Lyakhovich L.S., Perelmuter A.V., Slivker V.I.

UDC 624.04


Tomsk University of Architecture and Building,

2, Solyanaya Sq., 634003, Tomsk, Russia


NPO «SKAD Soft», Kiev


OAO «Institut Giprostroimost»,

St.-Petersburg, Russia


Paradoxes, reasons for their occurrence and the role in the assessment of design model correctness are discussed in this paper. On the examples from the theory of structures it has been shown that some paradoxes occur due the choice of design models that insufficiently account for the real-life object properties. It has been noted that certain properties of a real-life object insignificantly influencing the results of calculation in one instance might change it quite in another, and a paradox might vanish under the insignificant change of calculating and viewing conditions. Availability of paradox encourages carrying out new research, provides a deeper understanding of the theory and its postulates and, sometimes, leads to its complete review.

Key words: paradoxes; stability; natural vibrations; non-conservative systems; flexural plane; dissipation; destabilization; ultimate load; plastic hinge; structurally stable system.


  1. Andronov, A.A., Pontryagin, L.S. Grubye sistemy[Systèmes grossiers]. DAN SSSR. 1937. V. 14, No. 5. Pp. 247–250. (rus)
  2. Gordeev, V.N. Osobennosti raboty mnogoryadnykh friktsionnykh soedinenii na vysokoprochnykh boltakh [Operating features of multirow slip-critical high-strength bolted connection]. Zbirnyk naukovyh prac' Ukrai'ns'kogo naukovo-doslidnogo instytutu stalevyh konstrukcij imeni V.M. Shymanovs'kogo. Kiev: Stal', 2010. No. 5. Pp. 172–180. (rus)
  3. Le Xuan Anh. Paradoksy Panleve i zakon dvizheniya mekhanicheskikh sistem s kulonovym treniem [Painleve paradoxes and laws of motion for mechanical systems with Coulomb friction]. J. Appl. Math. Mech. 1990. V. 54, No. 4. Pp. 520–529. (rus)
  4. Lyakhovich, L.S. Razdelenie kriticheskikh sil i sobstvennykh chastot uprugikh sistem [Separation of critical forces and proper frequencies of elastic systems]. Tomsk: TSUAB Publishing House, 2004. 140 p. (rus)
  5. Panovko, Ya.G., Gubanova, I.I. Ustoichivost' i kolebaniya uprugikh sistem [Stable and vibratory systems. 3rd edition]. Moscow: Fizmatgiz, 1979. 384 p. (rus)
  6. Panovko, Ya.G. Mekhanika deformirumogo tverdogo tela: Sovremennye kontseptsii, paradoksy i oshibki [Deformable solid mechanics: modern concepts, paradoxes, and mistakes]. Moscow: Fizmatgiz, 1985. 288 p. (rus)
  7. Perel’muter, A.V., Slivker, V.I. Nekotorye oshibki v postanovkah i reshenijah zadach ustojchivosti ravnovesija konstrukcij [Mistakes in posing and solving structural equilibrium stability problems]. Proc. Int. Conf. 'Computational mechanics of deformable solids’. Moscow: MIIT Publishing House [Moscow State University of Communication Means], 2006. V. 2. Pp. 316–323. (rus)
  8. Perel’muter, A.V., Slivker, V.I. Ustoichivost' ravnovesiya konstruktsii i rodstvennye problemy [Structural stability of equilibrium and related problems]. Moscow: SKAD SOFT Publishing House, 2010. V. 1. 704 p. (rus)
  9. Smirnov, A.F. Staticheskaya i dinamicheskaya ustoichivost' sooruzhenii [Static and dynamic stability of constructions]. Moscow: Transzheldorizdat, 1947. 308 p. (rus)
  10. Thompson, J.M.T. Catastrophe theory and its role in applied mechanics, 14th IUTAM Congress on Theoretical and Applied Mechanics. Moscow: Mir, 1979. Pp. 695–710.
  11. Feodos'ev, V.I. Izbrannye zadachi i voprosy po soprotivleniyu materialov[Selected problems and questions on strength of materials]. Moscow: Nauka, 1967. 375 p. (rus)
  12. Fredkin, E. An Introduction to Digital Philosophy. Int. J. Theor. Phys., V. 42, No. 2, 2003. Рp. 189–247.
  13. Kazinczy, G. von, Die Weiterentwicklung der Plastizitatslehre. Technika, 1931/2, V. 12, No. 5–7, Pp. 168–172.
  14. Symonds, P.S., Neal, B.G. The Interpretation of Failure Loads in the Plastic Theory of Continuous Beams and Frames. J. Aeron. Sci., 1952, V. 19, No. 15, Pp. 15–22.
  15. Trefethen, L.N. Maxims About Numerical Mathematics. Computers, Science, and Life, SIAM News, 1998.

Full text | (564 Кб)