The stress and strain components for a weakened elastic plate by two curvilinear holes in presence of heat


  • M.A. Abdou Department of Mathematics, Faculty of Education, Alexandria University, Egypt.
  • E. Ibrahim Department of Mathematics, Faculty of Science, Helwan University, Egypt.
  • M. Basseem Department of Mathematics, Faculty of Engineering, Sinai University, Egypt.


Thermoelastic plate, Analytical modeling, curvilinear hole, Complex variable method, boundary value problems (BVPs), Gaursat functions, Conformal mapping


In this work, the first and second Gaursat functions for an unbounded plate with two curvilinear holes are deduced using the complex variable technique. The two holes in all previous works are conformally mapped outside the unit circle. In the presence of an initial heat flow perpendicular to the plate, these are conformally mapped into the unit circle. The holes take on a variety of shapes, allowing this study to be applied to a wide range of situations, including caves, tunnels, and excavations in solids or rocks. The physical meaning of stress components is investigated by obtaining and plotting them. The various forms are received using Maple 2019. There are several applications that are studied and discussed.