Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Kaplunov J. D., Zupancic B., Nikonov A. V. Asymptotic analysis of the axisymmetric problem for the transverse compression of a thin elastic disk in the case of mixed boundary conditions along its faces. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2024, vol. 24, iss. 1, pp. 57-62. DOI: 10.18500/1816-9791-2024-24-1-57-62, EDN: LNJVVN

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
01.03.2024
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Language: 
Russian
Heading: 
Mechanics
Article type: 
Article
UDC: 
539.3
DOI: 
10.18500/1816-9791-2024-24-1-57-62
EDN: 
LNJVVN

Asymptotic analysis of the axisymmetric problem for the transverse compression of a thin elastic disk in the case of mixed boundary conditions along its faces

Autors: 
Kaplunov Julius Davidovich, Keele University
Zupancic Barbara, National Institute of Chemistry
Nikonov Anatolij V., University of Ljubljana
Abstract: 

The axisymmetric problem for the transverse compression of a thin elastic disk is considered in slip absence.  An asymptotic solution for the interior stress-strain state is constructed. An approach to determining a plane boundary layer localized near the outer contour of the disk is outlined.

Key words: 
asymptotic methods
asymptotic solution
axisymmetric problem
compression problem
mixed boundary conditions
stress-strain state
flat boundary layer
References: 
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  3. Kaplunov J. D., Kossovich L. Yu., Nolde E. V. Dynamics of Thin Walled Elastic Bodies. San-Diego, Academic Press, 1998. 226 p. https://doi.org/10.1016/c2009-0-20923-8
  4. Kaplunov J. D., Kossovich L. Yu., Moukhomodiarov R. R. Impact normal compression of an elastic plate: analysis utilising an advanced asymptotic 2D model. Mechanics Research Communications, 2000, vol. 27, iss. 1, pp. 117–122. https://doi.org/10.1016/S0093-6413(00)00070-7
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  7. Kaplunov J., Prikazchikov D., Sultanova L. Justification and refinement of Winkler – Fuss hypothesis. Zeitschrift fur angewandte Mathematik und Physik, 2018, vol. 69, art. 80. https://doi.org/10.1007/s00033-018-0974-1
  8. Wilde M. V., Kaplunov J. D., Kossovich L. Yu. Kraevye i interfeysnye rezonansnye yavleniya v uprugikh telakh [Edge and Interfacial Resonance Phenomena in Elastic Bodies]. Moscow, Fizmatlit, 2010. 280 p. (in Russian).
  9. Kaplunov J. D., Kossovich L. Yu., Wilde M. V. Free localized vibrations of a semi-infinite cylindrical shell. The Journal of the Acoustical Society of America, 2000, vol. 107, iss. 3, pp. 1383–1393. https://doi.org/10.1121/1.428426 
Received: 
05.12.2023
Accepted: 
28.12.2023
Published: 
01.03.2024
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