3D symplectic expansion for piezoelectric media

International Journal for Numerical Methods in Engineering

Volumn 74, Issue 12, 2008, Pages 1848-1871

  Xu, Xin Sheng ^a   Leung, Andrew Y T ^b   Gu, Qian ^a   Yang, Hao ^b   Zheng, Jian Jun ^b  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

3D symplectic expansion; Hamiltonian system; Piezoelectric media; Transversely isotropic

Indexed keywords

PIEZOELECTRIC MATERIALS; PIEZOELECTRICITY; THREE DIMENSIONAL;

ANALYTICAL METHODS; EIGEN-SOLUTIONS; EIGENVALUES (OF GRAPHS); GOVERNING EQUATIONS; HAMILTONIAN; LOCALIZED SOLUTIONS; NUMERICAL EXAMPLES; NUMERICAL SCHEMES; ORTHONORMALIZATION; PIEZOELECTRIC MEDIUM; SERIES EXPANSION; SYMPLECTIC; THREE DIMENSIONAL (3D) PROBLEMS; TRANSVERSELY ISOTROPIC PIEZOELECTRIC MEDIA;

NUMERICAL METHODS;

EID: 47249142049     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2238     Document Type: Article

References (33)

1. Lin QR, Liu ZX, Jin ZL. A close-form solution to simply supported piezoelectric beams under uniform exterior pressure. Applied Mathematics and Mechanics - English Edition 2000; 21(6): 681-690.
2. Zhang LN, Shi ZF. Analytical solution of a simply supported piezoelectric beam subjected to a uniformly distributed loading. Applied Mathematics and Mechanics - English Edition 2003; 24(10): 1215-1223.
3. Ding HJ, Jiang AM. Polynomial solutions to piezoelectric beatos (I) - several exact solutions. Applied Mathematics and Mechanics English Edition 2005; 26(9): 1107-1114.
4. Ding HJ, Jiang AM. Polynomial solutions to piezoelectric beams (II) - analytical solutions to typical problems. Applied Mathematics and Mechanics - English Edition 2005; 26(9): 1115-1120.
5. Zhou YG, Chen YM, Ding HJ. Analytical solutions to piezoelectric bimorphs based on improved FSDT beam model. Smart Structures and Systems 2005; 1(3): 309-324.
6. Vel SS, Batra RC. Exact solution for rectangular sandwich plates with embedded piezoelectric shear actuators. AIAA Journal 2001; 39(7): 1363-1373.
7. Wu LH, Jiang ZQ, Feng WJ. An analytical solution for static analysis of a simply supported moderately thick sandwich piezoelectric plate. Structural Engineering and Mechanics 2004; 17(5): 641-654.
8. Ray MC, Sachade HM. Exact solutions for the functionally graded plates integrated with a layer of piezoelectric fiber-reinforced composite. Journal of Applied Mechanics - Transactions of the ASME 2006; 73(4): 622-632.
9. Kapuria S, Sengupta S, Dumir C. Three-dimensional solution for simply-supported piezoelectric cylindrical shell for axisymmetric load. Computer Methods in Applied Mechanics and Engineering 1997; 140(1-2): 139-155.
10. Li HY, Sun Y, Liu ZX. Three-dimensional analytical solutions for multilayered cylindrical shells with embedded piezoelectric shear actuators. Advances in Engineering Plasticity and its Applications 2004; 274-276(Parts 1 and 2): 1125-1130.
11. D'Ottavio M, Ballhause D, Kroplin B, Carrera E. Closed-form solutions for the free-vibration problem of multilayered piezoelectric shells. Computers and Structures 2006; 84(22-23): 1506-1518.
12. Kapuria S, Dumir PC, Sengupta S. An exact axisymmetric solution for a simply supported piezoelectric cylindrical shell. Archive of Applied Mechanics 1997; 67(4): 260-273.
13. Wang HM, Ding HJ, Chen YM. Dynamic solution of a multilayered orthotropic piezoelectric hollow cylinder for axisymmetric plane strain problems. International Journal of Solids and Structures 2005; 42(1): 85-102.
14. Rajapakse RKND, Chen Y, Senjuntichai T. Electroelastic field of a piezoelectric annular finite cylinder. International Journal of Solids and Structures 2005; 42(11-12): 3487-3508.
15. Hou PF, Wang HM, Ding HJ. Analytical solution for the axisymmetric plane strain electroelastic dynamics of a special non-homogeneous piezoelectric hollow cylinder. International Journal of Engineering Science 2003; 41(16): 1849-1868.
16. Lian GX, Li MX. Studying on the symmetric extensional modes in a piezoelectric cylinder. Progress in Natural Science 2001; 11: S27-S30.
17. Zhang TT, Shi ZF. Elastic solutions of graded piezoelectric hollow cylinders. Environmental Ecology and Technology of Concrete 2006; 302-303: 658-668.
18. Lu P, Lee HP, Lu C. An exact solution for functionally graded piezoelectric laminates in cylindrical bending. International Journal of Engineering Science 2005; 47(3): 437-458.
19. Chen WQ, Lee KY. Exact solution of angle-ply piezoelectric laminates in cylindrical bending with interfacial imperfections. Composite Structures 2004; 65(3-4): 329-337.
20. Tarn JQ. Exact solutions of a piezoelectric circular tube or bar under extension, torsion, pressuring, shearing, uniform electric loading and temperature change. Proceedings of the Royal Society of London, Series A - Mathematical, Physical and Engineering Sciences 2002; 458(2026): 2349-2367.
21. Tarn JQ. Exact solutions for electroelastic analysis of generalized plane strain and torsion of piezoelectric cylinders. Chinese Journal of Mechanics - Series A 2001; 17(3): 149-156.
22. Ding HJ, Guo FL, Hou PF. A general solution for piezothermoelasticity of transversely isotropic piezoelectric materials and its applications. International Journal of Engineering Science 2000; 38(13): 1415-1440.
23. Koc B, Cagatay S, Uchino K. A piezoelectric motor using two orthogonal bending modes of a hollow cylinder. IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 2002; 49(4): 495-500.
24. Vidoli S, Batra RC. Coupled extensional and torsional deformations of a piezoelectric cylinder. Smart Materials and Structures 2001; 10(2): 300-304.
25. Batra RC, Dell'Isola F, Vidoli S. A second-order solution of Saint-Venant's problem for a piezoelectric circular bar using Signorini's perturbation method. Journal of Elasticity 1998; 52(1): 75-90.
26. Bai H, Shah AH, Dong SB, Taciroglu E. End reflections in a layered piezoelectric circular cylinder. International Journal of Solids and Structures 2006; 43(20): 6309-6325.
27. Ding HJ, Liang JA. The fundamental solutions for transversely isotropic piezoelectricity and boundary element method. Computers and Structures 1999; 71(4): 447-455.
28. Galpchian PV. Boundary-value problem of antiplane deformation of compound transversally-isotropic piezoelectric cylinder with cross section in form of circular sector. International Journal of Applied Electromagnetics and Mechanics 2002; 16(1-2): 77-89.
29. Wang JG. State vector solutions for nonaxisymmetric problem of multilayered half space piezoelectric medium. Science in China Series A - Mathematics, Physics, Astronomy 1999; 42(12): 1323-1331.
30. Zhong WX. Duality System in Applied Mechanics and Optimal Control. Kluwer Academic Publishers: Dordrecht, 2004.
31. Leung AYT, Xu XS, Gu Q, Leung CTO, Zheng JJ. The boundary layer phenomena in two-dimensional transversely isotropic piezoelectric media by exact symplectic expansion. International Journal for Numerical Methods in Engineering 2007; 69: 2381-2408.
32. Dunn ML, Taya M. Electroelastic field concentrations in and around inhomogeneities in piezoelectric solids. Journal of Applied Mechanics 1994; 61: 474-475.
33. Ding HJ, Chen WQ. Three Dimensional Problems of Piezoelectricity. Nova Science Publishers: Huntington, New York, 2001.