 | | 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: | | 13205 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8140
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| In English (Mech. Solids): | | 5065 |
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| S.A. Kaloerov and A.V. Seroshtanov, "Solutions of Periodic and Doubly Periodic Bending Problems of a Thin Piezo Plate with Holes or Cracks," Mech. Solids. 60 (2), 812-824 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
2 |
Pages |
812-824 |
| DOI |
10.1134/S002565442460555X |
| Title |
Solutions of Periodic and Doubly Periodic Bending Problems of a Thin Piezo Plate with Holes or Cracks |
| Author(s) |
S.A. Kaloerov (Donetsk State University, Donetsk, DPR, 283001 Russia, kaloerov@mail.ru)
A.V. Seroshtanov (Donetsk State University, Donetsk, DPR, 283001 Russia, aleks.serosht@gmail.com) |
| Abstract |
The solutions of periodic and doubly periodic problems of bending of a piezo plate with
elliptical holes or cracks are given with an analysis of the results of numerical studies. In this case, complex potentials of the theory of bending of thin electro-magneto-elastic plates are used, holomorphic
functions outside the holes are represented by Laurent series in negative powers of variables from the
corresponding conformal mappings and, based on the periodicity or doubly periodicity of the electromagneto-elastic state of the plate, the coefficients of the series from all the holes are expressed through
the coefficients of the series from one, the so-called main hole. The determination of the last coefficients is carried out from the boundary conditions on the contour of the main hole using the generalized least squares method. The results of numerical studies for a plate with circular holes or cracks with
full or partial consideration of piezo properties, without taking them into account, are described. The
patterns of influence on the values of bending moments and their concentration of the geometric characteristics of the discussed plates and the physico-mechanical properties of their materials are established. |
| Keywords |
thin piezo plate with holes and cracks, periodic problem, doubly periodic problem, complex potentials |
| Received |
19 March 2024 | Revised |
25 September 2024 | Accepted |
26 September 2024 |
| Link to Fulltext |
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