An Infinite Elastic Plate Weakened by a Generalized Curvilinear Hole and Goursat Functions

Affiliation(s)

Department of Mathematics, Alexandria University, Alexandria, Egypt.

Department of Mathematics, Umm Al-Qura University, Mecca, KSA.

Department of Mathematics, Alexandria University, Alexandria, Egypt.

Department of Mathematics, Umm Al-Qura University, Mecca, KSA.

Abstract

Complex variables method has been used to
solve the first and second fundamental problems for an infinite plate weakened
by a generalized curvilinear hole *C*. The curvilinear hole is conformally
mapped on the domain outside or inside a unit circle *γ* using a general rational mapping function with
complex constants. Many special and new cases are derived from this work. Some
of the work of the previous authors in this domain will be considered as
special cases of this paper. Also the interesting cases when the shape of the
hole takes different famous shapes are included. The components of stresses for
some examples are obtained.

Cite this paper

Abdou, M. and Jan, A. (2014) An Infinite Elastic Plate Weakened by a Generalized Curvilinear Hole and Goursat Functions.*Applied Mathematics*, **5**, 728-743. doi: 10.4236/am.2014.54070.

Abdou, M. and Jan, A. (2014) An Infinite Elastic Plate Weakened by a Generalized Curvilinear Hole and Goursat Functions.

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