 | | 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
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| In English (Mech. Solids): | | 4760 |
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| S. A. Melkumyan and V. S. Tonoyan, "A class of contact problems of electroelasticity for a piezoelectric ceramic half-plane with vertical cuts," Mech. Solids. 39 (5), 48-57 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
5 |
Pages |
48-57 |
| Title |
A class of contact problems of electroelasticity for a piezoelectric ceramic half-plane with vertical cuts |
| Author(s) |
S. A. Melkumyan (Erevan)
V. S. Tonoyan (Erevan) |
| Abstract |
A class of contact problems of electroelasticity is considered for a piezoelectric ceramic half-plane weakened by (a) a finite vertical cut coming against the boundary, (b) semi-infinite vertical cut separated from the boundary by a finite distance, or (c) internal finite vertical cut. A rigid punch is applied to a finite portion of the half-plane boundary symmetrically with respect to the cut axis. The punch base may have an arbitrary smooth shape. It is assumed that the piezoelectric ceramic half-plane is contiguous with vacuum and that the direction of the preliminary polarization is either parallel or perpendicular to the half-space boundary. The half-plane boundary has either a short-circuited electric coating or no coating. The normal pressure is assumed to act on the horizontal boundary apart from the punch and in the cut. All problems are considered for the plane strain state. The elastic displacements and the electric potential are utilized as the basic functions to be determined.
The solutions of the problems are represented by the sum of two Fourier series. To determine an arbitrary function of integration one should first solve dual or triple integral equations or a system of such equations and then solve a Fredholm integral equation of the second kind. The solvability of the latter equation is proved. Analytical expressions are obtained for the mechanical stress tensor components and for the vector of electric potential under the punch and on the cut extension with an isolated square-root singularity. In addition, the expressions for the intensity factors of these components on the edges of the punch and the cut are obtained. Numerical analysis of the behavior of these components is carried out and the corresponding graphs are plotted. |
| References |
| 1. | V. T. Grinchenko, A. F. Ulitko, N. A. Shul'ga, Electroelasticity
[in Russian], Naukova Dumka, Kiev, 1989. |
| 2. | A. F. Ulitko, "Some specific features of the statement of boundary-value problems in electroelasticity,"
in Modern Issues of Mechanics and Aviation [in Russian], pp. 290-300,
Mashinostroenie, Moscow, 1982. |
| 3. | I. S. Gradshtein and I. M. Ryzhik,
Tables of Integrals, Sums, Series, and Products
[in Russian], Nauka, Moscow, 1971. |
| 4. | V. S. Tonoyan, "The solution of an axially symmetric contact problem for a half-plane with an inclusion,"
Izv. AN ArmSSR. Mekhanika, Vol. 21, No. 3, pp. 3-18, 1968. |
| 5. | V. S. Tonoyan and S. A. Melkumyan,
"Contact problem for a half-plane with an internal vertical
finite cut,"
Doklady AN ArmSSR, Vol. 65, No. 2, pp. 122-127, 1977. |
| 6. | V. S. Tonoyan and S. A. Melkumyan,
"A symmetric problem for an orthotropic half-plane with a vertical finite cut,"
Doklady AN ArmSSR, Vol. 92, No. 3, pp. 133-137, 1991. |
| 7. | S. A. Melkumyan, "A symmetric contact problem of electroelasticity for a piezoelectric ceramic half-plane with an internal vertical finite cut and a charged electrode under the punch,"
in Proceedings of the Conference devoted to Professors T. T. Khacatryan
and O. M. Sapondzhyan 90th Birthday [in Russian], pp. 107-112, Erevan, 1999. |
| 8. | A. A. Bobloyan, "Solution of some dual series," Doklady AN ArmSSR, Vol. 39, No. 3, pp. 149-157, 1964. |
|
| Received |
26 March 2002 |
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