Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
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IssuesArchive of Issues2013-4pp.445-451

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Yu.I. Vinogradov, "A multiplicative method of solving boundary value problems of shell theory," J. Appl. Math. Mech. 77 (4), 445-451 (2013)
Year 2013 Volume 77 Issue 4 Pages 445-451
Title A multiplicative method of solving boundary value problems of shell theory
Author(s) Yu.I. Vinogradov (Moscow, Russia,
Abstract The boundary conditions are transferred to an arbitrarily chosen point by multiplication of matrices (multiplicatively). The transfer matrices of the boundary conditions are an analytic solution of a system of first-order linear ordinary differential equations in canonical form of the mechanics of the deformation of shells in the form of values of Cauchy-Krylov functions. At an arbitrarily chosen point, the boundary conditions are combined in a system of algebraic equations in matrix form, columns of the unknown quantities of which are parameters of the required values of the problem. The effectiveness of the method – the simplicity with which it can be realized on a computer, the low costs of computer time and the RAM - is based on the multiplicative transfer of the boundary conditions into matrix form. The class of problems is limited by the possibilities of the Fourier method of separation of the variables in partial differential equations.
Received 10 October 2012
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