Geodesic
An elastic half space under the action of one-dimensional time-dependent diffusion perturbations
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 1, pp. 70-78

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The paper deals with a one-dimensional problem of elastic diffusion for a single-component half space. We use a locally static geometrically linear model of elastic diffusion, which contains mass transfer equations and a coupled system of the motion equations of an elastic body. To build the solution, we apply the integral Fourier and Laplace transforms. The problem of inversion of the Laplace transforms reduces to the inversion of rational functions; the inverse Fourier transform is performed numerically. A fundamental solution to the problem is developed. We consider the case when the diffusion flux at the boundary is constant. The obtained results provide a theoretical framework for the analysis of the stress-strain state in aeronautical and space structures working in the conditions of multifactorial external influences.
Mots-clés : elastic diffusion, Fourier transform, Laplace transform
Keywords: time-dependent problems, half space. 
@article{UZKU_2014_156_1_a6,
     author = {S. A. Davydov and A. V. Zemskov and D. V. Tarlakovskii},
     title = {An elastic half space under the action of one-dimensional time-dependent diffusion perturbations},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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     publisher = {mathdoc},
     volume = {156},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2014_156_1_a6/}
}
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S. A. Davydov; A. V. Zemskov; D. V. Tarlakovskii. An elastic half space under the action of one-dimensional time-dependent diffusion perturbations. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 1, pp. 70-78. http://geodesic.mathdoc.fr/item/UZKU_2014_156_1_a6/