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Volumetric element with vector approximation of the desired values for nonlinear calculation of the shell of rotation
- Authors: Gureeva N.A.1, Kiseleva R.Z.2, Kiselev A.P.2, Nikolaev A.P.2, Klochkov Y.V.2
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Affiliations:
- Financial University under the Government of the Russian Federation
- Volgоgrad State Agrarian University
- Issue: Vol 18, No 3 (2022)
- Pages: 228-241
- Section: Analytical and numerical methods of analysis of structures
- URL: https://journals.rudn.ru/structural-mechanics/article/view/32023
- DOI: https://doi.org/10.22363/1815-5235-2022-18-3-228-241
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Abstract
The usage of traditional approximating functions directly to the desired displacement vector of the internal point of a finite element to determine it through nodal unknowns in the form of displacement vectors and their derivatives is described. To analyze the stress state of a geometrically non-linearly deformable shell of rotation at the loading step, the developed algorithm for forming the stiffness matrix of a hexagonal finite element with nodal values in the form of displacement increments and their derivatives was used. To obtain the desired approximating expressions, the traditional interpolation theory is used, which, when calculated in a curved coordinate system, is applied to the displacement vector of the internal point of a finite element for its approximation of class C(1) through nodal displacement vectors and their derivatives. For the coordinate transformation, expressions of the bases of nodal points are obtained in terms of the basis vectors of the inner point of the finite element. After the coordinate transformations, approximating expressions of class C(1) are found for the components of the displacement vector of the internal point of the finite element, leading in a curved coordinate system to implicitly account for the displacement of the finite element as a rigid whole. Using calculation examples, the results of the developed method of approximation of the required values of the FEM with significant displacements of the structure as an absolute solid are obtained.
About the authors
Natalia A. Gureeva
Financial University under the Government of the Russian Federation
Email: nagureeve@fa.ru
ORCID iD: 0000-0003-3496-2008
Doctor of Physics and Mathematics, Associate Professor of the Department of Mathematics
49 Leningradskii Prospekt, Moscow, 125993, Russian FederationRumia Z. Kiseleva
Volgоgrad State Agrarian University
Email: rumia1970@yandex.ru
ORCID iD: 0000-0002-3047-5256
Candidate of Technical Sciences, Associate Professor of the Applied Geodesy, Environmental Engineering and Water Use Department, Ecology and Melioration Faculty
26 Universitetskii Prospekt, Volgograd, 400002, Russian FederationAnatoly P. Kiselev
Volgоgrad State Agrarian University
Email: apkiselev1969@yandex.ru
ORCID iD: 0000-0002-7138-2056
Candidate of Technical Sciences, Associate Professor of the Applied Geodesy, Environmental Engineering and Water Use Department, Ecology and Melioration Faculty
26 Universitetskii Prospekt, Volgograd, 400002, Russian FederationAnatoly P. Nikolaev
Volgоgrad State Agrarian University
Email: anpetr40@yandex.ru
ORCID iD: 0000-0002-7098-5998
Doctor of Technical Sciences, Professor of the Department of Mechanics, Faculty of Engineering and Technology
26 Universitetskii Prospekt, Volgograd, 400002, Russian FederationYuriy V. Klochkov
Volgоgrad State Agrarian University
Author for correspondence.
Email: klotchkov@bk.ru
ORCID iD: 0000-0002-1027-1811
Doctor of Technical Sciences, Professor, Head of the Department of Higher Mathematics, Electric Power and Energy Faculty
26 Universitetskii Prospekt, Volgograd, 400002, Russian FederationReferences
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