Closed forms of goursat functions in presence of heat for curvilinear holes

M. A. Abdou, S. A. Aseeri

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In this paper, we consider a general conformal mapping function with complex constant coefficients, to solve the elasticity problems for an infinite plate weakened by a curvilinear hole. Conformal was used outside and inside of a unit circle in the presence of an initial heat flowing perpendicular to the plate. The use of the complex variable method gives convenient expressions of Goursat functions in applications, it also achieves the objective rapidly. Several previous works are considered as special cases of this work. The hole takes different shapes that make this study applicable to many cases, like tunnels, caves, excavations in soil or rock, etc. Stress and strain components have been obtained and plotted to investigate their physical meanings. With the aid of a computer, shapes of holes were received, and distribution of stresses obtained.

Original languageEnglish (US)
Pages (from-to)1126-1148
Number of pages23
JournalJournal of Thermal Stresses
Issue number11
StatePublished - Nov 2009
Externally publishedYes


  • Complex variable method
  • Conformal mapping
  • Curvilinear hole
  • Flowing heat
  • Infinite elastic plane

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics


Dive into the research topics of 'Closed forms of goursat functions in presence of heat for curvilinear holes'. Together they form a unique fingerprint.

Cite this