Finite Element Algorithm for Calculating the Ellipsoidal Shell with Consideration of Its Displacement as a Rigid Whole

For the strength calculation of the ellipsoidal shell using continuous parametrization of the median surface, a finite element of a quadrangular shape, which is a fragment of the median surface of the ellipsoid, is developed. The displacements of nodal points and their derivatives are taken as nodal...

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Bibliographic Details
Published in:Mechanics of solids 2022-12, Vol.57 (7), p.1749-1757
Main Authors: Dzhabrailov, A. Sh, Nikolaev, A. P., Klochkov, Yu. V., Gureeva, N. A., Ishanov, T. R.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Classical Mechanics
Coordinate transformations
Displacement
Mathematical analysis
Parameterization
Physics
Physics and Astronomy
Rigid structures
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Summary:For the strength calculation of the ellipsoidal shell using continuous parametrization of the median surface, a finite element of a quadrangular shape, which is a fragment of the median surface of the ellipsoid, is developed. The displacements of nodal points and their derivatives are taken as nodal unknowns. To obtain the expressions for the approximating functions of the desired values of the internal point of a finite element through nodal unknowns, we use traditional approximating expressions of the displacement vector of the internal point of a finite element through the displacement vectors of element nodes and the derivatives of these vectors. To perform the coordinate transformation, we use the matrix relations between the basis vectors of the nodal points and the basis vectors of the internal point of the finite element, the implementation of which allows for the approximating expressions between vector quantities to be represented as approximating functions between the components of the displacement vector of the internal point of the finite element and the components of the displacement vectors of its nodal points. Using a concrete example, it is shown that the use of the approximating functions obtained allows us to consider the displacement of the finite element as that of an absolutely rigid body. The resulting approximating functions lead to a faster convergence of the results in the absence of a displacement as a rigid whole as well.
ISSN:0025-6544
1934-7936
DOI:10.3103/S0025654422070081