Three-Field FEM in Shell Calculations with Options for Interpolation of the Sought Values

M. Yu. Klochkov; Клочков М. Ю.; V. A. Pshenichkina; Пшеничкина В. А.; A. P. Nikolaev; Николаев А. П.; Yu. V. Klochkov; Клочков Ю. В.; O. V. Vakhnina; Вахнина О. В.; A. S. Andreev; Андреев А. С.

doi:10.31857/S0032823524050109

Three-Field FEM in Shell Calculations with Options for Interpolation of the Sought Values

Authors: Klochkov M.Y.¹, Pshenichkina V.A.¹, Nikolaev A.P.², Klochkov Y.V.², Vakhnina O.V.², Andreev A.S.²
Affiliations:
1. Volgograd State Technical University
2. Volgograd State Agricultural University
Issue: Vol 88, No 5 (2024)
Pages: 797-820
Section: Articles
URL: https://rjonco.com/0032-8235/article/view/682383
DOI: https://doi.org/10.31857/S0032823524050109
EDN: https://elibrary.ru/JPFBTH
ID: 682383

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Abstract

A three-field finite element of a quadrangular shape of a thin shell with nodal unknowns in the form of: displacements and their first derivatives has been developed; deformations and curvatures of the median surface; forces and moments of the middle surface.

The approximation of the required quantities was carried out in two versions. In the first version, the components of the displacement vector and the components of the strain and curvature tensors, as well as the force and moment tensors, were approximated using traditional shape functions as components of scalar fields. In the second version, tensor quantities were approximated through the corresponding tensors of nodal points, and only after coordinate transformations based on the relations of the used curvilinear coordinate system were approximating expressions for the components of the corresponding tensors obtained.

Specific examples show the effectiveness of using the second version of approximating expressions in shell calculations.

Keywords

displacement vector, strain tensor, stress tensor, force tensor, curvature tensor, three-field finite element, tensor-vector interpolation

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