An incremental Lagrangian formulation to the analysis of piezoelectric bodies subjected to geometric non-linearities

International Journal for Numerical Methods in Engineering

Volumn 59, Issue 7, 2004, Pages 963-987

  Cardoso, Eduardo Lenz ^a   Fonseca, Jun Sérgio Ono ^a  

^a FEDERAL UNIVERSITY OF RIO GRANDE DO SUL   (Brazil)

Author keywords

Arc length; Finite elements; Large deformations; Non linearities; Piezoelectricity

Indexed keywords

APPROXIMATION THEORY; ELECTRIC FIELDS; FINITE ELEMENT METHOD; LAGRANGE MULTIPLIERS; MATHEMATICAL MODELS;

ELECTRIC DISPLACEMENT; EULERIAN MEASURES; NEWTON-RAPHSON METHODS;

PIEZOELECTRIC MATERIALS;

PIEZOELECTRICITY;

EID: 1442264777     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.901     Document Type: Article

References (22)

1. Ikeda T. Fundamentals of Piezoelectricity. Oxford University Press: Oxford, 1996.
2. Silva ECN, Kikuchi N. Design of piezoelectric transducers using topology optimization. Smart Materials and Structures 1999; 8:350-364.
3. Pedersen CBW, Buhl T, Sigmund O. Topology synthesis of large displacement compliant mechanisms. International Journal for Numerical Methods in Engineering 2001; 50:2683-2705.
4. Albareda A, Gonnard P, Perrin V, Briot R, Guyomar D. Characterization of the mechanical nonlinear behaviour of piezoelectric ceramics. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 2000; 47(4):844-853.
5. Mulling J, Usher B, Dessent B, Palmer J, Franzon P, Grant E, Kingon A. Load characterization of high displacement piezoelectric actuators with various end conditions. Sensors and Actuators 2001; A94:19-24.
6. Yang JS. A nonlinear theory for thin piezoelectric plates in moderately large extensional deformations. Mechanics Research Communications 1999; 26(4):421-426.
7. Wang Q. On buckling of column structures with a pair of piezoelectric layers. Engineering Structures 2002; 24:199-205.
8. Tiersten HF. Analysis of nonlinear resonance in thickness-shear and trapped-energy resonators. Journal of the Acoustical Society of America 1976; 59(4):866-878.
9. Zhou Y-H, Tzou HS. Active control of nonlinear piezoelectric circular shallow spherical shells. International Journal of Solid and Structures 2000; 37:1663-1677.
10. Tiersten HF. Hamilton's principle for linear piezoelectric media. Proceedings of the IEEE, August 1967.
11. Kleiber M. Incremental Finite Element Modeling in Non-Linear Solid Mechanics. Ellis Horwood: Chichester, 1989.
12. Pai PF, Palazoto AN, Greer Jr. JM. Polar decomposition and appropriate strains and stresses for nonlinear structural analysis. Computers and Structures 1998; 66(6):823-840.
13. Tiersten HF. On the accurate description of piezoelectric resonators subject to biasing deformations. International Journal of Engineering Science 1995; 33(15):2239-2259.
14. Zieliński AP, Frey F. On linearization in non-linear structural finite element analysis. Computers and Structures 2001; 79:825-838.
15. Bathe KY. Finite Element Procedures. Springer: Berlin, 1996.
16. Atkin RJ, Fox N. An Introduction to the Theory of Elasticity. Longman Mathematical Texts: New York, 1980.
17. Wangsness RK. Electromagnetic Fields. Wiley: New York, 1979.
18. Naillon M, Coursant RH, Besnier F. Analysis of piezoelectric structures by a finite element method. Acta Electronica 1983; 25:341-362.
19. Crisfiled MA. Non-linear Finite Element Analysis of Solids and Structures. Volume 1: Essentials. Wiley: Chichester, 1997.
20. Fafard M, Massicote B. Geometrical interpretation of the arc-length method. Computers and Structures 1993; 46(4):603-615.
21. Hang Q, Daining F, Zhenhan Y. FEM analysis of electro-mechanical coupling effects of piezoelectric materials. Computational Material Science 1997; 8:283-290.
22. Lee SL, Manuel FS, Rossow EC. Large deflection and stability of elastic frames. ASCE Journal of Engineering Mechanics 1968; 94:521-533.