Differential Inclusions, Control and Optimization 24 (2004) 5-11
doi: 10.7151/dmdico.1048

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SOLUTION OF FREDHOLM INTEGRODIFFERENTIAL EQUATION FOR AN INFINITE ELASTIC PLATE

Alaa A. El-Bary

Department of Basic and Applied Science
Arab Academy for Science and Technology
P.O. Box 1029, Alexandria, Egypt

e-mail: aaelbary@aast.edu

Abstract

Many authors discussed the problem of an elastic infinite plate with a curvilinear hole, some of them considered this problem in z-plane and the others in the s-plane. They obtained an exact expression for Goursat's functions for the first and second fundamental problem. In this paper, we use the Cauchy integral method to obtain a solution to the first and second fundamental problem by using a new transformation. Some applications are investigated and also some special cases are discussed.

Keywords: integrodifferential equation, Cauchy method, complex variable, infinite plate, curvilinear hole.

2000 Mathematics Subject Classification: 45B05, 45E10.

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Received 16 January 2004