Mathematical Problems in Engineering
Volume 7 (2001), Issue 6, Pages 485-501

Fundamental problems for infinite plate with a curvilinear hole having finite poles

M. A. Abdou1 and A. A. El-Bary2

1Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt
2Department of Basic Science, Arab Academy for Science and Technology, P.O. Box: 1029 Alexandira, Alexandria, Egypt

Received 3 December 2000; Revised 14 May 2001

Copyright © 2001 M. A. Abdou and A. A. El-Bary. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the present paper Muskhelishvili's complex variable method of solving two-dimensional elasticity problems has been applied to derive exact expressions for Gaursat's functions for the first and second fundamental problems of the infinite plate weakened by a hole having many poles and arbitrary shape which is conformally mapped on the domain outside a unit circle by means of general rational mapping function. Some applications are investigated. The interesting cases when the shape of the hole takes different shapes are included as special cases.