Accounting for geometric nonlinearity in finite element strength calculations of thin-walled shell-type structures

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Abstract


Relevance. Currently, in connection with the wider spread of large-span thinwalled structures such as shells, an urgent issue is the development of computational algorithms for the strength calculation of such objects in a geometrically nonlinear formulation. Despite a significant number of publications on this issue, a rather important aspect remains the need to improve finite element models of such shells that would combine the relative simplicity of the resolving equations, allowance for shear deformations, compactness of the stiffness matrix being formed, the facilitated possibility of modeling and changing boundary conditions and etc. The aim of the work is to develop a finite element algorithm for calculating a thin shell with allowance for shear deformations in a geometrically nonlinear formulation using a finite element with a limited number of variable nodal parameters. Methods. As research tools, the numerical finite element method was chosen. The basic geometric relations between the increment of deformations and the increment of the components of the displacement vector and the increment of the components of the normal vector angle are obtained in two versions of the normal angle of the reference. The stiffness matrix and the column of nodal forces of the quadrangular finite element at the loading step were obtained by minimizing the Lagrange functional. Results. On the example of calculating a cylindrical panel rigidly clamped at the edges under the action of a concentrated force, the efficiency of the developed algorithm was shown in a geometrically nonlinear setting, taking into account the transverse shear strain.


About the authors

Yuriy V. Klochkov

Volgograd State Agricultural University

Author for correspondence.
Email: klotchkov@bk.ru
SPIN-code: 9436-3693
26 Universitetskii Ave., Volgograd, 400002, Russian Federation

Doctor of Technical Sciences, Professor, Head of the Department of Higher Mathematics

Anatoliy P. Nikolaev

Volgograd State Agricultural University

Email: klotchkov@bk.ru
SPIN-code: 2653-5484
26 Universitetskii Ave., Volgograd, 400002, Russian Federation

Doctor of Technical Sciences, Professor

Tlek R. Ishchanov

Volgograd State Agricultural University

Email: klotchkov@bk.ru
SPIN-code: 1556-1368
26 Universitetskii Ave., Volgograd, 400002, Russian Federation

Candidate of Technical Sciences, senior lecturer of the Department of Higher Mathematics

Alexandr S. Andreev

Volgograd State Agricultural University

Email: klotchkov@bk.ru
SPIN-code: 7568-5011
26 Universitetskii Ave., Volgograd, 400002, Russian Federation

senior lecturer of the Department of Higher Mathematics

Mikhail Yu. Klochkov

Lomonosov Moscow State University

Email: klotchkov@bk.ru
SPIN-code: 2767-3955
1 Leninskiye Gory, Moscow, 119899, Russian Federation

4th-year student of the Faculty of Physics

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Copyright (c) 2020 Klochkov Y.V., Nikolaev A.P., Ishchanov T.R., Andreev A.S., Klochkov M.Y.

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