Uncertainty of Parameters

  • Anatoly V. Perelmuter
  • Vladimir I. Slivker
Part of the Foundations of Engineering Mechanics book series (FOUNDATIONS)


A conventional engineering education is based on the principle of “accuracy”. Engineers have been recognizing and perceiving the accuracy as one of their key principles ever since they were students. Any deviations are deemed undesirable and thus become as if non-existent in the psychological sense, though everyone realizes there can be no fault-free technologies, perfectly accurate measurements etc. In this connection, operating uncertain parameters requires one to readjust one’s mind.


Design Variable Stiffness Matrix Elastic Foundation Sensitivity Coefficient Stiffness Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baker GA Jr, Graves-Morris PR (1985). Pade Approximants. Cambridge Univ. Press,. CambridgeGoogle Scholar
  2. 2.
    Bayer J (1966) Estimation of Uncertainties of Theoretical Natural Frequencies and Mode Shapes of Structures. Engineering Mechanics, vol. 3, 5:323–330Google Scholar
  3. 3.
    Birbraer AN (1998) Seismic analysis of structures (in Russian). Nauka Publishing House, Sankt-PetersburgGoogle Scholar
  4. 4.
    Blekhman II, Myshkis AD, Panovko YG (1983) Mechanics and applied mathematics: Logic and peculiarities of mathematical applications (in Russian). Nauka Publishing House, MoskowGoogle Scholar
  5. 5.
    Bondy H (1967) Assumption and myth in physical theory. Cambridge At the University Press, CambridgeGoogle Scholar
  6. 6.
    Chyornaya EG (1973) Empirical type dependencies of maximum deflections and stresses in nets made of cables and beams (in Russian). In: Basics of theory of instantaneously stiff systems. LenZNIIEP, Leningrad, pp. 48–53Google Scholar
  7. 7.
    Syras AA (1982) Mathematical models of analysis and optimization of elastic-plastic systems (in Russian). Mokslas publishing house , VilniusGoogle Scholar
  8. 8.
    Drozdov YP (1971) Reliability of flexible ferroconcrete columns (in Russian). Concrete and Reinforced Concrete, 4:16–20Google Scholar
  9. 9.
    Ermakov SM (ed) (1983) Mathematical theory of experiment planning (in Russian). Nauka, MoscowGoogle Scholar
  10. 10.
    Fox RL, Kapoor MP (1968) Rates of Change of Eigenvalues and Eigenvectors. AIAA Journal, 6:2426–2429CrossRefzbMATHGoogle Scholar
  11. 11.
    Gordeyev VN, Artemenko VV, Minkovich EI (1989) Choosing a worst possible load combination as a solution of a multi-criteria optimization problem (in Russian). In: Numerical methods of analysis and optimization of structural constructions, Proc. of Kucherenko Central Research Institute of Structural Constructions, Moscow, pp. 26–32Google Scholar
  12. 12.
    Grebenyuk GI, Yankov EV (1989) Approximation of state parameters of bar structures by rational functions (in Russian). In: Proc. of high schools, Structural engineering and architecture, 4:16–19Google Scholar
  13. 13.
    Haug EJ, Choi KK, Komkov V (1986) Design sensitiviti analysis of structural systems. Academic Press, Orlando San Diego New York Austin London Montreal Sydney Tokio TorontoGoogle Scholar
  14. 14.
    Huber PJ (1964) Robust estimation of a location parameter. Ann. Mathematical Statistics, 35:. 73–101CrossRefzbMATHGoogle Scholar
  15. 15.
    Kalinina LG, Perelmuter AV (1985) On the about optimal desidn of structures (in Russian). In: Abovsky NP (ed) Space structures in Krasnoyarsk region, Krasnoyarsk politechnical institute press, KrasnoyarskGoogle Scholar
  16. 16.
    Kulpa Z, Roslaniec K (1999) Solutionsets for systems of linear interval equations In: Proc. of the XIV Polish Conference on Computer Methods in Mechanocs, 26–28 May 1999, Rzeszów, Poland. Rzeszów University of Technology, Rzeszów: pp. 195–196Google Scholar
  17. 17.
    Malov VY, Pochtman YM (1987) Fuzzy estimation of nodal joint properties in models of optimal design (in Russian). In: Proc. of high schools. Structural engineering and architecture, 10:13–16Google Scholar
  18. 18.
    Nalimov VV (1971) Theory of experimenting (in Russian).Nauka, MoscowGoogle Scholar
  19. 19.
    Nelson RB (1976) Simplified calculation of eigenvector derivatives. AIAA Journal, 14:1201–1205CrossRefzbMATHGoogle Scholar
  20. 20.
    Perelmuter AV (1969) Principles of analysis of cable-bar systems (in Russian) Stroyzdat, MoskowGoogle Scholar
  21. 21.
    Perelmuter AV (1972) A limit equilibrium of an ideal elastic-plastic system in conditions of uncertainty (in Russian). In: Structural mechanics and analysis of structures, 5:23–25Google Scholar
  22. 22.
    Podolsky DM (1984) Analysis of structural systems with uncertain stiffness properties (in Russian). In: Reliability and durability of machines and structures, 6:78–86Google Scholar
  23. 23.
    Protsenko AM (1982) Theory of elastic-perfectly-plastic systems (in Russian). Nauka, MoscowGoogle Scholar
  24. 24.
    Rabinovich IM (1950) A course in structural mechanics. Part 1 (in Russian). Stroyizdat, Moscow-LeningradGoogle Scholar
  25. 25.
    Rodgers LC (1970) Derivaties of Eigenvalues and Eigenvectors. AIAA Journal, vol.8, 5: 943–944CrossRefGoogle Scholar
  26. 26.
    Seismic Analysis of Safety-Related Nuclear Structures and Commentary of Standard for Analysis of Safety-Related Nuclear Structures (1986). ASCE Standard, Sept., 1986.Google Scholar
  27. 27.
    Vorobiov NN (1967) Applications of the game theory to engineering. In: Proc. IV Internationaler Kongress über Anwendungen der Mathematik in den Ingenierwissenschaften.Weimar, 1:411–422.Google Scholar
  28. 28.
    Yusupov AK, Davletkhanova AD (1983) Analysis of plane frames on a statistically heterogeneous elastic foundation (in Russian). In: Structural mechanics and analysis of structures, 6:14–18Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Anatoly V. Perelmuter
    • 1
  • Vladimir I. Slivker
    • 2
  1. 1.SCAD GroupKievUkraine
  2. 2.JSC GiprostroymostSaint-PetersburgRussia

Personalised recommendations