 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4810 |
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| Yu. I. Vinogradov, Yu. I. Klyuev, and I. F. Obraztsov, "A method for solving boundary-value problems in the mechanics of deformation of thin-walled structures," Mech. Solids. 36 (1), 130-136 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
1 |
Pages |
130-136 |
| Title |
A method for solving boundary-value problems in the mechanics of deformation of thin-walled structures |
| Author(s) |
Yu. I. Vinogradov (Moscow)
Yu. I. Klyuev (Moscow)
I. F. Obraztsov (Moscow) |
| Abstract |
A method is suggested to integrate systems of ordinary differential
equations of boundary value problems for thin-walled axisymmetric
structures. This method follows the algorithm of analytical
solution of boundary value problems. The method is easy to
implement. The integral of a system of differential equations
is calculated numerically by using the
matrix Taylor series. This series is determined for the matrix
differential equation by using either the Picard method of
successive approximations or the matrix binomial obtained from the
definition of the Volterra integral. The
integral is calculated for an interval the length of which is
smaller than the critical length of stable calculation. In this
case, one need not perform the cumbersome procedure of
orthonormalization at the ends of integration intervals.
The method suggested permits one to solve problems
with arbitrary boundary conditions for structures with
reinforcement rings and solid bodies axisymmetrically attached in an
arbitrary way for once obtained values of the integral of
differential equations. An important specific feature of this
numerical method is the possibility of estimating a priori the
error of results.
As an example of using the method, the results of the stability analysis
are presented for a conic shell reinforced by rings
under combined loading. |
| References |
| 1. | F. R. Gantmakher, Theory of Matrices [in Russian], Nauka,
Moscow, 1967. |
|
| Received |
02 July 2000 |
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