الفهرس 
Deformation of long thermoelastic rods with normal cross-section bounded by an ellipse with elliptical hump under mixed mechanical and thermal conditions by a boundary integral method
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Abstract
A numerical boundary integral scheme is used for the solution of the system of eld equations of plane, linear, thermoelasticity in stresses for homogeneous, isotropic media occupying a simply connected cross-section domain under mixed mechanical and thermal boundary conditions. The problem is solved after smoothing the contour enclosing the domain. The imposed boundary conditions are of three cases. A previously introduced boundary integral method is used to nd an ap- proximate solution to a problem of plane, uncoupled thermoelasticity inside an ellipse with elliptical hump. Three problems are considered. Two of this problems was su ering a given variable pressure on the half of the, bound- ary enclosing the domain, while the other part is completely xed. This two boundary conditions was formed together with thermal Robin (case I) and Neu- mann (case II). While mechanical boundary conditions for the third problem was given variable extension at half of the boundary and a completely xed condition for the other half together with Dirichlet thermal condition at whole the boundary . The singular behavior of the solution is assumed to be a nite jump at tangential and normal components of the stress tensor at separation points so that it is put in evidence at those points where the boundary condi- tions change. The solution is then sought for in the form of series in Cartesian regular harmonics, enriched with a specially chosen harmonic function with sin- gular boundary behavior to simulate the existing singularities. The results are analyzed in detail and the functions of practical interest are represented on the boundary and also inside the domain by three-dimensional plots. This model may be useful in analyzing the stresses that arise in long elastic pad supports