Abstract
Complex variable methods are used to obtain exact and closed expressions for Gaursat's functions for the stretched infinite plate weakened by one inner hole which is free from stresses. The plates considered are conformally mapped on the area of the right half-plane. The interesting cases of an infinite plate weakened by a crescent-like hole or by a cut having the shape of a circular arc, are included as special cases.
Zusammenfassung
Mit Hilfe komplexer Methoden werden exakte und geschlossene Ausdrücke für die Gaursat-Funktionen einer gezogenen Scheibe erhalten, welche durch ein spannungsfreies Loch geschwächt ist. Die betrachteten Scheiben werden konform auf die rechte Halbebene abgebildet. Als Sonderfälle sind neumondförmige Löcher und Schlitze in Form von Kreisbogen in den Resultaten mitenthalten.
References
W. A. Bassali andR. H. Dawoud, Proc. Camb. Phil. Soc.53, 755 (1957).
W. R. Dean, Proc. Camb. Phil. Soc.50, 623 (1954).
I. H. El-Sirafy, MSc Thesis, Faculty of Science, Alexandria Univ. (1968).
N. I. Muskhelishvili,Some Basic Problems of the Mathematical Theory of Elasticity, Moscow (1949).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
El-Sirafy, I.H. Stretched plates weakened by inner curvilinear holes. Journal of Applied Mathematics and Physics (ZAMP) 28, 1153–1159 (1977). https://doi.org/10.1007/BF01601683
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01601683