Thermoelastic Problem of an Infinite Plate Weakened by a Curvilinear Hole

  • R. T. Matoog Department of Mathematics, Faculty of Applied Sciences, University of Umm Al-Qura, KSA
Keywords: Boundary value problems, thermoelastic plate, Gaursat functionsl, rational mapping, curvilinear hole, AMS (2010), 74B10, 30C20.


Mathematical model is considered, to discuss the analytic solution of the first and second boundary value problems (BVPs), for an infinite plate weakened by a curvilinear hole C having two poles. The elastic plate carries a steady   uniformly distributed axial current of density J and is placed in an ambient medium of steady temperature Using a conformal mapping function, the curvilinear hole is conformally mapped on the domain outside (inside) a unit circle  Then, the Gaursat functions (GFs) are determined. Moreover, the three components of stresses, in the presence of  temperature T distributed around the curvilinear hole are completely determined.  Many special and new cases are derived from the work.  In addition, many, applications for the first and second BVPs are discussed. Moreover, the three stresses components, in each application, are computed. 


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