 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| A. A. Pan’kov, "Asymptotic Solutions by the Successive Disordering Method," Mech. Solids. 44 (6), 927-934 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
6 |
Pages |
927-934 |
| DOI |
10.3103/S0025654409060107 |
| Title |
Asymptotic Solutions by the Successive Disordering Method |
| Author(s) |
A. A. Pan’kov (Perm State Technical University, Komsomolsky pr-t 29, Perm, 614600 Russia, pankov@mkmk.pstu.ac.ru) |
| Abstract |
We develop the periodic component method [1] and represent the solution of a stochastic boundary value elasticity problem for a random quasiperiodic structure with a given disordering degree of inclusions in the matrix via the deviations from the corresponding solution for a random structure with a smaller disordering degree. An example in which the tensor of elastic properties of a composite is calculated is used to illustrate the asymptotic and differential approaches of the successive disordering method. The asymptotic approach permits representing the quasiperiodic structure with a given chaos coefficient and the desired tensor of effective elastic properties as a result of small successive disordering of an originally ideally periodic structure of a composite with known tensor of elastic properties. In the differential approach, a differential equation is obtained for the tensor of effective elastic properties as a function of the chaos coefficient. Its solution coincides with the solution provided by the asymptotic approach. The solution is generalized to the case of piezoactive composites, and a numerical analysis of the effective properties is performed for a PVF (polyvinylidene fluoride) piezoelectric with various quasiperiodic structures on the basis of the cubic structure with spherical inclusions of a high-module elastic material. |
| Keywords |
composite, boundary value elasticity problem, effective properties of a composite, quasiperiodic structures |
| References |
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[in Russian]. |
| 2. | V. A. Lomakin,
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| 4. | B. E. Pobedrya,
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[in Russian]. |
| 6. | Yu. V. Sokolkin and A. A. Pan'kov,
Electroelasticity of Piezocomposites with Irregular Structures
(Fizmatlit, Moscow, 2003)
[in Russian]. |
| 7. | A. A. Pan'kov and Yu. C. Sokolkin,
"A Solution to a Boundary Value Problem of Electro-Elasticity for Piezo-Active Composites Based on the Method of Periodic Components,"
Mekh. Komp. Mater. Konstr.
8 (3), 365-384 (2002)
[J. Comp. Mech. Design (Engl. Transl.)]. |
| 8. | A. A. Pan'kov and Yu. C. Sokolkin,
"Influence of Geometry of Ellipsoidal Pours on the Properties of Piezo-Ceramics and on the Distribution of Fields of Deformation,"
Mekh. Komp. Mater. Konstr.
9 (1), 87-95 (2003)
[J. Comp. Mech. Design (Engl. Transl.)]. |
| 9. | W. P. Mason,
Piezoelectric Crystals and Their Application to Ultrasonics
(Van Nostrand, New York, 1950; Izd-vo Inostr. Lit., Moscow, 1952). |
| 10. | V. Z. Parton and B. A. Kudryavtsev,
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[in Russian]. |
| 11. | L. P. Khoroshun, B. P. Maslov, and P. V. Leshchenko,
Prediction of Effective Properties of Piezoactive Composite Materials (Naukova Dumka, Kiev, 1989) [in Russian]. |
|
| Received |
30 October 2007 |
| Link to Fulltext |
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