Steel and Composite Structures

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A functionally graded magneto-thermoelastic half space with memory-dependent derivatives heat transfer

  • Ezzat, Magdy A. (Department of Mathematics, Faculty of Education, Alexandria University) ;
  • El-Bary, Alaa A. (Arab Academy for Science and Technology)
  • Received : 2017.05.10
  • Accepted : 2017.06.29
  • Published : 2017.10.10
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Abstract

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 $Lam{\acute{e}}^{\prime}s$ 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.

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