The second 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/dopovidi2018.05.036

Keywords:

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

Abstract

We have proposed a way of the investigation of the possible loss of stability by a rotating thin circular disk by the method of small parameter on the basis of Saint-Venant's yield condition. We have obtained a characteristic equation for the critical radius of the plastic zone as the second approximation. We also have found the critical angular rotational velocity.

Downloads

Download data is not yet available.

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).

Ishlinskii, A. Yu. & Ivlev, D. D. (2001). Mathematical Theory of Plasticity. 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).

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. & 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. Math., No. 14, pp. 92-98 (in Russian).

Published

15.05.2024

How to Cite

Lila, D. (2024). The second 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, (5), 36–43. https://doi.org/10.15407/dopovidi2018.05.036