Abstract
In the curvilinear coordinate system, we describe an algorithm for generating the stiffness matrix of the quadrilateral element of the middle surface of a thin shell based on Kirchhoff’s hypothesis with nodal unknowns in the form of displacements and their derivatives using a vector approximation of the displacement fields. The developed finite element is verified by calculating the shell with the middle surface in the form of a triaxial ellipsoid in the two-dimensional formulation. The results are compared with the calculation results obtained using ANSYS software. The efficiency of the vector approximation of the displacement fields for the calculation of arbitrary thin shells in the moment stress state is shown.
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References
Novozhilov, V.V., Chernykh, K.F., and Mikhailovskii, E.I., Lineinaya teoriya tonkikh obolochek (Linear Theory of Thin Shells), Leningrad: Politekhnika, 1991.
Grigolyuk, E.N. and Lopanitsyn, E.A., Konechnye progiby, ustoichivost’ i zakriticheskoe povedenie tonkikh pologikh obolochek (Finite Deflection, Stability and Overcritical Behavior of Thin Mildly Sloping Shells), Moscow: Moscow State Univ. of Mechanical Engineering, 2004.
Pikul’, V.V., Mekhanika obolochek (Shells Mechanics), Vladivostok: Dal’nauka, 2009.
Bathe, K.-J., Finite Element Procedures, Prentice Hall, 1996.
Golovanov, A.I., Tyuleneva, O.N., and Shigabutdinov, A.F., Metod konechnykh elementov v statike i dinamike tonkostennykh konstruktsii (Finite Element Method in Static and Dynamic of Thin-Walled Structures), Moscow: Fizmatlit, 2006.
Postnov, V.A. and Kharkhurim, I.Ya., Metod konechnykh elementov v raschetakh sudovykh konstruktsii (Finite Element Method in Ship Structure Calculations), Leningrad: Sudostroenie, 1974.
Nikolaev, A.P., Klochkov, Yu.V., Kiselev, A.P., et al., Vektornaya interpolyatsiya polei peremeshchenii v raschetakh obolochek (Vector Interpolation of Displacement Fields in Shells Calculation), Volgograd: Volgograd State Agricultural Univ., 2012.
Skopinskii, V.N., Napryazheniya v peresekayushchikhsya obolochkakh (Stresses in Cross-Shells), Moscow: Fizmatlit, 2008.
Matvienko, Y.G., Chernyatin, A.S., and Rasumovskii, 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.
Moaveni, S., Finite Element Analysis. Theory and Application with ANSYS, Pearson, 2008.
Klochkov, Yu.V., Nikolaev, A.P., and Kiseleva, T.A., A Comparative evaluation of the scalar and vector approximations of sought quantities in the finite-element method of arbitrary shells, J. Mach. Manuf. Reliab., 2015, vol. 44, no. 2, p. 166.
Sedov, L.I., Mekhanika sploshnoi sredy (Mechanics of Continua), Moscow: Nauka, 1976, vol. 1.
Zienkiewicz, O.C., Taylor, R.L., and Zhu, J.Z., The Finite Element Method: Its Basis and Fundamentals, Butterworth-Heinemann, 2013.
Belyaev, N.M., Soprotivlenie materialov (Strength of Materials), Moscow: Nauka, 1965.
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Original Russian Text © Yu.V. Klochkov, A.P. Nikolaev, T.A. Kiseleva, S.S. Marchenko, 2016, published in Problemy Mashinostroeniya i Nadezhnosti Mashin, 2016, No. 4, pp. 44–53.
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Klochkov, Y.V., Nikolaev, A.P., Kiseleva, T.A. et al. Comparative analysis of the results of finite element calculations based on an ellipsoidal shell. J. Mach. Manuf. Reliab. 45, 328–336 (2016). https://doi.org/10.3103/S1052618816040063
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DOI: https://doi.org/10.3103/S1052618816040063