 | | 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
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| In English (Mech. Solids): | | 3212 |
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| V.V. Korepanov, V.P. Matveenko, A.Yu. Fedorov, and I.N. Shardakov, "Numerical Analysis of Singular Solutions of Two-Dimensional Problems of Asymmetric Elasticity," Mech. Solids. 48 (4), 397-404 (2013) |
| Year |
2013 |
Volume |
48 |
Number |
4 |
Pages |
397-404 |
| DOI |
10.3103/S0025654413040067 |
| Title |
Numerical Analysis of Singular Solutions of Two-Dimensional Problems of Asymmetric Elasticity |
| Author(s) |
V.V. Korepanov (Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of Sciences, Akad. Koroleva 1, Perm, 614013 Russia, kvv@icmm.ru)
V.P. Matveenko (Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of Sciences, Akad. Koroleva 1, Perm, 614013 Russia, mvp@icmm.ru)
A.Yu. Fedorov (Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of Sciences, Akad. Koroleva 1, Perm, 614013 Russia)
I.N. Shardakov (Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of Sciences, Akad. Koroleva 1, Perm, 614013 Russia, shardakov@icmm.ru) |
| Abstract |
An algorithm for the numerical analysis of singular solutions of two-dimensional problems of asymmetric elasticity is considered. The algorithm is based on separation of a power-law dependence from the finite-element solution in a neighborhood of singular points in the domain under study, where singular solutions are possible. The obtained power-law dependencies allow one to conclude whether the stresses have singularities and what the character of these singularities is. The algorithm was tested for problems of classical elasticity by comparing the stress singularity exponents obtained by the proposed method and from known analytic solutions.
Problems with various cases of singular points, namely, body surface points at which either the smoothness of the surface is violated, or the type of boundary conditions is changed, or distinct materials are in contact, are considered as applications. The stress singularity exponents obtained by using the models of classical and asymmetric elasticity are compared. It is shown that, in the case of cracks, the stress singularity exponents are the same for the elasticity models under study, but for other cases of singular points, the stress singularity exponents obtained on the basis of asymmetric elasticity have insignificant quantitative distinctions from the solutions of the classical elasticity. |
| Keywords |
Cosserat theory of elasticity, stress singularity, finite element method |
| References |
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|
| Received |
08 October 2012 |
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