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Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie, 2015, Volume 8, Issue 2, Pages 138–142
DOI: https://doi.org/10.14529/mmp150213
(Mi vyuru271)
 

This article is cited in 8 scientific papers (total in 8 papers)

Short Notes

About modelling of deformations of plates

A. L. Ushakov

South Ural State University (Chelyabinsk, Russian Federation)
Full-text PDF (358 kB) Citations (8)
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Abstract: Of concern are the elliptic boundary problems of the fourth order which are underlying in mathematical models of deformations of plates on the elastic bases under the mixed boundary conditions of four theoretically possible types. Replacements of these problems in a variation form to their fictitious continuations are proposed. Solutions of the last problems by means of modifications of fictitious components methods are reduced to solutions of problems in a rectangular area. Optimum estimates of convergence of iterative processes at the continuous level are given. At simple sampling of fictitiously continued problems by method of final elements on parabolic completions, effective numerical modifications of fictitious components methods turn out to be suitable for practical realization on the computer. The received systems of linear algebraic equations can be optimally solved by means of iterative factorizations methods. As a result the proposed numerical methods are log-optimal or optimal by number of arithmetic operations necessary for achievement of set relative errors.
Keywords: deformations of plates; fictitious continuations.
Received: 27.01.2015
Bibliographic databases:
Document Type: Article
UDC: 519.63
MSC: 65N85
Language: Russian
Citation: A. L. Ushakov, “About modelling of deformations of plates”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 8:2 (2015), 138–142
Citation in format AMSBIB
\Bibitem{Ush15}
\by A.~L.~Ushakov
\paper About modelling of deformations of plates
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2015
\vol 8
\issue 2
\pages 138--142
\mathnet{http://mi.mathnet.ru/vyuru271}
\crossref{https://doi.org/10.14529/mmp150213}
\elib{https://elibrary.ru/item.asp?id=23442162}
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  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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