Coupled variational principles of piezoelectricity

International Journal of Engineering Science

Volumn 39, Issue 3, 2001, Pages 323-341

  He, Ji Huan ^a  

^a SHANGHAI UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; ELASTICITY; FINITE ELEMENT METHOD; INVERSE PROBLEMS; LAGRANGE MULTIPLIERS; PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

SEMI INVERSE METHOD; TRIAL FUNCTIONAL;

PIEZOELECTRICITY;

EID: 0035254769     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7225(00)00035-5     Document Type: Article

References (19)

1. Zhou S.A., Hsien R.K.T., Maugin G.A. Electric and elastic multipole defects in finite piezoelectric media. Int. J. Solids Struct. 22(12):1986;1411-1422.
2. Maugin G.A. The Mechanical Behavior of Electromagnetic Solid Continua. 1984;North-Holland, Amsterdam.
3. Maugin G.A. Continuum Mech. Electromagnetic Solids. 1991;Elsevier, Amsterdam.
4. G.L. Liu, A systematic approach to the search and transformation for variational principles in fluid mechanics with emphasis on inverse and hybrid problems, in: First International Symposium on Experimental and Computational Aerothermodynamics of Internal Flows, Beijing, 1990, pp. 128-135.
5. J.H. He, Modified Lagrange multiplier method and generalized variational principles in fluid mechanics, J. Shanghai University (English Edition), 2(2) (1997) 117-122. (Find the paper in the Internet: http//www.shu.edu.cn ).
6. Santilli R.M. Foundations of Theoretical Mechanics I: The Inverse Problem in Newtonian Mechanics. 1978;Springer, Berlin.
7. Santilli R.M. Foundations of Theoretical Mechanics II: Birkhoffian Generalization of Hamiltonian Mechanics. 1983;Springer, Berlin.
8. Tonti E. Variational Principles. 1968;Tamburini, Milano.
9. He J.H. Semi-inverse method of establishing generalized variational principles for fluid mechanics with emphasis on turbomachinery aerodynamics. Int. J. Turbo & Jet-Engines. 4(1):1997;23-28.
10. He J.H. A generalized variational principle for 3-D unsteady transonic rotational flow in rotor using Clebsch variables. Int. J. Turbo & Jet-Engines. 14(1):1997;17-22.
11. He J.H. A variational theory for one-dimensional unsteady compressible flow: an image plane approach. Appl. Math. Modell. 22:1998;395-403.
12. He J.H. A family of variational principles for compressible rotational blade-to-blade flow using semi-inverse method. Int. J. Turbo and Jet-Engines. 15(2):1998;95-100.
13. He J.H. Generalized Variational Principle for compressible S2-flow in mixed-flow turbomachinery using semi-inverse method. Int. J. Turbo & Jet-Engines. 15(2):1998;101-107.
14. J.H. He, Generalized Hellinger-Reissner principle, ASME J. Appl. Mech. (accepted).
15. Chien W.Z. Method of high-order Lagrange multiplier and generalized variational principles of elasticity with more general forms of functionals. Applied Math. & Mech. 4(2):1983;137-150.
16. Washizu K. Variational Methods in Elasticity and Plasticity. 1982;Pergamon Press, Oxford.
17. J.H. He, Variational crisis in elasticity and its removal, Shanghai J. Mech., 18 (4) (1997) 305-310 (in Chinese).
18. G.L. Liu, The variational crisis and generalized variational principles in elasticity, J. Shanghai University, 4 (6) (1998) 591-599 (Natural Science, in Chinese).
19. Felippa C. Parametrized multifield variational principles in elasticity. Comm. Appl. Num. Engr. 5:1989;79-99.