Two-Scale Finite Element Method for Piezoelectric Problem in Periodic Structure

DENG Ming-xiang; FENG Yong-ping

doi:10.3879/j.issn.1000-0887.2011.12.004

Volume 32 Issue 12

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2011 > 32(12): 1424-1438

DENG Ming-xiang, FENG Yong-ping. Two-Scale Finite Element Method for Piezoelectric Problem in Periodic Structure[J]. Applied Mathematics and Mechanics, 2011, 32(12): 1424-1438. doi: 10.3879/j.issn.1000-0887.2011.12.004

Citation:

PDF( 2608 KB)

Two-Scale Finite Element Method for Piezoelectric Problem in Periodic Structure

doi: 10.3879/j.issn.1000-0887.2011.12.004

College of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, P. R. China

Received Date: 2011-02-21
Rev Recd Date: 2011-09-28
Publish Date: 2011-12-15

Abstract

Abstract

The prediction of the mechanical and electric properties of piezoelectric fibre composites had become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element method for solutions of the electric potential and the displacement for composite material in periodic structure under coupled piezoelectricity were derived. The coupled twoscale relation of the electric potential and the displacement was set up. And some finite element approximate estimates and numerical examples which show the effectiveness of the method are presented.
- two-scale method,
- piezoelectricity, periodic structure,
- finite element method,
- homogenization constant,

FullText(HTML)

References(19)

References

[1]	Telega J J. Piezoelectricity and homogenization: application to biomechanics[C]Maugin G A. Continuum Models and Discrete Systems, Vol 2. London: Longman,1991: 220-229.
[2]	Smith W A, Auld B A. Modeling 1-3 composite piezoelectrics:thickness-mode oscillations[J]. IEEE Trans Ultrason Ferr, 1991, 38(1): 40-47. doi: 10.1109/58.67833
[3]	Odegard G M. Constitutive modeling of piezoelectric polymer composites[J]. Acta Materialia, 2004, 52(18): 5315-5330. doi: 10.1016/j.actamat.2004.07.037
[4]	Gomez Alvarez-Arenas T E, Espinosa F M. Highly coupled dielectric behavior of porous ceramics embedding a polymer[J]. Appl Phys Lett, 1996, 68(2): 263-265. doi: 10.1063/1.115657
[5]	Gomez Alvarez-Arenas T E, Freijo F M. New constitutive relations for piezoelectric composites and porous piezoelectric ceramics[J]. J Acoust Soc Amer, 1996, 100(5): 3104-3114. doi: 10.1121/1.417122
[6]	Gomez Alvarez-Arenas T E, Espinosa F M. Characterization of porous piezoelectric ceramics: the length expander case[J]. J Acoust Soc Amer, 1997, 102(6): 3507-3515. doi: 10.1121/1.420143
[7]	Zheng Q S, Du D X. An explicit and universally applicable estimate for the effective properties of multiphase composites which accounts for inclusion distribution[J]. Journal of the Mechanics and Physics of Solids, 2001, 49(11): 2765-2788. doi: 10.1016/S0022-5096(01)00078-3
[8]	Ramesh R, Kara H, Bowen C R. Finite element modelling of dense and porous piezoceramic disc hydrophones[J]. Ultrasonics, 2005, 43(3): 173-181. doi: 10.1016/j.ultras.2004.05.001
[9]	FANG Dai-ning, MAO Guan-zhong, LI Fa-xin, FENG Xue, WANG Yong- ping, LI Chang-qing, JIANG Bing, LIU Bin, BING Qi-da. Experimental study on electro-magneto-mechanical coupling behavior of smart materials[J]. Journal of Mechanical Strength, 2005, 27(2): 217-226.
[10]	Yamaguchi M, Hashimoto K Y, Makita H. Finite element method analysis of dispersion characteristics for 1-3 type piezoelectric composite[C]Proc IEEE Ultrasonic Symposium, 1987: 657-661.
[11]	Ballandras S, Pierre G, Blanc F A. Periodic finite element formulation for the design of 2-2 composite transducers[C]Proc IEEE Ultrasonic Symposium, 1999: 957-960.
[12]	Qi W K, Cao W W. Finite element analysis of periocdic and random 2-2 piezocomposite transducers with finite dimensions[J]. IEEE Trans UFFC, 1997, 44: 1168-1171. doi: 10.1109/58.655642
[13]	Cui J Z, Shin T M, Wang Y L. The two-scale analysis method for the bodies with small periodic configurations[J]. Struct Ens Mech, 1999,7(6): 601-614.
[14]	Cao L Q. Multiscale asymptotic expansion and finite element methods for the mixed boundary value problems of second order elliptic equation in perforated domains[J]. Numer Math, 2006, 103(1): 11-45. doi: 10.1007/s00211-005-0668-4
[15]	Yang J S, Batra R C. Conservation laws in linear piezoelectricity[J]. Engineering Fracture Mech, 2005, 51(6):1041-1047.
[16]	Gautschi G. Piezoelectric Sensorics[M]. Berlin: Springer, 2002: 50.
[17]	Zhang F X. Modern Piezoelectricity[M]. Beijing: Science Press, 2001: 20.
[18]	Oleinik O A, Shamaev A S, Yosifian G A. Mathematical Problems in Elasticity and Homogenization[M]. Amsterdan: North-Holland, 1992: 96.
[19]	Feng Y P, Cui J Z. Multi-scale FE computation for the structure of composite materials with small period configuration under condition of coupled thermoelasticity[J]. Acta Mechanica Sinica, 2004, 20(1): 54-63.