Abstract
At the loading step when the shell is deformed outside the elastic limits, the relations between strain increments and stress increments are used in three forms. In the first two forms, the dependences of the strain increments were obtained by differentiating the relations of the deformation theory of plasticity both with the use of the hypothesis of the material incompressibility during plastic deformation and without it. In the third form, to obtain the governing equations, we proposed an algorithm based on the hypothesis that the deviator components of the strain increments are proportional to the deviator components of the stress increments without taking into account the hypothesis of the material incompressibility during elastoplastic deformation and without dividing the stress increments into elastic and plastic parts.
Similar content being viewed by others
REFERENCES
Reissner, E., Linear and nonlinear theory of shells, in Thin-Shell Structures: Theory, Experiment and Design, Prentice Hall Inc, 1974, p. 29.
Green, A.E., On the linear theory of thin elastic shells, Proc. R. Soc. London, Ser. A, 1962, vol. 266, p. 143.
Kayumov, R.A., 2017 postbuckling behavior of compressed rods in an elastic medium, Mech. Solids, 2017, vol. 52, no. 5, p. 575.
Chernykh, K.F. and Cabritsa, S.A., General Nonlinear Theory of Elastic Shells, St. Petersburg: Publ. House St. Petersburg Univ., 2002.
Tupyshkin, N.D. and Zapara, M.A., Constitutive relations of the tensor theory of plastic damageability of metals, in Problemy prochnosti, plastichnosti i ustoichivosti v mekhanike deformiruemogo tverdogo tela (Problems of Strength, Plasticity, and Stability in Mechanics of Deformable Solids), Tver: Tversk. Gos. Tekh. Univ., 2011.
Lalin, V., Rybakov, V., and Sergey, A., The finite elements for design of frame of thin-walled beams, Appl. Mech. Mater., 2014, vols. 578–579, p. 858.
Rozin, L.A., Zadachi teorii uprugosti i chislennye metody ikh resheniya (Problems of Elasticity Theory and Numerical Methods of Their Solution), St. Petersburg: S.-Peterb. Gos. Tekh. Univ., 1998.
Badriev, I.B. and Paimushin, V.N., Refined models of contact interaction of a thin plate with postioned on both sides deformable foundations, Lobachevskii J. Math., 2017, vol. 38, no. 5, p. 779.
Beirao da Veiga, L., Lovadina, C., and Mora, D., A virtual element method for elastic and inelastic problems on polytope meshes, Comput. Methods Appl. Mech. Eng., 2015, vol. 295, p. 327.
Aldakheel, F., Hudobivnik, B., and Wriggers, P., Virtual element formulation for phase-field modeling of ductile fracture, Int. J. Multiscale Comput. Eng., 2019 (in press).
Magisano, D., Leonetti, L., and Garcea, G., Koiter asymptotic analysis of multilayered composite structures using mixed solid-shell finite elements, Compos. Struct., 2016, vol. 154, p. 296. https://doi.org/10.1016/j.compstruct
Chi, H., Talischi, C., Lopez-Pamies, O., and Paulino, G.H., Polygonal finite elements for finite elasticity, Int. J. Numer. Methods Eng., 2015, vol. 101, p. 305.
Tyukalov, Yu.Ya., Equilibrium finite elements for plane problems of the theory of elasticity, Inzh.-Stroit. Zh., 2019, no. 7, p. 80.
Sedov, L.I., A Course in Continuum Mechanics, Wolters-Noordhoff Publ., 1971, vol. 1.
Dzhabrailov, A.Sh., Klochkov, Yu.V., Nikolaev, A.P., and Fomin, S.D., Determination of stresses in shells of revolution in the presence of articulation zones based on a triangular finite element taking into account elastoplastic deformation, Izv. Vyssh. Uchebn. Zaved., Aviats. Tekh., 2015, no. 1, p. 8.
Malinin, M.M., Applied Theory of Plasticity and Creep, Moscow: Mashinostroenie, 1975.
Funding
This work was supported by the Russian Foundation for Basic Research and the Volgograd Region Administration, grant no. 19-41-340002 r_a.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare that they have no conflict of interest.
Additional information
Translated by A. Ivanov
About this article
Cite this article
Dzhabrailov, A.S., Nikolaev, A.P., Klochkov, Y.V. et al. Calculation of an Elliptic Cylindrical Shell Outside Elastic Limits Based on the FEM with Various Forms of Defining Equations. J. Mach. Manuf. Reliab. 49, 518–529 (2020). https://doi.org/10.3103/S1052618820060023
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1052618820060023