Modelization and numerical approximation of piezoelectric thin shells Part I: The continuous problems

Computer Methods in Applied Mechanics and Engineering

Volumn 192, Issue 37-38, 2003, Pages 4003-4043

  Bernadou, Michel ^a,b   Haenel, Christophe ^a,b  

^a PÔLE UNIVERSITAIRE LÉONARD DE VINCI   (France)

^b INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE ELEMENT METHOD; PIEZOELECTRICITY;

THIN SHELLS;

SHELLS (STRUCTURES);

PIEZOELECTRICITY;

EID: 0141573327     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(03)00364-5     Document Type: Article

References (31)

1. Ikeda T. Fundamental of Piezoelectricity 1990 Oxford Univeristy Press Oxford
2. Rogers C.A. Rogers R.C. Recent Advances in Adaptive and Sensory Materials and their Applications 1992 Technomic Publishing Co. Lancaster
3. Tzou H.S. Piezoelectric Shells: Distributed Sensing and Control of Continua 1993 Kluwer Academic Publishers Dordrecht, The Netherlands
4. Green A.E. Zerna W. Theoretical Elasticity 2nd ed. 1968 Oxford University Press Oxford
5. Eringen A.C. Maugin G. Electrodynamics of Continua, Volume I: Foundations and Solid Media 1990 Springer-Verlag New York
6. Necas J. Les Méthodes Directes en Théorie des Equations Elliptiques 1967 Masson Paris
7. Brézis H. Analyse Fonctionnelle 1992 Masson Paris
8. Ciarlet P.G. Mathematical Elasticity, Volume III: Theory of Shells 2000 North-Holland Amsterdam
9. Adams R.A. Sobolev Spaces 1975 Academic Press New York
10. C. Haenel, Modélisation, Analyse et Simulation Numérique de Coques Piézoélectriques, Thèse de l'Université Pierre et Marie Curie, Paris, France, 2000
11. Ekeland I. Temam R. Analyse Convexe et Problèmes Variationnels 1974 Dunod-Gauthier-Villars Paris
12. Kirchhoff G. Vorlesungen über Mathematische Physik 1876 Mechanik Leipzig
13. Love A.E.H. The Mathematical Theory of Elasticity 1934 Cambridge University Press Cambridge
14. Koiter W.T. A consistent first approximation in the general theory of thin elastic shells Proceedings of Symposium on Theory of Thin Elastic Shells Delft, August 1959 1959 12-33 North-Holland Amsterdam
15. Koiter W.T. On the nonlinear theory of thin elastic shells Proc. Kon. Nederl. Akad. Wetensch. B69 1966 1-54
16. Koiter W.T. On the foundations of the linear theory of thin elastic shells Proc. Kon. Nederl. Akad. Wetensch. B73 1970 169-195
17. Cosserat E. Cosserat F. Théorie des Corps Déformables 1909 Hermann Paris
18. Naghdi P.M. Foundations of elastic shell theory Progress in Solid Mechanics vol. 4 1963 1-90 North-Holland Amsterdam
19. Naghdi P.M. The theory of shells and plates Handbuch der Physik vol. VI a.2 1972 425-640 Springer-Verlag Berlin
20. Le Khan'Chau N.N. The theory of piezoelectric shells Prikl. Matem. Mekhan. USSR 50 1 1986 98-105
21. Rogacheva N.N. The Theory of Piezoelectric Shells and Plates 1993 CRC Press Boca Raton, FL
22. Dökmeci M.C. On the higher order theories of piezoelectric crystal surfaces J. Math. Phys. 15 12 1974 2248-2252
23. A. Sène, Modélisation Asymptotique de Plaques: Contrôlabilité Exacte Frontière, Piézoélectricité, Thèse d'Université, Grenoble I, 1999
24. M. Bernadou, M.C. Delfour, Intrinsic models of piezoelectric shells, in: Proceedings of ECCOMAS 2000, Barcelona, 11-14 Septembre 2000, CD-Rom, 21p
25. Collard C. Miara B. Modeling of geometrically nonlinear thin piezoelectric shells Ohayon R. Bernadou M. Tenth International Conference on Adaptive Structures and Technologies 2000 516-523 Technomic Publishing Co Lancaster
26. Bernadou M. Finite Element Methods for Thin Shell Problems 1996 Wiley Chichester
27. Bernadou M. Ciarlet P.G. Miara B. Existence theorems for two-dimensional linear shell theories J. Elastic. 34 1994 111-138
28. Ciarlet P.G. The Finite Element Method for Elliptic Problems 1978 North-Holland Amsterdam
29. Bernadou M. Haenel C. Modelization and numerical approximation of piezoelectric thin shells, Part II: approximation by finite element methods and numerical experiments Comput. Methods Appl. Mech. Engrg. 192 37-38 2003 4045-4073
30. Kraus H. Thin Elastic Shells 1967 Wiley and Sons New York
31. Dym C.L. Introduction to the Theory of Shells 1974 Pergamon Press Oxford