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Numerical solution to a nonlinear, one-dimensional problem of anisotropic thermoelasticity with volume force and heat supply in a half-space: interaction of displacements

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Abstract

A numerical solution is presented for a one-dimensional, coupled nonlinear wave propagation problem of thermoelasticity for an anisotropic, elastic half-space involving body force and heat supply, under a periodic in-depth displacement at the boundary. This is a generalization of a previous work by the same authors with only the in-depth displacement. The volume force and bulk heating simulate the effect of a beam of particles infiltrating the medium. No phase transition is considered, and the domain of the solution excludes any shock wave formation at breaking distance. Three interacting components of the mechanical displacement are taken into account. The numerical scheme is investigated rigorously. It is shown to exhibit unconditional stability and a correct reproduction of the process of coupled thermo-mechanical wave propagation and the coupling between the displacement components. The interplay between these two factors and the applied boundary disturbance is outlined. The results are discussed and compared with those when only the in-depth displacement is considered. The presented figures show the effects of volume force and heat supply on the distributions of the mechanical displacements and temperature inside the medium. The presence of more than one velocity of propagation of the waves due to anisotropy is put in evidence. It turns out that the effect of the transversal displacements on the in-depth displacement and on the temperature for the considered values of the different material constants becomes weaker as time grows. The different forms of the propagating waves allow, if proper measurements are carried out, to detect the presence of a force field or bulk heating in the medium.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Cairo University, Giza, 12613, Egypt

    W. Mahmoud, A. F. Ghaleb, E. K. Rawy, H. A. Z. Hassan & A. A. Mosharafa

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  1. W. Mahmoud
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  2. A. F. Ghaleb
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  3. E. K. Rawy
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  4. H. A. Z. Hassan
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  5. A. A. Mosharafa
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Correspondence to A. F. Ghaleb.

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Mahmoud, W., Ghaleb, A.F., Rawy, E.K. et al. Numerical solution to a nonlinear, one-dimensional problem of anisotropic thermoelasticity with volume force and heat supply in a half-space: interaction of displacements. Arch Appl Mech 85, 433–454 (2015). https://doi.org/10.1007/s00419-014-0921-3

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