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Numerical Solution of Electro-magneto-thermo-mechanical Shock Problem

100%

El-Bary A.

2006

tom Vol. 12, nr 2

101-108

A conducting half-space, permeated by an initial magnetic field governed by the generalized equations of thermoelasticity is considered. The bounding plane is acted upon by a combination of thermal and mechanical shock. The formulation is applied to both generalizations, Lord-Shulman theory and the Green-Lindsay theory, as well as to the coupled theory. Laplace transform techniques together with the method of potentials are used. The inversion of the Laplace is carried out using a numerical approach. Numerical results for the temperature, the stress and the induced magnetic and electric field distributions are obtained and illustrated graphically for a particular case. Comparisons are made with the results obtained in the case of the absence of the magnetic field.

Fredholm - Volterra integral equation in three dimensional problem with Macdonald kernel

100%

El-Bary A.

tom z. 26 [199]

59-65

Regular and singular asymptatic method are applied to three dimensional Fredholm-Volterra integral equation of the first kind. In this paper we constract Fredholm-Volterra integri equation in three dimensional contact problem with Macdonald kernel in many cases of contact problem.

Mathematical Model for Thermal Shock Problem of a Generalized Thermoelastic Layered Composite Material with Variable Thermal Conductivity

63%

Youssef H. , El-Bary A.

2006

tom Vol. 12, nr 2

165-171

One-dimensional generalized thermoelastic mathematical model with variable thermal conductivity for heat conduction problem is constructed for a layered thin plate. The basic equations are transformed by Laplace transform and solved by a direct method. The solution was applied to a plate of sandwich structure, which is thermally shocked, and traction free in the outer sides. The inverses of Laplace transforms are obtained numerically. The temperature, the stress and the displacement distributions are represented graphically.