Abstract
In this paper, we consider a general conformal mapping function with complex constant coefficients, to solve the elasticity problems for an infinite plate weakened by a curvilinear hole. Conformal was used outside and inside of a unit circle in the presence of an initial heat. owing perpendicular to the plate. The use of the complex variable method gives convenient expressions of Goursat functions in applications, it also achieves the objective rapidly. Several previous works are considered as special cases of this work. The hole takes different shapes that make this study applicable to many cases, like tunnels, caves, excavations in soil or rock, etc. Stress and strain components have been obtained and plotted to investigate their physical meanings. With the aid of a computer, shapes of holes were received, and distribution of stresses obtained.