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Mathematical Models and Computer Simulations

Erschienen in:

01.08.2023

Modeling Unsteady Elastic Diffusion Processes in a Hollow Cylinder Taking into Account the Relaxation of Diffusion Fluxes

verfasst von: N. A. Zverev, A. V. Zemskov

Erschienen in: Mathematical Models and Computer Simulations | Ausgabe 4/2023

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Abstract

A one-dimensional problem of elastic diffusion for a hollow orthotropic multicomponent cylinder under the action of external pressure, which is uniformly distributed over its inner and outer surfaces is considered. The mathematical model includes a system of equations of elastic diffusion in a cylindrical coordinate system, which takes into account relaxation diffusion effects, implying finite propagation velocities of diffusion processes. The problem is solved by the method of equivalent boundary conditions. For this an auxiliary problem is considered, whose solution is obtained by expansion into series in terms of the eigenfunctions of the elastic-diffusion operator. The relations that connect the right parts of the boundary conditions of both problems are constructed. These relations represent a system integral equation. They are solved using quadrature formulas. A calculation example for a three-component hollow cylinder is considered.

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Titel: Modeling Unsteady Elastic Diffusion Processes in a Hollow Cylinder Taking into Account the Relaxation of Diffusion Fluxes
verfasst von: N. A. Zverev
A. V. Zemskov
Publikationsdatum: 01.08.2023
Verlag: Pleiades Publishing
Erschienen in: Mathematical Models and Computer Simulations / Ausgabe 4/2023
Print ISSN: 2070-0482
Elektronische ISSN: 2070-0490
DOI: https://doi.org/10.1134/S2070048223040208

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