539.384 Modeling the stability of compressed and twisted rods in precise problem statement

Dubrovin V. M. (Bauman Moscow State Technical University), Butina T. A. (Bauman Moscow State Technical University)

ROD, COMPRESSION, TORSION, STABILITY, FLEXURAL STIFFNESS, CRITICAL FORCE, TORQUE


doi: 10.18698/2309-3684-2015-3-316


The article describes the method for calculating the stability of a rod under simultaneous action of axial force and torque, considering changing the torsion of the rod when it’s bent. The method is based on the use of the complete system of equations. The following cases are considered: end clamped rod, rod with a hinged support, the rod in the form of compressed and twisted console. Diagrams of dependence of the critical axial force versus the critical torque are obtained, i.e., the range of rod stability for the case of loading is determined.


[1] Shashkov I.E. Prikladnaya mekhanika – Applied Mechanics, 1976, vol. XII, no. 1, pp. 71−76.
[2] Dubrovin V.M., Butina T.A. Inzhenernyi zhurnal: nauka i innovatsii — Engineering Journal: Science and Innovations, 2014, no. 9 (21). Available at: http://engjournal.ru/catalog/mathmodel/solid/44.html
[3] Feodosyev V.I. Izbrannye zadachi i voprosy po soprotivleniyu materialov [Selected Problems and Questions about the Strength of Materials]. Moscow, Nauka Publ., 1993, 400 p.
[4] Ponomarev S.D., ed. Raschety na prochnost v mashinostroenii [Calculations of Strength in Mechanical Engineering]. Vol. 3. Moscow, Mashgiz Publ., 1959, 861 p.
[5] Rabotnov Yu.N. Problemy mekhaniki deformiruemogo tela [The Problems of Deformable Solid Body Mechanics]. Moscow, Nauka Publ., 1991, 194 p.
[6] Frolov K.V. Izbrannye Trudy [Selected Works]. Moscow, Nauka Publ., 2007, 526 p.
[7] Dimitrienko Yu. I. Universalnye zakony mekhaniki i elektrodinamiki sploshnoy sredy. Tom 2. Mekhanika sploshnoy sredy [Universal Laws of Mechanics and Electrodynamics of Continuum. Vol. 2. Continuum Mechanics]. Moscow, BMSTU Publ., 2011, 560 p.
[8] Dimitrienko Yu.I. Vestnic MGTU im. N.E. Baumana. Seria Estestvennye nauki – Herald of the Bauman Moscow State Technical University. Series: Natural Sciences, 2014, no. 1, pp. 17−26.
[9] Dimitrienko Yu.I. Vestnic MGTU im. N.E. Baumana. Seria Estestvennye nauki – Herald of the Bauman Moscow State Technical University. Series: Natural Sciences, 2014, no. 2, pp. 77−89.
[10] Gavryushin S.S. Matematicheskoe modelirovanie i chislennye menody – Mathematical Modeling and Numerical Methods, 2014, no. 1, pp. 115–130.
[11] Zhilin P.A. Aktualnye problem y mekhaniki [Topical Problems in Mechanics]. St. Petersburg, Institute of Problems of Mechanical Engineering, RAS Publ., 2006, 306 p.
[12] Pikovskiy A., Rozenblum N. Kurts Yu. Sinkhronizatsiya. Fundamentalnoe nelineynoe yavlenie [Synchronization. The Fundamental Nonlinear Phenomenon]. Moscow, Tekhnosfera Publ., 2003, 493 p.
[13] Volmir A.S. Ustoychivost deformiruemykh system [Stability of Deformable Systems]. Moscow, Nauka Publ., 1967, 987 p.
[14] Butina T.A., Dubrovin V.M. Inzhenernyi zhurnal: nauka i innovatsii — Engineering Journal: Science and Innovations, 2012, no. 2. Available at: http://engjournal.ru/catalog/mathmodel/solid/44.html.


Dubrovin V., Butina T. Modeling the stability of compressed and twisted rods in precise problem statement. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 3-16



Download article

Количество скачиваний: 552