Mathematical Problems in Engineering 
Volume 7 (2001), Issue 6, Pages 485-501
doi:10.1155/S1024123X01001740

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

Abstract

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.