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
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.
shell, the stress-strain state, nonlinear shell model, serial parameters perturbation method.
PDF file (557 kB)
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
\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.
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