Numerical analysis of the stress-strain state of thin shells based on a joint triangular finite element

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Abstract

Relevance. The use of the finite element method for determining the stressstrain state of thin-walled elements of engineering structures predetermines their discretization into separate finite elements. Splitting irregular parts of the structure is impossible without the use of triangular areas. The triangular elements of shell structures are joint in displacements and in their derivatives only at the nodal points. Therefore, ways to improve the compatibility conditions at the boundaries of triangular elements are relevant. Aims of research. The aim of the work is to improve the compatibility conditions at the boundaries of adjacent triangular elements based on equating the derivatives of normal displacements in the middle of the boundary sides. Methods. In order to improve the compatibility conditions at the boundaries of triangular elements in this work, the Lagrange functional is used with the condition of ensuring equality in the middle of the sides of adjacent elements derived from normal displacements in the directions of perpendiculars tangent to the middle surface of the shell. Results. Using the example of analysing an elliptical shell, the efficiency of using a joint triangular finite element is shown, whose stiffness matrix is formed in accordance with the algorithm outlined in this article.

About the authors

Yuriy V Klochkov

Volgograd State Agricultural University

Author for correspondence.
Email: klotchkov@bk.ru
SPIN-code: 9436-3693

DSc. in Technical Sciences, Professor, Head of the Higher Mathematics Department, Volgograd State Agricultural University. He published 165 scientific articles, 4 monographs, 4 titles of educational literature

26 University Ave., Volgograd, 400002, Russian Federation

Anatoliy P Nikolaev

Volgograd State Agricultural University

Email: anpetr40@yandex.ru
SPIN-code: 2653-5484

DSc. in Technical Sciences, Professor, Professor of the Applied Geodesy, Environmental Engineering and Water Use Department, Volgograd State Agricultural University. He published 149 scientific articles, 6 monographs, 5 titles of educational literature

26 University Ave., Volgograd, 400002, Russian Federation

Olga V Vakhnina

Volgograd State Agricultural University

Email: ovahnina@bk.ru
SPIN-code: 3593-0159

PhD in Technical Sciences, Associate Professor of Higher Mathematics Department, Volgograd State Agricultural University. She published 47 scientific articles, 1 monograph, 8 titles of educational literature.

26 University Ave., Volgograd, 400002, Russian Federation

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Copyright (c) 2019 Klochkov Y.V., Nikolaev A.P., Vakhnina O.V.

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