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Allowance for Transverse Shear Deformations in the Finite Element Calculation of a Thin Elliptic Cylinder Shell

  • Reliability, Strength, and Wear Resistance of Machines and Structures
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Abstract

In this paper, we present an algorithm for finite element calculation of thin shells with allowance for transverse shear deformations. In deriving the basic geometric relations, two options of counting the rotation angle of the normal to the middle surface were considered. In the first option, the reading of the rotation angle of the normal was carried out from its initial state. In the second option, the reading of the rotation angle of the normal was carried out from its position in the deformed state. A comparative analysis of the efficiency of two options of reading the rotation angle of the normal is performed based on calculating a thin elliptical cylinder shell rigidly pinched along the ends and loaded with an internal pressure of intensity q.

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References

  1. Novozhilov, V.V., Teoriya tonkikh obolochek (Theory of Thin Shells), St. Petersburg: SPb. Gos. Univ., 2010.

    Google Scholar 

  2. Pikul’, V.V., Mekhanika obolochek (Mechanics of Shells), Vladivostok: Dal’nauka, 2009.

    Google Scholar 

  3. Rikards, R.B., Metod konechnykh elementov v teorii obolochek i plastin (Finite Elements Method in the Theory of Shells and Plates), Riga: Zinatne, 1988.

    MATH  Google Scholar 

  4. Chernykh, K.F., Lineinaya teoriya obolochek. Ch. 2. Nekotorye voprosy teorii (Linear Theory of Shells. Part 2: Some Questions of the Theory), Leningrad: Leningr. Gos. Univ., 1964.

    Google Scholar 

  5. Timoshenko, S.P. and Voinovskii–Kriger, S., Plastinki i obolochki (Plates and Shells), Moscow: Nauka, 1966.

    Google Scholar 

  6. Vol’mir, A.S., Gibkie plastinki i obolochki (Flexible Plates and Shells), Moscow: Gos. Izdat. Tekh.–Teor. Liter., 1956.

    Google Scholar 

  7. Matvienko, Yu.G., Chernyatin, A.S., and Razumovskii, I.A., Numerical analysis of the components of the three–dimensional non–singular stress field at a mixed–type crack tip, J. Mach. Manuf. Reliab., 2013, vol. 42, no. 4, pp. 293–299.

    Article  Google Scholar 

  8. Nikishkov, G.P., Matvienko, Yu.G., and Razumovskii, I.A., The distribution of the fracture index along the front of the elastoplastic crack, Mashinostr. Inzhen. Obrazov., 2016, no. 4.

    Google Scholar 

  9. Kayumov, R.A., Shakirzyanov, R.A., and Shakirzyanov, F.R., Modeling of the deformation process and evaluation of the bearing capacity of soil and polyethylene corrugated pipe with allowance for temperature, Uch. Zap. Kazan. Univ., 2015, vol. 157, pp. 107–113.

    Google Scholar 

  10. Badriev, I.B., Makarov, M.V., and Paimushin, V.N., Contact statement of mechanical problems of reinforced on a contour sandwich plates with transversal–soft core, Russ. Math. (Iz. VUZ Mat.), 2016, vol. 61, no. 1, pp. 69–75.

    Article  MATH  Google Scholar 

  11. Serazutdinov, M.N. and Ubaidulloev, M.N., Calculation of open profile thin–walled rod systems strengthened under load in elastic and plastic deformations, Uch. Zap. Kazan. Univ., Ser.: Fiz.–Mat. Nauki, 2015, vol. 157, no. 1, pp. 141–146.

    MathSciNet  Google Scholar 

  12. Golovanov, A.I., Konoplev, Yu.G., and Sultanov, L.U., Numerical investigation of large deformations of hyperelastic solids. I. Kinematics and variational equations, Uch. Zap. Kazan. Univ., Ser.: Fiz.–Mat. Nauki, 2008, vol. 150, no. 1, pp. 29–37.

    MATH  Google Scholar 

  13. Kuznetsov, E.B., Continuation of solutions in multiparameter approximation of curves and surfaces, Comput. Math. Math. Phys., 2012, vol. 52, no. 8, pp. 1149–1162.

    Article  MathSciNet  Google Scholar 

  14. Zheleznov, L.P., Kabanov, V.V., and Boiko, D.V., Nonlinear deformation and stability of discretely reinforced elliptical cylindrical shells under transverse bending and internal pressure, Russ. Aeronaut., 2014, vol. 57, no. 2, pp. 118–126.

    Article  Google Scholar 

  15. Kositsyn, S.B. and Lin’, Ch.S., Numerical analysis of stress–strain states of intersecting cylindrical shells of lining tunnels interacting with the surrounding soil massif, taking into account the sequence of their erection, IJCCSE, 2015, vol. 11, no. 2, pp. 101–106.

    Google Scholar 

  16. Bespalova, E.I. and Urusova, G.P., Vibrations of shells of revolution with branched meridian, Int. Appl. Mech., 2016, vol. 52, no. 1, pp. 82–89.

    Article  MathSciNet  Google Scholar 

  17. Sheshenin, S.V. and Bakhmet’ev, S.G., A model of the effective rubber–cord ply, Mosc. Univ. Mech. Bull., 2014, vol. 69, no. 5, pp. 109–113.

    Article  MATH  Google Scholar 

  18. Sedov, L.I., Mekhanika sploshnoi sredy (Mechanics of Continuous Media), Moscow: Nauka, 1976, vol. 1.

    Google Scholar 

  19. Golovanov, A.I., Tyuleneva, O.N., and Shigabutdinov, A.F., Metod konechnykh elementov v statike i dinamike tonkostennykh konstruktsii (Finite Element Method for Statics and Dynamics of Thin–Walled Constructions), Moscow: Fizmatlit, 2006.

    Google Scholar 

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Correspondence to Yu. V. Klochkov.

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Original Russian Text © Yu.V. Klochkov, A.P. Nikolaev, T.R. Ishchanov, 2018, published in Problemy Mashinostroeniya i Nadezhnosti Mashin, 2018, No. 4.

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Klochkov, Y.V., Nikolaev, A.P. & Ishchanov, T.R. Allowance for Transverse Shear Deformations in the Finite Element Calculation of a Thin Elliptic Cylinder Shell. J. Mach. Manuf. Reliab. 47, 349–355 (2018). https://doi.org/10.3103/S1052618818040076

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  • DOI: https://doi.org/10.3103/S1052618818040076

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