

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Complex variable method (Cauchy integral method) has been applied to derive exact and closed expressions of Goursat functions for the first and second fundamental problems for an infinite plate weakened by a curvilinear hole. The area outside the hole with the hole itself is conformally mapped on the right half-plane by the use of a rational mapping function. This rational mapping consists of complex constants, in order to make the hole take different famous shapes, which can be found throughout the nature. Many previous works are considered as special cases of this work. Also many new cases can be derived from the problem.

Original languageEnglish (US)
Pages (from-to)397-413
Number of pages17
JournalActa Mathematica Academiae Paedagogicae Nyiregyhaziensis
Issue number3
StatePublished - Dec 29 2008


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

ASJC Scopus subject areas

  • General Mathematics
  • Education


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