Unsteady Coupled Elastic Diffusion Processes in an Orthotropic Cylinder Taking into Account Relaxation of Diffusion Fluxes

We consider the problem of determining the stress-strain state of an orthotropic multicomponent cylinder affected by unsteady surface elastic diffusive perturbations. The coupled system of elastic diffusion equations in the polar coordinate system is used as a mathematical model. Diffusion relaxatio...

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Bibliographic Details
Published in:Russian mathematics 2022, Vol.66 (1), p.19-30
Main Authors: Zverev, N. A., Zemskov, A. V., Tarlakovskii, D. V.
Format: Article
Language:English
Subjects:
Bessel functions
Diffusion effects
Diffusion rate
Exact solutions
Fourier series
Green's functions
Laplace transforms
Mathematical analysis
Mathematics
Mathematics and Statistics
Operational calculus
Orthotropic cylinders
Perturbation
Polar coordinates
Series expansion
Strain
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Summary:We consider the problem of determining the stress-strain state of an orthotropic multicomponent cylinder affected by unsteady surface elastic diffusive perturbations. The coupled system of elastic diffusion equations in the polar coordinate system is used as a mathematical model. Diffusion relaxation effects, implying finite rates of diffusion flux propagation, are taken into account. The solution to this problem is sought in the integral form and is represented as convolutions of Green’s functions with functions defining surface elastodiffusive perturbations. We use the Laplace transform by time and Fourier series expansion in Bessel functions of the first kind to find Green’s functions. The Laplace transform inversion is done analytically due to residues and operational calculus tables. An analytical solution to the problem is obtained. A numerical study of the interaction of mechanical and diffusion fields in a continuous orthotropic cylinder is performed. We used three-component material as an example. The cylinder is under pressure, which is uniformly distributed over it surface. We use three-component material as an example.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X2201008X