Free Access
Volume 15, Number 1, January-March 2009
Page(s) 149 - 172
Published online 23 January 2009
  1. M. Bernadou and C. Haenel, Modelization and numerical approximation of piezoelectric thin shells. I. The continuous problems. Comput. Methods Appl. Mech. Engrg. 192 (2003) 4003–4043. [CrossRef] [MathSciNet] [Google Scholar]
  2. P. Bisegna, F. Lebon and F. Maceri, The unilateral frictional contact of a piezoelectric body with a rigid support, in Contact mechanics (Praia da Consolação, 2001), Solid Mech. Appl., Kluwer Acad. Publ., Dordrecht (2002) 347–354. [Google Scholar]
  3. P.G. Ciarlet, Mathematical Elasticity, Vol. II: Theory of Plates, Studies in Mathematics and its Applications 27. North-Holland Publishing Co., Amsterdam (1997). [Google Scholar]
  4. P.G. Ciarlet, Mathematical Elasticity. Vol. III: Theory of Shells, Studies in Mathematics and its Applications 29. North-Holland Publishing Co., Amsterdam (2000). [Google Scholar]
  5. P.G. Ciarlet and P. Destuynder, Une justification d'un modèle non linéaire en théorie des plaques. C. R. Acad. Sci. Paris Sér. A-B 287 (1978) A33–A36. [Google Scholar]
  6. P.G. Ciarlet and P. Destuynder, A justification of the two-dimensional linear plate model. J. Mécanique 18 (1979) 315–344. [Google Scholar]
  7. C. Collard and B. Miara, Two-dimensional models for geometrically nonlinear thin piezoelectric shells. Asymptotic Anal. 31 (2002) 113–151. [Google Scholar]
  8. L. Costa, I. Figueiredo, R. Leal, P. Oliveira and G. Stadler, Modeling and numerical study of actuator and sensor effects for a laminated piezoelectric plate. Comput. Struct. 85 (2007) 385–403. [CrossRef] [Google Scholar]
  9. G. Duvaut and J.-L. Lions, Inequalities in Mechanics and Physics, Grundlehren der mathematischen Wissenschaften 219. Springer-Verlag, Berlin (1976). [Google Scholar]
  10. I. Ekeland and R. Temam, Convex Analysis and Variational Problems, Classics in Applied Mathematics 28. SIAM, Philadelphia (1999). [Google Scholar]
  11. I. Figueiredo and C. Leal, A piezoelectric anisotropic plate model. Asymptotic Anal. 44 (2005) 327–346. [Google Scholar]
  12. I. Figueiredo and C. Leal, A generalized piezoelectric Bernoulli-Navier anisotropic rod model. J. Elasticity 85 (2006) 85–106. [CrossRef] [MathSciNet] [Google Scholar]
  13. R. Glowinski, Numerical Methods for Nonlinear Variational Inequalities. Springer-Verlag, New York (1984). [Google Scholar]
  14. J. Haslinger, M. Miettinen and P. Panagiotopoulos, Finite Element Method for Hemivariational Inequalities, Nonconvex Optimization and its Applications 35. Kluwer Academic Publishers, Dordrecht (1999). [Google Scholar]
  15. S. Hüeber, A. Matei and B.I. Wohlmuth, A mixed variational formulation and an optimal a priori error estimate for a frictional contact problem in elasto-piezoelectricity. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 48 (2005) 209–232. [MathSciNet] [Google Scholar]
  16. S. Hüeber, G. Stadler and B. Wohlmuth, A primal-dual active set algorithm for three-dimensional contact problems with Coulomb friction. SIAM J. Sci. Comp. 30 (2008) 572–596. [CrossRef] [Google Scholar]
  17. T. Ikeda, Fundamentals of Piezoelectricity. Oxford University Press (1990). [Google Scholar]
  18. N. Kikuchi and J.T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM Studies in Applied Mathematics 8. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (1988). [Google Scholar]
  19. S. Klinkel and W. Wagner, A geometrically non-linear piezoelectric solid shell element based on a mixed multi-field variational formulation. Int. J. Numer. Meth. Engng. 65 (2005) 349–382. [CrossRef] [Google Scholar]
  20. A. Léger and B. Miara, Mathematical justification of the obstacle problem in the case of a shallow shell. J. Elasticity 9 (2008) 241–257. [Google Scholar]
  21. J.-L. Lions, Perturbations singulières dans les problèmes aux limites et en contrôle optimal, Lecture Notes in Mathematics 323. Springer-Verlag, Berlin (1973). [Google Scholar]
  22. F. Maceri and P. Bisegna, The unilateral frictionless contact of a piezoelectric body with a rigid support. Math. Comput. Model. 28 (1998) 19–28. [Google Scholar]
  23. G.A. Maugin and D. Attou, An asymptotic theory of thin piezoelectric plates. Quart. J. Mech. Appl. Math. 43 (1990) 347–362. [CrossRef] [MathSciNet] [Google Scholar]
  24. B. Miara, Justification of the asymptotic analysis of elastic plates. I. The linear case. Asymptotic Anal. 9 (1994) 47–60. [MathSciNet] [Google Scholar]
  25. M. Rahmoune, A. Benjeddou and R. Ohayon, New thin piezoelectric plate models. J. Int. Mat. Sys. Struct. 9 (1998) 1017–1029. [CrossRef] [Google Scholar]
  26. A. Raoult and A. Sène, Modelling of piezoelectric plates including magnetic effects. Asymptotic Anal. 34 (2003) 1–40. [Google Scholar]
  27. N. Sabu, Vibrations of thin piezoelectric flexural shells: Two-dimensional approximation. J. Elast. 68 (2002) 145–165. [CrossRef] [Google Scholar]
  28. A. Sene, Modelling of piezoelectric static thin plates. Asymptotic Anal. 25 (2001) 1–20. [Google Scholar]
  29. R.C. Smith, Smart Material Systems: Model Development, Frontiers in Applied Mathematics 32. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2005). [Google Scholar]
  30. M. Sofonea and El-H. Essoufi, A piezoelectric contact problem with slip dependent coefficient of friction. Math. Model. Anal. 9 (2004) 229–242. [MathSciNet] [Google Scholar]
  31. M. Sofonea and El-H. Essoufi, Quasistatic frictional contact of a viscoelastic piezoelectric body. Adv. Math. Sci. Appl. 14 (2004) 613–631. [MathSciNet] [Google Scholar]
  32. L. Trabucho and J.M. Viaño, Mathematical modelling of rods, in Handbook of Numerical Analysis IV, P.G. Ciarlet and J.-L. Lions Eds., Elsevier, Amsterdam, North-Holland (1996) 487–974. [Google Scholar]
  33. T. Weller and C. Licht, Analyse asymptotique de plaques minces linéairement piézoélectriques. C. R. Math. Acad. Sci. Paris 335 (2002) 309–314. [CrossRef] [MathSciNet] [Google Scholar]

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