Abstract
In the present paper Cauchy integral methods have been applied to derive exact and expressions for Goursat’s function for the first and second fundamental problems of isotropic homogeneous perforated infinite elastic media in the presence of uniform flow of heat. For this, we considered the problem of a thin infinite plate of specific thickness with a curvilinear hole where the origins lie in the hole is conformally mapped outside a unit circle by means of a specific rational mapping. Moreover, the three stress components σxx, σyy and σxy of the boundary value problem in the thermoelasticity plane are obtained. Many special cases of the conformal mapping and four applications for different cases are discussed and many main results are derived from the work.
Highlights
The boundary value problems for isotropic performed plates have been discussed by several authors
From the previous discussions we have the following results: 1) We find that the effect of heat is very clear; we find that the values of components stress are reduced with existence of heat, while at absence of heat we find the values of components of stresses are increasing
2) With increasing angle and with absence f (t ), we find that max
Summary
The boundary value problems for isotropic performed plates have been discussed by several authors. In thermoelastic problems for elastic media, the first and second boundary value problems are equivalent to two finite analytic functions φ ( z) and ψ ( z) of one complex argument z= x + iy. These functions must satisfy the boundary condition, Kφ1 (t ) − tφ1′(t ) −ψ1 (t ) = f (t ) (1). (2015) Presence of Heat on an Infinite Plate with a Curvilinear Hole Having Two Poles.
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