Techno Press


Steel and Composite Structures   Volume 25, Number 2, October10 2017, pages 177-186
DOI: http://dx.doi.org/10.12989/scs.2017.25.2.177
 
A functionally graded magneto-thermoelastic half space with memory-dependent derivatives heat transfer
Magdy A. Ezzat and Alaa A. El-Bary

 
Abstract     [Full Text]
    In this work, the model of magneto-thermoelasticity based on memory-dependent derivative (MDD) is applied to a one-dimensional thermal shock problem for a functionally graded half-space whose surface is assumed to be traction free and subjected to an arbitrary thermal loading. The Lamé's modulii are taken as functions of the vertical distance from the surface of thermoelastic perfect conducting medium in the presence of a uniform magnetic field. Laplace transform and the perturbation techniques are used to derive the solution in the Laplace transform domain. A numerical method is employed for the inversion of the Laplace transforms. The effects of the time-delay on the temperature, stress and displacement distribution for different linear forms of Kernel functions are discussed. Numerical results are represented graphically and discussed.
 
Key Words
    magneto-thermoelasticity; FGMs; variable Lamé's modulii; memory-dependent derivatives; perturbation method; numerical results
 
Address
(1) Magdy A. Ezzat:
Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt;
(2) Alaa A. El-Bary:
Arab Academy for Science and Technology, P.O. Box 1029, Alexandria, Egypt.
 

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