 | | 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
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| In English (Mech. Solids): | | 4810 |
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| Babeshko V.A., Evdokimova O.V., and Babeshko O.M., "On the Decomposition of Solutions of Scalar Boundary Value Problems in Mechanics in Terms of Block Elements," Mech. Solids. 56 (6), 895-901 (2021) |
| Year |
2021 |
Volume |
56 |
Number |
6 |
Pages |
895-901 |
| DOI |
10.3103/S0025654421060029 |
| Title |
On the Decomposition of Solutions of Scalar Boundary Value Problems in Mechanics in Terms of Block Elements |
| Author(s) |
Babeshko V.A. (South Scientific Center, Russian Academy of Sciences, Rostov-on-Don, 344006 Russia; Kuban State University, Krasnodar, 350040 Russia, babeshko41@mail.ru)
Evdokimova O.V. (South Scientific Center, Russian Academy of Sciences, Rostov-on-Don, 344006 Russia)
Babeshko O.M. (Kuban State University, Krasnodar, 350040 Russia) |
| Abstract |
Earlier, the authors developed a method for reducing boundary value problems in continuum mechanics for systems of differential equations to boundary value problems for individual equations, called scalar. This approach is based on the B. G. Galerkin transformation for systems of partial differential equations and the block element method. In this article, based on the well-known properties of the block element method, three approaches are developed that make it possible to implement the application of the block element method to fairly complex scalar boundary value problems. For the first time, by analogy with the exponential substitution used in ordinary differential equations with constant coefficients, a block substitution is used in this article, which makes it possible to solve boundary value problems for partial differential equations. As a result of the study, the sought solutions of scalar boundary value problems are represented as a sum using the simplest block elements, which greatly simplifies the study of the exact solutions obtained. |
| Keywords |
block element, scalar boundary value problems, biharmonic equation, inverse operators |
| Received |
01 March 2021 | Revised |
07 March 2021 | Accepted |
18 March 2021 |
| Link to Fulltext |
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