|1Lila, DM |
1Bohdan Khmelnytsky National University of Cherkasy
|Dopov. Nac. akad. nauk Ukr. 2018, 5:36-43|
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.
|Keywords: boundary shape perturbation method, critical angular velocity, elastoplastic problem, rotating disk, stability loss|
- 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).