Abstract
Abstract
In this paper, we presented an integro differential equation (IDE), in compelx plane, with singular kernel. The IDE is investigated from the first and second boundary value problem (BVP) of a weakened infinite plate by a curvilinear hole (C,) in the presence of heat. The hole is conformally mapped inside a unit circle by a special transformation with complex constants coefficients\(z=\omega (\zeta ),\,\zeta =\xi +i\eta ,\,i=\sqrt { - 1} .\) This mapping will conform the curvilinear hole in the infinite elastic plate into a unit circle \(\gamma ,\left| \zeta \right|\;<\,\,1,\) such that inside the circle. The stress and strain compounds were calculated, in the presence of heat effect, and this was clarified by numerical results. Many applications for the problem are discussed. Maple 2019 is used for computations results.
MSC (2010): 74B10, 30C20.
Publisher
Research Square Platform LLC
Reference20 articles.
1. Fundamental contact problem and singular mixed integral equation;Abdou MA;Life Sci. J,2014
2. The behavior of the generalized potential kernel of axisymmetric contact problems and the structure resolvent of the fundamental problems;Tatoog RT;Int. J. Res. Scien Res.,2016
3. New model for solving mixed integral equation of the first kind with generalized potential kernel;Al-Hazmi SE;J. Math. Res.,2017
4. On the solution of quadratic nonlinear integral equation with different singular kernels;Basseem M,2020
5. Solvability of quadratic integral equations with singular kernel;Abdou MA;J. Contemp. Math. Anal.,2021