 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
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| V. I. Gorbachev, "Averaging of linear problems in the mechanics of composites with nonperiodic inhomogeneities," Mech. Solids. 36 (1), 24-29 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
1 |
Pages |
24-29 |
| Title |
Averaging of linear problems in the mechanics of composites with nonperiodic inhomogeneities |
| Author(s) |
V. I. Gorbachev (Moscow) |
| Abstract |
Initial boundary value problems are considered for linear differential
equations with variable coefficients. Such equations describe processes in
composite materials whose mechanical characteristics may either have a jump
or be continuous at the interface between the phases. Moreover, many
problems in various branches of the mechanics of deformable solids reduce
to linear equations with variable coefficients. In particular, this
pertains to the problems of A. A. Il'yushin's theory of small
elastic-plastic deformations [1], whenever these problems are solved by the
methods involving variable elastic parameters [3]. The basic aim of any
averaging method is to express the solution of a problem for an equation
with variable coefficients through the solution of an equation with
constant coefficients. If the coefficients periodically depend on the
coordinates, good results can be obtained by the method of small
geometrical parameter [4-6].
In the present paper, we propose an averaging method
which is applicable both in the periodic and the nonperiodic cases. |
| References |
| 1. | A. A. Il'yushin, Plasticity [in Russian], Gostekhizdat, Moscow, 1948. |
| 2. | A. A. Il'yushin, Plasticity: Basic Principles of the Mathematical
Theory [in Russian], Izd-vo AN SSSR, 1963. |
| 3. | I. A. Birger, "Some general methods for solving problems in
the theory of plasticity," PMM [Applied Mathematics and Mechanics],
Vol. 15, No. 6, pp. 765-770, 1951. |
| 4. | N. S. Bakhvalov and G. P. Panasenko, Averaging of Processes in
Periodic Media [in Russian], Nauka, Moscow, 1984. |
| 5. | B. E. Pobedrya, Mechanics of Composite Materials, Izd-vo
MGU, Moscow, 1984. |
| 6. | B. E. Pobedrya and V. I. Gorbachev, "On static problems for
elastic composites," Vestnik MGU. Ser. Mat. Mekh., No. 5, pp. 101-111,
1975. |
|
| Received |
03 October 2000 |
| << Previous article | Volume 36, Issue 1 / 2001 | Next article >> |
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