Simulation of a thin long rod that does not have critical forces and does not lose stability to Euler
DOI:
https://doi.org/10.31891/2079-1372-2020-97-3-25-31Keywords:
stable rods, critical force, bending modes, simulation, flexible rodAbstract
The paper proposes a method of preventing the loss of Euler stability by thin rods. Such rods do not have critical forces and therefore do not lose stability from longitudinal compressive force. The method is based on a temporary change in the stiffness of the rod-support system, in particular, a change in the length of the rod between the supports when approaching the value of critical forces, and after passing the return to the previous value. The results of simulation modeling of the rod behavior are presented, which confirm the possibility to eliminate the loss of its stability with increasing compressive force to the maximum allowable value, which is determined from the condition of strength
References
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10. Sharafutdinova G. G. An operator method for studying the Euler problem on types of the loss of stability for a pivoted rod under buckling load. Russian Math. (Iz. VUZ), 54:11 (2010), 77–82
11. Glazkov Т. V. Критическая нагрузка стержня с начальной неправильностью / Т. В. Глазков. — Текст : непосредственный // Молодой ученый. — 2015. — № 23 (103). — С. 125-129.
12. Bekshaev S. Ya. On the optimal position of the intermediate support of a three-span rod // Bulletin of Odessa State Academy of Civil Engineering and Architecture. 60 (2015) 400 – 406.
13. V Chudnovsky, A Mukherjee, J Wendlandt, D Kennedy Modeling flexible bodies in simmechanics //MatLab Digest. – Vol. 14 (3) (2006).
14. Miller S. et al. Modeling flexible bodies with simscape multibody software //An Overview of Two Methods for Capturing the Effects of Small Elastic Deformations, MathWorks. – 2017.
15. Zmeu K.V., Notkin B. S., Kovalyov V.A., Vara A.V. Modeling the Flexible Mechanical System In Matlab for Control System Synthesis // Izvestia of Samara Scientific Center of the Russian Academy of Sciences. 1-2. (2012)
2. Euler L., 1759. Sur la force de colonnes (in French). Memoires de l’Academie de Berlin, 13, 251-282. (op.cit.)
3. Pisarenko S. S. Strength of materials. К. : «Technics», 1967. − 791 p. (in Russian)
4. Grashof F., 1878. Theorie der Elasticität und Festigkeit. Berlin (op.cit.)
5. Yasinsky F.S. Experience in the development of the theory of buckling. // F.S. Yasinsky. Selected papers on the stability of compressed rods. M. - L .: Gostekhizdat, 1952 . p. 138-194 (in Russian)
6. Timoshenko S. P., Gere J. M., 1963.Teoria stateczności sprężystej. Arkady Warszawa.
7. Lembo, Marzio. (2003). On the stability of elastic annular rods. International Journal of Solids and Structures. 40. 317-330. 10.1016/S0020-7683(02)00546-2.
8. Karimbaev K.D., Palchikov D.S. About criteria of loss of stability of the squeezed cores outside elasticity at rigid loading // Vestnik of Ufa State Aviation Technical University. Vol. 19. 3 (69). (2015) 126-131.
9. Murawski K. The Euler's modified theory of stability with stresses and strains analysis on example of very slender cylindrical shells made of steel. Acta Scientiarum Polonorum, Architectura, 3(1) 2004
10. Sharafutdinova G. G. An operator method for studying the Euler problem on types of the loss of stability for a pivoted rod under buckling load. Russian Math. (Iz. VUZ), 54:11 (2010), 77–82
11. Glazkov Т. V. Критическая нагрузка стержня с начальной неправильностью / Т. В. Глазков. — Текст : непосредственный // Молодой ученый. — 2015. — № 23 (103). — С. 125-129.
12. Bekshaev S. Ya. On the optimal position of the intermediate support of a three-span rod // Bulletin of Odessa State Academy of Civil Engineering and Architecture. 60 (2015) 400 – 406.
13. V Chudnovsky, A Mukherjee, J Wendlandt, D Kennedy Modeling flexible bodies in simmechanics //MatLab Digest. – Vol. 14 (3) (2006).
14. Miller S. et al. Modeling flexible bodies with simscape multibody software //An Overview of Two Methods for Capturing the Effects of Small Elastic Deformations, MathWorks. – 2017.
15. Zmeu K.V., Notkin B. S., Kovalyov V.A., Vara A.V. Modeling the Flexible Mechanical System In Matlab for Control System Synthesis // Izvestia of Samara Scientific Center of the Russian Academy of Sciences. 1-2. (2012)
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Published
2020-09-28
How to Cite
Goroshko, A., Royzman, V., & Petraschuk, S. (2020). Simulation of a thin long rod that does not have critical forces and does not lose stability to Euler. Problems of Tribology, 25(3/97), 25–31. https://doi.org/10.31891/2079-1372-2020-97-3-25-31
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