Two-scale finite element method for piezoelectric problem in periodic structure
- 75 Downloads
The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic structure under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element approximate estimates and numerical examples which show the effectiveness of the method are presented.
Key wordstwo-scale method piezoelectricity periodic structure finite element method homogenization constant
Chinese Library ClassificationO241.82 O242.21 O482.41
2010 Mathematics Subject Classification34E13 35Q60 78M10 78M40
Unable to display preview. Download preview PDF.
- Fang, D. N. and Mao, G. Z. Experimental study on electro-magneto-mechanical coupling behavior of smart materials (in Chinese). Journal of Mechanical Strength, 27(2), 217–226 (2005)Google Scholar
- Yamaguchi, M., Hashimoto, K. Y., and Makita, H. Finite element method analysis of dispersion characteristics for 1–3 type piezoelectric composite. Proceeding of IEEE Ultrasonic Symposium, 657–661 (1987)Google Scholar
- Ballandras, S., Pierre, G., and Blanc, F. A. Periodic finite element formulation for the design of 2–2 composite transducers. Proceeding of IEEE Ultrasonic Symposium, 957–960 (1999)Google Scholar
- Cui, J. Z., Shin, T. M., and Wang, Y. L. The two-scale analysis method for the bodies with small periodic configurations. Structural Engineering and Mechanics, 7(6), 601–614 (1999)Google Scholar
- Gautschi, G. Piezoelectric Seneorics, Springer, Berlin (2002)Google Scholar
- Zhang, F. X. Modern Piezoelectricity, Science Press, Beijing (2001)Google Scholar
- Oleinik, O. A., Shamaev, A. S., and Yosifian, G. A. Mathematical Problems in Elasticity and Homogenization, North-Holland, Amsterdan, 96 (1992)Google Scholar