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Elliptic Boundary Layer in Shells of Revolution Under Normal Edge Shock Loading

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Multiscale Solid Mechanics

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 141))

Abstract

The present paper is aimed to construction the asymptotic theory of the elliptic boundary layer in shells of revolution under normal edge shock loading. Asymptotic equations of this boundary layer are derived in the small vicinity of the surface Rayleigh wave front. First of all the problem for normal edge shock loading is reduced to the problem for surface shock loading by constructing the particular solution, satisfying only the boundary conditions on the shell edge. Asymptotic solution of the governing equations for addition problem is obtained by using the Lourye symbolic approach and the front asymptotic near the surface Rayleigh wave front. The symbolic solution allows us to derive governing equations of the boundary layer. The behaviour of this boundary layer along the thickness is defined by elliptic equations and the boundary conditions on the faces are defined by hyperbolic equations, characterized wave motion on these faces. Considered component together with early constructed ones allows describe solution for transient waves in all parts of the phase plane.

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Authors and Affiliations

  1. Saratov State University, 83 Astrakhanskaya Street, Saratov, 410012, Russian Federation

    Irina V. Kirillova & Leonid Yu. Kossovich

Authors
  1. Irina V. Kirillova
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  2. Leonid Yu. Kossovich
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Correspondence to Irina V. Kirillova .

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Editors and Affiliations

  1. Faculty of Mechanical Engineering, Otto von Guericke University Magdeburg, Magdeburg, Sachsen-Anhalt, Germany

    Holm Altenbach

  2. Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Gdańsk, Poland

    Victor A. Eremeyev

  3. Research Institute for Mechanics, State University of Nizhny Novgorod, Nizhny Novgorod, Russia

    Leonid A. Igumnov

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Kirillova, I., Kossovich, L. (2021). Elliptic Boundary Layer in Shells of Revolution Under Normal Edge Shock Loading. In: Altenbach, H., Eremeyev, V.A., Igumnov, L.A. (eds) Multiscale Solid Mechanics. Advanced Structured Materials, vol 141. Springer, Cham. https://doi.org/10.1007/978-3-030-54928-2_19

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  • DOI: https://doi.org/10.1007/978-3-030-54928-2_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-54927-5

  • Online ISBN: 978-3-030-54928-2

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