Abstract
The system of equilibrium equations for nonthin transversely isotropic piezoceramic plates subject to antisymmetric (about the mid-plane) deformation is set up by expanding the unknown functions into Fourier-Legendre series in the thickness coordinate. To find the general solution of the system of equations, a method is proposed, which is then used to solve the stress problem for a plate with a circular hole under mechanical loading
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. A. Boriseiko, V. T. Grinchenko, and A. F. Ulitko, “Relations of electroelasticity for piezoceramic shells of revolution,” Int. Appl. Mech., 12, No. 2, 126–131 (1976).
V. O. Boriseiko, V. S. Martynenko, and A. F. Ulitko, “General theory of thin piezoceramic shells,” Visn. Kyiv. Univ., Ser. Mat. Mekh., 25, 26–40 (1983).
É. I. Grigolyuk, L. A. Fil’shtinskii, and Yu. D. Kovalev, “Bending of a piezoceramic layer with through tunnel holes and sliding restraint at the edges,” Dokl. RAN, 379, No. 6, 745–747 (2001).
V. T. Grinchenko, A. F. Ulitko, and N. A. Shul’ga, Electroelasticity, Vol. 5 of the five-volume series Mechanics of Coupled Fields in Structural Members [in Russian], A.S.K., Naukova Dumka, Kyiv (1989).
I. Yu. Khoma, “Stress state of a nonthin piezoceramic plate with a circular hole,” Teor. Prikl. Mekh., 39, 48–58 (2004).
I. Yu. Khoma, Yu. I. Khoma, and T. M. Proshchenko, “Three-dimensional distribution of stresses around a circular hole in a nonthin piezoceramic plate,” Teor. Prikl. Mekh., 40, 18–23 (2005).
L. A. Fil’shtinskii and Yu. D. Kovalev, “Concentration of mechanical stresses around a hole in a piezoceramic layer,” Mekh. Komp. Mater., 38, No. 2, 183–188 (2002).
L. A. Fil’shtinskii and L. V. Shramko, “Homogeneous solutions to an antisymmetric problem with mixed boundary conditions for a piezoceramic layer,” Fiz.-Khim. Mater., 39, No. 1, 35–40 (2003).
P. Bisegna and G. Caruso, “Evolution of higher order theories of piezoelectric plates in bending and in stretching,” Int. J. Solids Struct., 38, No. 48–49, 8805–8830 (2001).
Cheng Zhen-Qiang, C. W. Lim, and S. Kitipornchai, “Three-dimensional asymptotic approach to inhomogeneous and laminated piezoelectric plates,” Int. J. Solids Struct., 37, No. 33, 3153–3175 (2000).
I. Yu. Khoma, “Thermopiezoelectric equations for nonthin ceramic shells,” Int. Appl. Mech., 41, No. 2, 118–128 (2005).
I. F. Kirichok and T. V. Karnaukhova, “Resonant vibrations and dissipative heating of an infinite pizoceramic cylinder,” Int. Appl. Mech., 41, No. 3, 309–314 (2005).
Yu. N. Podil’chuk and O. G. Dashko, “Stress state of a soft ferromagnetic with an ellipsoidal cavity in a homogeneous magnetic field,” Int. Appl. Mech., 41, No. 3, 283–290 (2005).
Yu. N. Podil’chuk and I. G. Myasoedova, “Stress state of a transversely isotropic piezoceramic body with a spheroidal cavity,” Int. Appl. Mech., 40, No. 11, 1269–1280 (2004).
Yu. N. Podil’chuk and T. M. Proshchenko, “The stress state of piezoceramic medium with elliptic inclusion under pure shear and pure bending,” Int. Appl. Mech., 39, No. 5, 573–582 (2003).
J. S. Yang, “Equation for the extension and flexure of electroelastic plates under strong electric fields,” Int. J. Solids Struct., 36, No. 21, 3171–3192 (1999).
Author information
Authors and Affiliations
Additional information
__________
Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 96–106, October 2006.
Rights and permissions
About this article
Cite this article
Khoma, I.Y., Proshchenko, T.M. & Kondratenko, O.A. Solving the equilibrium equations for a transversely isotropic piezoceramic plate. Int Appl Mech 42, 1160–1169 (2006). https://doi.org/10.1007/s10778-006-0188-7
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10778-006-0188-7