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Complex variable methods are used to obtain exact and closed expressions for Goursat's functions for the stretched infinite plate weakened by two inner holes which are free from stresses. The plate considered is conformally mapped on the area of the right half-plane. Previous work is considered as special cases of this work.  Cases of different shapes of  holes are included. Also, many new cases are discussed  using this mapping

international journal of mathematics and mathematical sciences

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$S$" id="E1"><mml:mi>S</mml:mi></mml:math>-plane analysis for the fundamental problems of a stretched infinite plate weakened by curvilinear holes

S-plane analysis for the fundamental problems of a stretched infinite plate weakened by curvilinear holes