 | | 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 |
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| D.V. Georgievskii, "Asymptotics of Solutions of the Three-Dimensional Elasticity Equations for Compressible and Incompressible Bodies," Mech. Solids. 46 (1), 96-103 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
1 |
Pages |
96-103 |
| DOI |
10.3103/S0025654411010158 |
| Title |
Asymptotics of Solutions of the Three-Dimensional Elasticity Equations for Compressible and Incompressible Bodies |
| Author(s) |
D.V. Georgievskii (Lomonosov Moscow State University, GSP-2, Leninskie Gory, Moscow, 119992 Russia, georgiev@mech.math.msu.su) |
| Abstract |
We analyze the leading terms in the general asymptotic expansions of solutions of the first boundary value problem of three-dimensional elasticity in displacements. The cases of compressible and incompressible bodies, which have substantially different statements, are considered separately. The minimum-to-maximum ratio of characteristic dimensions of the elastic body is a natural small asymptotic parameter. The third dimension can be of any "intermediate" order, including the endpoints. For example, such a geometry is typical of bodies that simultaneously have characteristic macro-, micro-, and nano-dimensions in three coordinate axes.
An asymptotic analysis showed that a necessary condition for the existence and uniqueness of the leading terms of asymptotics of displacements in the interior of a three-dimensional thin body is that the orders (with respect to the small geometric parameter) of the displacement components prescribed on the boundary be related to each other in a certain way. Exact solutions of the leading approximation systems in displacements are written out. |
| Keywords |
Lamé equations, theory of thin bodies, asymptotic method, plate |
| References |
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|
| Received |
04 December 2008 |
| Link to Fulltext |
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