Projection-iterative version of the method of local variations for the problems of local stability of spherical shells
DOI:
https://doi.org/10.15407/dopovidi2015.08.035Keywords:
local stability, method of local variations, projection-iterative scheme of implementation, spherical shellAbstract
A projection-iterative scheme of a realization of the method of local variations for solving the variational problems with quadratic functional is proposed and theoretically grounded. By the example of solving the problem of local stability of a spherical shell, the practical efficiency of the proposed modification of the method of local variations is demonstrated.
Downloads
References
Chernous'ko F. L. J. vychislitelnoy matematiki i matematicheskoy physiki, 1965, 5, No 4: 749–754 (in Russian).
Chernous'ko F. L., Banichuk N.V. Variational Problems of Mechanics and Control, Moscow: Nauka, 1973 (in Russian).
Krasnosel'skii M.A., Vainikko G.M., Zabreiko P. P. et al. Approximate Solution of the Operator Equations, Moscow: Nauka, 1969 (in Russian).
Samarskii A.A., Nikolaev ES. Methods for Solving Finite-Difference Equations, Moscow: Nauka, 1978 (in Russian).
Marchuk G. I., Agoshkov V. I. Introduction to Projection-Grid Methods, Moscow: Nauka, 1981 (in Russian).
Kluge R. Monatsber. Detsch. Akad. Wiss. Berlin, 1969, 11, No 8–9: 599–609.
Hart E. L., Borisovskaja I.V. Vestnik Dnepropetrovskogo universiteta, Ser. Mechanika, 2004, Is. 8, 2: 44–51 (in Russian).
Hart E. L. J. Math. Sci., 2010, 167, No 1: 76–88. https://doi.org/10.1007/s10958-010-9903-3
Hudramovich V. S., Hart E. L., Rjabokon' S.A. J. Math. Eng, 2013, 78, No 1: 181–197. https://doi.org/10.1007/s10665-010-9409-5
Hart E. L., Hudramovich V. S. J. Math. Sci, 2014, 203, No 1: 55–69. https://doi.org/10.1007/s10958-014-2090-x
Mukhamediev Sh.A., Nikitin L.V., Junga S. L. Izvestiya AN SSSR. MTT, 1976, No 1: 76–83 (in Russian).
Hart E. L., Hudramovich V. S. Modern problems of mechanics and mathematics. Materialy mezhdunarodnoy nauch. konf. Lvov: IPPMM NANU, 2008, 3: 18–20 (in Ukrainian).
Mossakowskii V. I., Hudramovich V. S., Makeev E.M. Contact Problems in the Theory of Shells and Rods, Moscow: Mashinostrojenie, 1978 (in Russian).
Hudramovich V. S. Int. Appl. Mech. 2009, 45, No 7: 708–729. https://doi.org/10.1007/s10778-009-0224-5
Mushtari Ch.M., Galimov K. Z. Nonlinear Theory of Elastic Shells, Kazan': Tatknigoizdat, 1957 (in Russian).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Reports of the National Academy of Sciences of Ukraine
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
