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Solution of Fredholm integrodifferential equation for an infinite elastic plate

Alaa A. El-Bary — 2004

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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.

Mathematical treatment for thermoelastic plate with a curvilinear hole in S-plane

Alaa A. El-Bary — 2006

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The Cauchy integral method has been applied to derive exact and closed expressions for Goursat's functions for the first and second fundamental problems for an infinite thermoelastic plate weakened by a hole having arbitrary shape. The plate considered is conformally mapped to the area of the right half-plane. Many previous discussions of various authors can be considered as special cases of this work. The shape of the hole being an ellipse, a crescent, a triangle, or a cut having the shape of a...

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