Investigation of Geometrically Nonlinear Deformation of a Thin Shell Based on a Finite Element with Vector Approximation of the Desired Quantities

封面

如何引用文章

全文:

开放存取 开放存取
受限制的访问 ##reader.subscriptionAccessGranted##
受限制的访问 订阅存取

详细

At the loading step, taking into account geometric nonlinearity, the stiffness matrix of the quadrangular finite element of the median surface of the thin shell is obtained, the nodal unknowns of which are the contravariant components of the displacement vectors of the nodal points and the components of their first derivatives. Approximating expressions of the desired quantities are obtained by implementing bicubic interpolation functions for the corresponding vector quantities with subsequent coordinate transformations leading to approximating expressions of individual components. Specific examples show the effectiveness of using vector approximation of the calculated kinematic parameters of the shell.

作者简介

A. Dzhabrailov

Volgograd State Agrarian University

编辑信件的主要联系方式.
Email: arsen82@yandex.ru
俄罗斯联邦, Volgograd

A. Nikolaev

Volgograd State Agrarian University

Email: arsen82@yandex.ru
俄罗斯联邦, Volgograd

Yu. Klochkov

Volgograd State Agrarian University

Email: arsen82@yandex.ru
俄罗斯联邦, Volgograd

N. Kirsanova

Financial University under the Government of the Russian Federation

Email: arsen82@yandex.ru
俄罗斯联邦, Moscow

参考

  1. Volmir A.S. Flexible Plates and Shells. Moscow: Gostekhizdat, 1956. 420 p.
  2. Galimov K.Z. Fundamentals of Nonlinear Theory of Shells. Kazan: Kazan State Univ., 1975. 326 p.
  3. Vorovich I.I. Mathematical Problems of the Nonlinear Theory of Shallow Shells. Moscow: Nauka. 1989. 376 p.
  4. Bakulin V.N., Obraztsov I.F., Potopakhin V.A. Dynamic Problems of the Nonlinear Theory of Multilayer Shells: The Effect of Intense Thermal Force Loads, Concentrated Energy Flows. Moscow: Fizmatlit, 1998. 464 p.
  5. Golovanov A.I., Tyuleneva O.N., Shigabutdinov A.F. Finite Element Method in Statics and Dynamics of Thin-Walled Structures. Moscow: Fizmatlit, 2006. 392 p.
  6. Levin V.A., Morozov E.M., Matvienko Yu.G. Selected Nonlinear Problems of Fracture Mechanics / ed. by Levin V.A., Moscow: Fizmatlit, 2004. 407 p.
  7. Levin V.A., Vershinin A.V. Nonlinear Computational Mechanics of Strength. Vol. II. Numerical Methods. Moscow: Fizmatlit, 2015. 544 p.
  8. Agapov V.P. Finite Element Method in Statics, Dynamics and Stability of Spatial Thin-Walled Reinforced Structures. Moscow: DIA Publ. House, 2000. 152 p.
  9. Beirao Da Veiga L., Lovadina C., Mora D. A virtual element method for elastic and inelastic problems on polytope meshes // Computer Methods in Appl. Mech. & Eng., 2017, vol. 295, pp. 327–346. https://doi.org/10.1016/J.CMA.2015.07.013
  10. Liang K., Ruess M., Abdalla M. Co-rotational finite element formulation used in the Koiter–Newton method for nonlinear buckling analyses // Finite Elements in Anal. & Design, 2016, vol. 116, pp. 38–54. https://doi.org/10.1016/j.finel.2016.03.006
  11. Agapov V.P., Vasiliev A.V. Consideration of geometric nonlinearity in the calculation of reinforced concrete columns of rectangular cross-section by the finite element method // Bull. of MGSU, 2014/4. pp. 37.
  12. Plautov V.M., Mukhin D.E., Panin A.N. Strength and stability of shallow ribbed shells taking into account geometric and physical nonlinearity // Earthquake-Resistant Construction. Safety of Structures, 2008, no. 2, pp. 41–44.
  13. Karpov V.V., Ignatiev O.V., Salnikov A.Yu. Nonlinear Mathematical Models of Deformation of Shells of Variable Thickness and Algorithms for Their Research. Moscow: DIA; St. Petersburg: SPbGASU, 2002. 420 p.
  14. Skopinsky V.N. Stresses in Intersecting Shells. Moscow: Fizmatlit, 2008. 400 p.
  15. Kantin G. Displacement of curved finite elements as a rigid whole // Rocket Sci. Tech. Kosmon., 1970, no. 7, pp. 84–88.
  16. Bakulin V.N., Demidov V.I. Three-layer finite element of natural curvature // Izv. vuzov. Mech. Eng., 1978, no. 5, pp. 5–10.
  17. Bakulin V.N. Finite Element Method for Studying the Stress-Strain State of Three-Layer Cylindrical Shells. Moscow: Central Res. Inst. of Information, 1985. 140 p.
  18. Zheleznov L.P., Kabanov V.V. Displacement functions of the finite elements of the shell of rotation as solids // Izv. RAS. MTТ, 1990, no. 1, pp. 131–136.
  19. Bakulin V.N. Effective model of bearing layers for layered analysis of the stress-strain state of three-layer cylindrical irregular shells of rotation // News of the RAS. Solid State Mech., 2020, no. 3, pp. 69–79.
  20. Bakulin V.N. A model for the refined calculation of the stress-strain state of three-layer conical irregular shells of rotation // JAMM, 2019, no. 2, pp. 315–327.
  21. Bakulin V.N. A block-layer approach for analyzing the stress-strain state of three-layer irregular cylindrical shells of rotation // JAMM, 2021, vol. 85, no. 3, pp. 383–395. https://doi.org/10.31857/S0032823521030036
  22. Bakulin V.N. Block finite element model of layered analysis of generally three-layered irregular shells of double curvature rotation // Rep. of the Academy of Sciences, 2019, vol. 484, no. 1, pp. 35–40.
  23. Klochkov Yu.V., Nikolaev A.P., Sobolevskaya T.A., Vakhnina O.V., Klochkov M.Yu. Calculation of an ellipsoidal shell based on FEM with vector interpolation of displacements with variable parameterization of the median surface // Lobachevsky J. of Mathematics, 2020, no. 41(3), pp. 373–381.
  24. Dzhabrailov A.Sh., Nikolaev A.P., Klochkov Yu.In, Gureeva N.A., Ishchanov T.R. A finite element algorithm for calculating an ellipsoidal shell taking into account displacement as a rigid whole // Appl. Math. & Mech., 2022, vol. 86, no. 2, pp. 1749–1757.
  25. Nikolaev A.P., Kiselev A.P., Gureeva N.A., Kiseleva R.Z. Calculation of Composite Engineering Structures Based on the Finite Element Method. Volgograd: Volgograd State Agrarian Univ. Niva, 2016. 128 p.
  26. Dzhabrailov A.Sh., Nikolaev A.P., Klochkov Yu.V., Gureeva N.A. Consideration of displacement as a rigid body in the FEM algorithm for calculating shells of rotation// Proc. of the Russian Academy of Sciences. Solid State Mech., 2023, no. 6, pp. 1946–1959.
  27. Sedov L.I. Continuum Mechanics. Russian Academy of Sciences. Moscow: Nauka, 1994. 560 p.
  28. Papenhausen J. Eine energiegrechte, incrementelle for mulierung der geometrisch nichtlinearen Theorie elastischer Kontinua und ihre numerische Behandlung mit Hilfe finite Elemente. “Techn. – Wiss. Mitt. Jnst. Konstr. Jngenierlau Ruhr. – Univ. Bochum”, 1975, № 13, III, 133 p.
  29. Ruditsky M.N., Artyomov P.Ya., Lyuboshits M.I. A Reference Manual on the Resistance of Materials. Minsk: Higher School, 1970. 630 p.

补充文件

附件文件
动作
1. JATS XML
下载

版权所有 © Russian Academy of Sciences, 2025