Cybernetics and Systems Analysis

, Volume 55, Issue 2, pp 329–335 | Cite as

Numerical Methods for Determining Stiffness Properties of a Bar Cross-Section

  • O. S. Gorodetsky
  • M. S. BarabashEmail author
  • Y. B. Filonenko


This paper considers some aspects of determining stiffness properties of cross-sections of bar elements and modeling the stress-strain states of bar systems. A method is proposed to find stresses based on nonlinear “stress-strain” dependencies. When numerically determining stiffness properties of a cross-section, a nonlinear analysis of a given collection of forces was performed. Using the method for performing nonlinear analysis, which is implemented in the software package “LIRA-SAPR,” the tangent and secant stiffness properties are determined. The methods proposed for determining and modeling stiffness properties allow to more precisely specify characteristics of nonlinear strain in materials and to apply them to elements of the cross-sections being designed.


numerical method stiffness property computer modeling stress-strain state deformation modulus nonlinear analysis 


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  1. 1.
    A. S. Gorodetsky, M. S. Barabash, and V. N. Sidorov, Computer Modelling in Problems of Building Mechanics [in Russian], ASV Publishing House, Moscow (2016).Google Scholar
  2. 2.
    M. S. Barabash, Computer Modelling of Life Cycle Processes of Construction Objects [in Russian], Stal’, Kyiv (2014).Google Scholar
  3. 3.
    V. A. Bazhenov, O. I. Gulyar, S. O. Pyskunov, and O. S. Sakharov, Semianalytic Method of Finite Elements in Problems of the Continual Destruction of Spatial Bodies [in Ukrainian], Karavela, Kyiv (2014).Google Scholar
  4. 4.
    I. A. Birger and Ya. G. Panovko (eds.), Strength, Stability, Fluctuations [in Russian], Vol. 1, Mashinostroeniye, Moscow (1968).Google Scholar
  5. 5.
    I. N. Molchanov, L. D. Nikolenko, and Yu. B. Filonenko, “Solution of the Neumann problem for the Poisson equation by the finite element method,” Computational and Applied Mathematics: Interdepartmental Scientific Compendium, Kyiv, Iss. 33, 137–143 (1977).Google Scholar
  6. 6.
    I. N. Molchanov, A. V. Popov and A. N. Khimich, “Algorithm to solve the partial eigenvalue problem for large profile matrices,” Cybernetics and Systems Analysis, Vol. 28, No. 2, 281–286 (1992).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    A. N. Khimich, A. V. Popov and V. V. Polyanko, “Algorithms of parallel computations for linear algebra problems with irregularly structured matrices,” Cybernetics and Systems Analysis, Vol. 47, No. 6. 973–985 (2011).MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    E. A. Velikoivanenko, A. S. Milenin, A. V. Popov, V. A. Sidoruk, and A. N. Khimich, “Methods and technologies of parallel computing for mathematical modeling of stress-strain state of constructions taking into account ductile fracture,” Journal of Automation and Information Sciences, Vol. 46, Iss. 11, 23–35 (2014).CrossRefGoogle Scholar
  9. 9.
    A. Yu. Baranov, A. V. Popov, Ya. E. Slobodyan, and A. N. Khimich, “Mathematical modeling of building constructions using hybrid computing systems,” Journal of Automation and Information Sciences, Vol. 49, Iss. 7, 18–32 (2017).CrossRefGoogle Scholar
  10. 10.
    S. P. Timoshenko and J. N. Goodier, Theory of Elasticity [Russian translation], Nauka, Moscow (1975).Google Scholar
  11. 11.
    A. I. Lurie, Theory of Elasticity [in Russian], Nauka, Moscow (1970).Google Scholar
  12. 12.
    L. D. Landau and E. M. Lifshits, Theory of Elasticity [in Russian], Nauka, Moscow (1987).Google Scholar
  13. 13.
    W. Nowacki, Theory of Elasticity [Russian translation], Mir, Moscow (1975).Google Scholar
  14. 14.
    S. Yu. Fialko and D. E. Lumelskyy, “On numerical realization of torsion and bending problems for prismatic bars with arbitrary cross-sections,” Mathematical Methods and Physicomechanical Fields, Vol. 55, No. 2, 156–169 (2012).zbMATHGoogle Scholar
  15. 15.
    O. C. Zienkiewicz, The Finite Element Method in Engineering Science [Russian translation], Mir, Moscow (1975).Google Scholar
  16. 16.
    A. N. Khimich, A. V. Popov, and A.V. Chistyakov, “Hybrid algorithms for solving the algebraic eigenvalue problem with sparse matrices,” Cybernetics and Systems Analysis, Vol. 53, N 6, 937–949 (2017).Google Scholar
  17. 17.
    A. S. Gorodetsky and M. S. Barabash, “Nonlinear behaviour of reinforced concrete in LIRA-SAPR software. Nonlinear Engineering method (NL Engineering),” International Journal for Computational Civil and Structural Engineering, Vol. 12, Iss. 2, 92–98 (2016).Google Scholar
  18. 18.
    M. S. Barabash, M. M. Soroka, and M. G. Suryaninov, Nonlinear Construction Mechanics with PC LIRA-SAPR [in Ukrainian], Ekologiya, Odessa (2018).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • O. S. Gorodetsky
    • 1
  • M. S. Barabash
    • 2
    Email author
  • Y. B. Filonenko
    • 1
  1. 1.LLC “LIRA-SAPR”KyivUkraine
  2. 2.National Aviation University, Kyiv, Ukraine and LLC “LIRA-SAPR”KyivUkraine

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