Geodesic
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, Tome 24 (2024) no. 1, pp. 57-62 
J. D. Kaplunov; B. Zupančič; A. V. Nikonov. 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, Tome 24 (2024) no. 1, pp. 57-62. http://geodesic.mathdoc.fr/item/ISU_2024_24_1_a5/
@article{ISU_2024_24_1_a5,
     author = {J. D. Kaplunov and B. Zupan\v{c}i\v{c} and A. V. Nikonov},
     title = {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},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {57--62},
     year = {2024},
     volume = {24},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2024_24_1_a5/}
}
TY  - JOUR
AU  - J. D. Kaplunov
AU  - B. Zupančič
AU  - A. V. Nikonov
TI  - 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
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2024
SP  - 57
EP  - 62
VL  - 24
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ISU_2024_24_1_a5/
LA  - ru
ID  - ISU_2024_24_1_a5
ER  - 
%0 Journal Article
%A J. D. Kaplunov
%A B. Zupančič
%A A. V. Nikonov
%T 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
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2024
%P 57-62
%V 24
%N 1
%U http://geodesic.mathdoc.fr/item/ISU_2024_24_1_a5/
%G ru
%F ISU_2024_24_1_a5

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Goldenweiser A. L., Theory of Elastic Thin Shells, Nauka, M., 1976, 512 pp. (in Russian) | MR

[2] Kossovich L. Yu., Nonstationary Problems in the Theory of Elastic Thin Shells, Saratov State University Publ, Saratov, 1986, 176 pp. (in Russian)

[3] Kaplunov J. D., Kossovich L. Ju., Nolde E. V., Dynamics of Thin Walled Elastic Bodies, Academic Press, San-Diego, 1998, 226 pp. | DOI | MR | Zbl

[4] Kaplunov J. D., Kossovich L. Ju., Moukhomodiarov R. R., “Impact normal compression of an elastic plate: analysis utilising an advanced asymptotic 2D model”, Mechanics Research Communications, 27:1 (2000), 117–122 | DOI | MR | Zbl

[5] Agalovyan L. A., The Asymptotic Theory of Anisotropic Plates and Shells, Nauka, M., 1997, 414 pp. (in Russian)

[6] Goldenweiser A. L., “General theory of thin elastic bodies (shells, coatings, and gaskets)”, Mechanics of Solids, 3 (1992), 5–17 (in Russian)

[7] Kaplunov J., Prikazchikov D., Sultanova L., “Justification and refinement of Winkler – Fuss hypothesis”, Zeitschrift für angewandte Mathematik und Physik, 69 (2018), 80 | DOI | MR | Zbl

[8] Wilde M. V., Kaplunov J. D., Kossovich L. Yu., Edge and Interfacial Resonance Phenomena in Elastic Bodies, Fizmatlit, M., 2010, 280 pp. (in Russian)

[9] Kaplunov J. D., Kossovich L. Ju., Wilde M. V., “Free localized vibrations of a semi-infinite cylindrical shell”, The Journal of the Acoustical Society of America, 107:3 (2000), 1383–1393 | DOI