The third approximation in a small parameter to a solution of the problem of elastoplastic instability of a rotating disk

Authors

  • D.M. Lila Bohdan Khmelnytsky National University of Cherkasy

DOI:

https://doi.org/10.15407/dopovidi2019.04.042

Keywords:

boundary shape perturbation method, critical angular velocity, elastoplastic problem, rotating disc, stability loss

Abstract

We have proposed a way of investigation of the possible loss of stability by a rotating thin circular disk by the method of small parameter. We have obtained a characteristic equation for the critical radius of the plastic zone in the third approximation. We also have found the critical angular rotational velocity.

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References

Ivlev, D. D. & Ershov, L. V. (1978). Perturbation Method in the Theory of Elastoplastic Bodies. Moscow: Nauka (in Russian).

Ivlev, D. D. (2002). Mechanics of Plastic Media. Vol. 2: General Problems. Rigid-Plastic and Elastoplastic State of Bodies. Hardening. Deformation Theories. Complex Media. Moscow: Fizmatlit (in Russian).

Guz’, A. N. & Nemish, Yu. N. (1989). Method of Perturbation of the Shape of the Boundary in Continuum Mechanics. Kyiv: Vyshcha Shkola (in Russian).

Guz, A. N. (2012). Stability of elastic bodies under uniform compression (review). Int. Appl. Mech., 48, No. 3, pp. 241-293. doi: https://doi.org/10.1007/s10778-012-0520-3

Lila, D. M. & Martynyuk, A. A. (2011). About the stability loss of a rotating elastoplastic circular disc. Dopov. Nac. akad. nauk Ukr., No. 1, pp. 44-51 (in Russian).

Lila, D. M. (2011). Eccentric form of stability loss of a rotating elastoplastic disc. Dopov. Nac. akad. nauk Ukr., No. 2, pp. 49-53 (in Russian).

Lila, D. M. & Martynyuk, A. A. (2012). Development of instability in a rotating elastoplastic annular disk. Int. Appl. Mech., 48, No. 2, pp. 224-233. doi: https://doi.org/10.1007/s10778-012-0518-x

Lila, D. M. (2016). Elasto-plastic instability of thin rotating disc. Appl. Probl. Mech. and Math., No. 14, pp. 92-98 (in Russian).

Lila, D. M. (2017). On the method of perturbations in the problem of elastoplastic instability of a rotating disk. Dopov. Nac. akad. nauk Ukr., No. 9, pp. 48-54 (in Russian). doi: https://doi.org/10.15407/dopovidi2017.09.048

Lila, D. M. (2018). The second approximation in a small parameter to a solution of the problem of elastoplastic instability of a rotating disk. Dopov. Nac. akad. nauk Ukr., No. 5, pp. 36-43 (in Russian). doi: https://doi.org/10.15407/dopovidi2018.05.036

Lila, D. M. (2018). The second approximation in a small parameter to a solution of the problem of loss of the stability of a rotating disk in the refined formulation. Dopov. Nac. akad. nauk Ukr., No. 7, pp. 33-39 (in Russian). doi: https://doi.org/10.15407/dopovidi2018.07.033

Published

21.04.2024

How to Cite

Lila, D. (2024). The third approximation in a small parameter to a solution of the problem of elastoplastic instability of a rotating disk . Reports of the National Academy of Sciences of Ukraine, (4), 42–49. https://doi.org/10.15407/dopovidi2019.04.042