Abstract
The problem of bending of a plate with arbitrary holes and cracks is solved with the use of complex potentials of the theory of bending of thin electro-magneto-elastic plates. Moreover, with the help of conformal mappings, expansion of holomorphic functions into the Laurent series or Faber polynomials owing to satisfaction of boundary conditions by the generalized least squares method, the problem is reduced to an overdetermined system of linear algebraic equations, which is then solved by the method of singular value decomposition. Results of numerical investigations for a plate with two elliptical holes or cracks and for a plate with a hole and a crack (including an edge crack) are reported. The influence of physical and mechanical properties of the plate material and geometric characteristics of holes and cracks on the basic characteristics of the electro-magneto-elastic state is studied.
Similar content being viewed by others
REFERENCES
D. Berlincourt, D. R. Curran, and H. Jaffe, “Piezoelectric and Piezomagnetic Materials and Their Function in Transducers," in Physical Acoustics, Ed. by W. P. Mason (Academic Press, New York, 1964).
M. I. Bichurin, V. M. Petrov, D. A. Filippov, et al., Magnetoelectric Composites (Akad. Estestv., Moscow, 2006; Jenny Stanford Publishing, 2019).
A. P. Pyatakov, “Magnetoelectric Materials and Their Application in Practice," Bul. Ros. Magnit. Obshchestva 5 (2), 1-3 (2006).
S. Srinivas and Y. L. Jiang, “The Effective Magnetoelectric Coefficients of Polycrystalline Multiferroic Composites," Acta Materialia 53, 4135–4142 (2005).
A. C. Eringen, “Theory of Electromagnetic Elastic Plates," Intern. J. Engng Sci. 27 (4), 363–375 (1989).
L. Librescu, D. Hasanyan, and D. R. Ambur, “Electromagnetically Conducting Elastic Plates in a Magnetic Field: Modeling and Dynamic Implications," Intern. J. Non-Linear Mech. 39 (5), 723–739 (2004).
C. Gales and N. Baroiu, “On the Bending of Plates in the Electromagnetic Theory of Microstretch Elasticity," Z. angew. Math. Mech. Bd 94 (1/2), 55–71 (2014).
S. A. Kaloerov and A. V. Petrenko, “Two-Dimensional Problem of Electro-Magneto-Elasticity for Multiply Connected Media," Mat. Metody I Fiz.-Mekh. Polya 51 (2), 208-221 (2008).
S. A. Kaloerov, “Complex Potentials of the Theory of Bending of Thin Electro-Magneto-Elastic Plates," Vestn. Don. Nats. Univ., Ser. A, Estestv. Nauki, No. ?, 37-57 (2019).
S. A. Kaloerov and A. V. Seroshtanov, “Bending of Thin Electromagnetoelastic Plates," Prikl. Mekh. Tekh. Fiz. 63 (2), 151-165 (2022) [J. Appl. Mech. Tech. Phys. 63 (2), 308-320 (2022)].
V. V. Voevodin, Computational Basis of Linear Algebra (Nauka, Moscow, 1977).
J. E. Forsythe, M. A. Malcolm, and C. B. Moler, Computer Methods for Mathematical Computations (Prentice-Hall, 1977).
Z. Drmaç and K. Veseliç, “New Fast and Accurate Jacobi SVD Algorithm. 1." SIAM J. Matrix Anal. Appl. 29 (4), 1322–1342 (2008).
Z. Drmaç and K. Veseliç, “New Fast and Accurate Jacobi SVD Algorithm. 2," SIAM J. Matrix Anal. Appl. 29 (4), 1343–1362 (2008).
S. A. Kaloerov and A. I. Zanko, “Solution of the Problem of Linear Viscoelasticity for Multiply Connected Isotropic Plates," Prikl. Mekh. Tekh. Fiz. 58 (2), 141–151 (2017).
Y. Yamamoto, “Electromagnetomechanical Interactions in Deformable Solids and Structures," Eds. by Y. Yamamoto, K. Miya. (Amsterdam: Elsevier Sci. North Holland, 1987).
W.-Y. Tian and U. Gabbert, “Multiple Crack Interaction Problem in Magnetoelectroelastic Solids," Europ. J. Mech. Pt A 23, 599–614 (2004).
P. F. Hou, G.-H. Teng, and H.-R. Chen, “Three-Dimensional Greens Function for a Point Heat Source in Two-Phase Transversely Isotropic Magneto-Electro-Thermo-Elastic Material," Mech. Materials 41, 329–338 (2009).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Vol. 63, No. 4, pp. 143-155. https://doi.org/10.15372/PMTF20220415.
Rights and permissions
About this article
Cite this article
Kaloerov, S.A., Seroshtanov, A.V. SOLVING THE PROBLEM OF ELECTRO-MAGNETO-ELASTIC BENDING OF A MULTIPLY CONNECTED PLATE. J Appl Mech Tech Phy 63, 676–687 (2022). https://doi.org/10.1134/S0021894422040150
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894422040150