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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 3, Pages 418–428 (Mi zvmmf10169)  

This article is cited in 5 scientific papers (total in 5 papers)

Comparison of scalar and vector FEM forms in the case of an elliptic cylinder

T. A. Kiseleva, Yu. V. Klochkov, A. P. Nikolaev

Volgograd State Agricultural University, 26, Volgograd, 400002, Russia

Abstract: An invariant vector approximation of unknown quantities is proposed and implemented to construct the stiffness matrix of a quadrilateral curved finite element in the form of a fragment of the mid-surface of an elliptic cylinder with 18 degrees of freedom per node. Numerical examples show that the vector approximation has significant advantages over the scalar one as applied to arbitrary shells with considerable mid-surface curvature gradients.

Key words: vector approximation, scalar approximation, finite element, elliptic cylinder, shell theory.

DOI: https://doi.org/10.7868/S0044466915030102

Full text: PDF file (499 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:3, 422–431

Bibliographic databases:

UDC: 519.63
MSC: 65N30
Received: 19.05.2014
Revised: 28.08.2014

Citation: T. A. Kiseleva, Yu. V. Klochkov, A. P. Nikolaev, “Comparison of scalar and vector FEM forms in the case of an elliptic cylinder”, Zh. Vychisl. Mat. Mat. Fiz., 55:3 (2015), 418–428; Comput. Math. Math. Phys., 55:3 (2015), 422–431

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. V. Klochkov, A. P. Nikolaev, O. V. Vakhnina, “Finite element analysis of revolution shells by using high order triangle element of discretization with correcting Lagrange multipliers”, Moscow University Mechanics Bulletin, 71:5 (2016), 114–117  mathnet  crossref  isi
    2. E. A. Storozhuk, A. V. Yatsura, “Exact solutions of boundary-value problems for noncircular cylindrical shells”, Int. Appl. Mech., 52:4 (2016), 386–397  crossref  mathscinet  isi
    3. E. A. Storozhuk, I. S. Chernyshenko, O. V. Pigol', “Elastoplastic state of an elliptical cylindrical shell with a circular hole”, Int. Appl. Mech., 53:6 (2017), 647–654  crossref  mathscinet  isi
    4. E. A. Storozhuk, A. V. Yatsura, “Analytical-numerical solution of static problems for noncircular cylindrical shells of variable thickness”, Int. Appl. Mech., 53:3 (2017), 313–325  crossref  mathscinet  isi
    5. E. A. Storozhuk, S. M. Komarchuk, “Stress distribution near a circular hole in a flexible orthotropic cylindrical shell of elliptical cross-section”, Int. Appl. Mech., 54:6 (2018), 687–694  crossref  mathscinet  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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