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The differential equations are received and the new exact solution of a problem for a rec- tangular cross section and flat statically determination beam structure at action of longitudinal and transvers loadings is constructed. Three characteristic areas of the beam, distinguished by schemes of position of elastic core section were considered. All the components of the stress- strain state, borders of elastic-plastic zones are determined. A numerical analysis of linear and nonlinear formulation was presented.

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LTD «Globaltanksengineering» , Samara, Russia

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к.т.н., доцент

443010, г. Самара, ул. Галактионовская, д.139, кв.4


  1. Petrov V.V. (2014). Nelinejnaya inkrementalnaya stroitelnaya mekhanika, Moscow: Infa-Inzheneriya, 480 p.
  2. Ilyushin A.A. (1948). Plastichnost, Moscow: Gostekhizdat, 376 p.
  3. Birger I.A. (1975). Obshchie algoritmy resheniya zadach teorii uprugosti, plastichnosti i polzuchesti // Uspekhi mekhaniki deformiruemyh sred, – №2. M.: Nauka, p.51-73.
  4. Kantorovich L.V. (1948). Funkcionalnyj analiz i prikladnaya matematika // Uspekhi matematicheskih nauk, t. III, №6. M.: Izd. AN SSSR, p.89-185.
  5. Zenkevich O. (1975). Metod konechnyh ehlementov v tekhnike, Moscow: Mir, 541 p.
  6. Petrov V.V. (1975). Metod posledovatel'nyh nagruzhenij v nelinejnoj teorii plastin i obolochek, Saratov: Izd-vo Saratovskogo un-ta, 119 p.
  7. Novozhilov V.V. (1948). Osnovy nelinejnoj teorii uprugosti, Moscow: Gostekhizdat, 211 p.
  8. Rzhanicyn A.R. (1954). Raschet sooruzhenij s uchetom plasticheskih svojstv materiala, Moscow: Gosstrojizdat, 288 p.
  9. Stok B., Halilovic M. (2009). Analytical solutions in elasto-plastic bending of beams with rectangular cross section, Applied Mathematical Modelling, Vol. 33, №3, p.1749-1760.
  10. Bin J. Wanji C. (2010). A new analytical solution of pure bending beam in couple stress elasto-plasticity: theory and applications, International Journal of Solids and Structures, Vol. 47, №6, p. 779-785.
  11. Joudaki J., Sedighi M. (2015). Effect of material's behavior on residual stress distribution in elastic–plastic beam bending: An analytical solution, Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials Design and Applications, p.1-12.
  12. Nie G. J., Zhong Z. (2013). Analytical solution for elastic and elastoplastic bending of a curved beam composed of inhomogeneous materials, Key Engineering Materials. – Trans Tech Publications, Vol. 535, p.353-356.
  13. Lukash P.A. (1978). Osnovy nelinejnoj stroitelnoj mekhaniki. Moscow: Strojizdat, 208 p.
  14. Bezuhov N.I., Luzhin O.V. (1974). Prilozhenie metodov teorii uprugosti i plastichnosti k resheniyu inzhenernyh zadach. Moscow: Vysshaya shkola, 200 p.
  15. Salazar J. A., Lange D.F., Cruz A.T., Castillo H.I., Rodriguez G.M. (2013). Elastoplastic Analysis of a Cantilever Beam under Combined Compressive and Bending Load, ASME 2013 International Mechanical Engineering Congress and Exposition.–American Society of Mechanical Engineers, p. V009T10A025-V009T10A033.
  16. Darkov A.V., Shaposhnikov N.N. (2008). Stroitelnaya mekhanika, St. Petersburg: Lan, 656 p.
  17. Sokolovskij V.V. (1969). Teoriya plastichnosti, Moscow: Vysshaya shkola, 608 p.
  18. Chica E., Teran J. M. G., Iban A. L. (2008). Yield surface for elastoplastic beam 2D element considering damage material, 8th World Congress on Computational Mechanics (WCCM8), 5th European Congress on Computational Methods in Applied Sciences and Engineering (Eccomas 2008).
  19. Elenitskiy E.Ya. (2016). Boundary value problem for branching type flexible compound structures, Structural Mechanics of Engineering Construction and Building, №6, p.73-80.

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