RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Chebyshevskii Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Chebyshevskii Sb., 2016, Volume 17, Issue 3, Pages 28–37 (Mi cheb495)  

About numerical realization of the method of subsequent parameters perturbation for calculating a stress-strain state of shallow shells

L. V. Bessonova, T. A. Kuznetsovaa, S. V. Chumakovab

a Saratov State University
b Saratov State Agrarian University named after N. I. Vavilov

Abstract: The paper investigates a class of nonlinear dynamic shell models, which non-linearity reflects Gaussian curvature of a surface; in the case when loads are smaller than critical ones in every point in time. Moreover, every unknown function from the system of equations, can be uniquely identified through the deflection function. Domain that is defined by the middle shell surface is bounded with piecewise smooth boundary. Such models as Kirchhoff–Love model (that specify Tymoshenko model, defined both in transferences and mixed forma), a model that reflects the bond between deformation fields and temperature and others can represent that equation class.
The method of subsequent parameters perturbation developed by professor V. Petrov in 1970s is used as a numerical method for such models. This method brings the solution of nonlinear equations to the solution of a sequence of linear equations. The paper discusses problems connected with the realization of this method. It is known, that method of V. Petrov converges slowly. That is why questions of convergence improvement are examined. The usage of variation methods for solving systems of linear equations requires defined convergence speed and orthogonal system of functions that satisfies the boundary conditions. These questions are investigated in the paper as well.

Keywords: shell, the stress-strain state, nonlinear shell model, serial parameters perturbation method.

Full text: PDF file (557 kB)
References: PDF file   HTML file
UDC: 517.5
Received: 11.06.2016
Accepted:13.09.2016

Citation: L. V. Bessonov, T. A. Kuznetsova, S. V. Chumakova, “About numerical realization of the method of subsequent parameters perturbation for calculating a stress-strain state of shallow shells”, Chebyshevskii Sb., 17:3 (2016), 28–37

Citation in format AMSBIB
\Bibitem{BesKuzChu16}
\by L.~V.~Bessonov, T.~A.~Kuznetsova, S.~V.~Chumakova
\paper About numerical realization of the method of subsequent parameters perturbation for calculating a stress-strain state of shallow shells
\jour Chebyshevskii Sb.
\yr 2016
\vol 17
\issue 3
\pages 28--37
\mathnet{http://mi.mathnet.ru/cheb495}
\elib{http://elibrary.ru/item.asp?id=27452080}


Linking options:
  • http://mi.mathnet.ru/eng/cheb495
  • http://mi.mathnet.ru/eng/cheb/v17/i3/p28

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Number of views:
    This page:117
    Full text:34
    References:24

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020