Comparative analysis of efficiency of use of finite elements of different dimensionality in the analysis of the stress-strain state of thin shells

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Abstract


Relevance. To determine the stress-strain state (SSS) of thin-walled shells due to the complexity of obtaining numerical results, the theory of thin shells was developed with the introduction of the direct normal hypothesis to reduce the three-dimensional SSS to the two-dimensional one. With the modern development of digital technology and numerical methods of calculation, in particular the finite element method (FEM), it became possible to obtain numerical results without the use of the direct normal hypothesis, namely on the basis of the theory of elasticity in three-dimensional formulation even for thin shells. Aims. The aim of this work is to compare the efficiency of algorithms for the use of finite element stiffness matrices obtained on the basis of the theory of thin shells with the hypothesis of a straight normal and on the basis of the relations of the three-dimensional theory of elasticity. Methods. The results of comparative analysis of finite element calculations of thin shells using a two-dimensional sampling element in the form of a quadrangular fragment of the middle surface and a three-dimensional element in the form of an eight-node six-face are presented. The components of the displacement vector and their first derivatives were chosen as the nodal variable parameters. The functions of the form for both types of discretization elements were represented by products of Hermite polynomials of the third degree. Results. On the example of calculation of the cylindrical shell clamped at the ends it is shown that the two-dimensional statement in calculations of thin shells is adequate and allows to receive acceptable results at optimum costs of machine time.


About the authors

Yuriy V Klochkov

Volgograd State Agricultural University

Author for correspondence.
Email: klotchkov@bk.ru
26 University Ave., Volgograd, 400002, Russian Federation

Dr Sci. (Eng.), Professor, Head of the Department of Higher Mathematics

Anatoliy P Nikolaev

Volgograd State Agricultural University

Email: anpetr40@yandex.ru
26 University Ave., Volgograd, 400002, Russian Federation

Dr Sci. (Eng.), Professor, Professor of the Department of Applied Geodesy, Environmental Engineering and Water Use

Tatyana A Sobolevskaya

Volgograd State Agricultural University

Email: moonway13@rambler.ru
26 University Ave., Volgograd, 400002, Russian Federation

Cand. Sci. (Eng.), Associate Professor of Higher Mathematics Department

Mikhail Yu Klochkov

Lomonosov Moscow state University

Email: m.klo4koff@yandex.ru
1 Leninskiye Gory, Moscow, 119899, Russian Federation

a third-year student of the Faculty of Physics

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Copyright (c) 2018 Klochkov Y.V., Nikolaev A.P., Sobolevskaya T.A., Klochkov M.Y.

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