An elastic plate with a curvilinear hole and flowing heat in S-plane

Abstract

 In the present paper, we apply complex variable method, Cauchy method, to derive exact expressions for Goursat functions for the boundary value problems of an infinite elastic plate weakened by a curvilinear hole. The hole considered is conformally mapped on the area of the right half-plane. Also, when an initial heat is uniformly flowing in the perpendicular direction of the hole, the thermo potential function and the stress components, in this case, are obtained. Some applications are considered, and the work of many previous authors is established as special cases of this work. Also, when the hole is conformally mapped inside and outside the unit circle is established from this work.