Viscous fluid-thin cylindrical elastic layer interaction: asymptotic analysis

Abstract

This article represents a generalization of our previous work. We consider a periodic, non-steady, axially symmetric, creeping flow of a viscous incompressible fluid that fills a cylindrical elastic hollow tube. We study the interaction problem “viscous fluid-thin cylindrical elastic layer” when the thickness of the tube wall, , tends to zero, while the density and the Young’s modulus of the elastic material are of order and , respectively. We construct a complete asymptotic expansion when tends to zero. The error between the exact solution and the asymptotic one is evaluated in order to justify the asymptotic construction.

Keywords:

• fluid-structure interaction
• cylindrical elastic hollow tube
• axially symmetric flow
• periodic case
• asymptotic solution
• error estimate

AMS Subject Classifications:

• 76M30
• 76M45

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Erratum

Acknowledgments

This work was done during the stay of the second author in Camille Jordan Institute. This work was performed within the framework of the LABEX MILYON (ANR-10-LABX-0070) of University of Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). It was supported by the Research Federations MODMAD FED 4169 and FR CNRS 3490 and the grants PROCOPE EGIDE “Homogenization based optimization for elasticity on the network of beams” and RFBR “Construction analysis and applications of multiscale methods for solution of the boundary value problems” No. 12.740.11.1405.