Calculation of the stability of the equilibrium form of discrete systems

  • Authors

    • Oleksandr Shkurupiy
    • Pavlo Mytrofanov
    • Oksana Dovzhenko
    • Volodymyr Pohribnyi
    2018-10-13
    https://doi.org/10.14419/ijet.v7i4.8.27220
  • equilibrium form, compressed reinforced concrete columns, software complex, stability loss equation.

  • On the basis of the displacement method, together with the methods of iterations and half-division, an algorithm for stability calculation of the first kind equilibrium form of compressed reinforced concrete columns with hinged fixing at the ends, considering the stiffness changing was developed. The use of the above methods makes it possible to determine the minimum critical load or stress at the first bifurcation and their stability loss corresponding form. The use of matrix forms contributes to simplification of high order stability loss equation. This approach allows to obtain the form of stability loss that corresponds to the critical load.

     

     

  • References

    1. [1] Friedel Hartmann, The Mathematical Foundation of Structural Mechanics, Springer, Berlin, Heidelberg, (1985), 371 p., https://doi.org/10.1007/978-3-642-82401-2.

      [2] Walter Lacarbonara, Nonlinear Structural Mechanics, Springer, Boston, MA, (2013), 802 p., https://doi.org/10.1007/978-1-4419-1276-3.

      [3] Keith D. Hjelmstad, Fundamentals of Structural Mechanics, Springer, Boston, MA, (2005), 480 p., https://doi.org/10.1007/b101129.

      [4] Ray Hulse, Jack Cain, Structural Mechanics, Palgrave, London, (1991), 294 p., https://doi.org/10.1007/978-1-349-11897-7.

      [5] Shkurupiy O., Mytrofanov P., Masiuk V. (2018), Calculation of The Stability of the Form of Equilibrium of Discrete Systems. International Journal of Engineering & Technology, Vol. 7 (3.2), pp: 401-407, http://dx.doi.org/10.14419/ijet.v7i3.2.14561.

      [6] Shkurupiy O.A. Stiykist' formy rivnovahy ta dynamika dyskretnykh system: navchal'nyy posibnyk [Stability of equilibrium and dynamics of discrete systems: Tutorial]. – Poltava: PoltNTU, 2015. – 228 p. [in Ukrainian].

      [7] Kyselev V.A. Stroitel'naya mekhanika. Spetsial'niy kurs [Structural mechanics. Special course]. – Moscow: Stroyyzdat, 1980. – 616 p. [in Russian].

      [8] Smyrnov A.F., Aleksandrov A.V., Lashchenykov B.Ya., Shaposhnykov N.N. Stroitel'naya mekhanika. Dynamika i ustoichivost' sooruzheniy [Structural mechanics. Dynamics and stability of structures]. – Moscow: Stroyyzdat, 1984. – 415 p. [in Russian].

      [9] Bazhenov V.A. Perel'muter A.V., Shyshov O.V. Budivel'na mekhanika. Kompyuterni tekhnolohiyi: pidruchnyk [Structural Mechanics. Computer Technology: Tutorial]. – Kyiv.: Karavela, 2009. – 696 p. [in Ukrainian].

      [10] Faddeev D.K., Faddeeva V.N. Vichyslytel'nie metody lyneynoy alhebry [Computational methods of linear algebra]. – Moscow: Hosudarstvennoe yzdatel'stvo fyzyko-matematycheskoy lyteratury, 1960. – 656 p. [in Russian].

      [11] Bazhenov V.A. Dekhtyaryuk Ye.S. Budivel'na mekhanika. Dynamika sporud: navch. posibnyk [Structural Mechanics. Dynamics of structures: Tutorial]. – K.: IZMN, 1998. – 208 p. [in Ukrainian].

      [12] Smith P. An Introduction to Structural Mechanics / P. Smith. – Palgrave Macmillan, 2001. – 368 p.

      [13] Severyn V., Pashchenko A., Mytrofanov P. (2018). Probabilistic Analysis of Structures Under Snow Load. International Journal of Engineering & Technology, Vol. 7(3.2), pp: 339-342, http://dx.doi.org/10.14419/ijet.v7i3.2.14431.

      [14] Pohribnyi V, Dovzhenko О, Maliovana O (2018), The Ideal Plasticity Theory Usage Peculiarities to Concrete and Reinforced Concrete. International Journal of Engineering & Technology, Vol. 7(3.2), pp: 19 – 26, http://dx.doi.org/10.14419/ijet.v7i3.2.14369.

      [15] Perelmuter, A. V., & Pichugin, S. F. (2014). Issues on estimation of building structure vulnerability. Magazine of Civil Engineering, 49(5), 5-14+121. https://doi.org/10.5862/MCE.49.1

      [16] Piskunov, V. G., Goryk, A. V., & Cherednikov, V. N. (2000). Modeling of transverse shears of piecewise homogeneous composite bars using an iterative process with account of tangential loads. 1. construction of a model.Mechanics of Composite Materials, 36(4), 287-296. https://doi.org/10.1007/BF02262807

      [17] Leshchenko M. V., Semko V. O. Thermal characteristics of the external walling made of cold-formed steel studs and polystyrene concrete. Magazine of Civil Engineering. № 8, (2015), pp. 44–55. https://doi.org/10.5862/MCE.60.6

      [18] Semko O., Yurin O., Avramenko Yu., Skliarenko S. Thermophysical aspects of cold roof spaces. MATEC Web of Conferences. Vol. 116, (2017), р. 02030. https://doi.org/10.1051/matecconf/201711602030

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  • How to Cite

    Shkurupiy, O., Mytrofanov, P., Dovzhenko, O., & Pohribnyi, V. (2018). Calculation of the stability of the equilibrium form of discrete systems. International Journal of Engineering & Technology, 7(4.8), 84-96. https://doi.org/10.14419/ijet.v7i4.8.27220