Free Access
Issue
ESAIM: COCV
Volume 15, Number 1, January-March 2009
Page(s) 149 - 172
DOI https://doi.org/10.1051/cocv:2008022
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]
  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.
  3. P.G. Ciarlet, Mathematical Elasticity, Vol. II: Theory of Plates, Studies in Mathematics and its Applications 27. North-Holland Publishing Co., Amsterdam (1997).
  4. P.G. Ciarlet, Mathematical Elasticity. Vol. III: Theory of Shells, Studies in Mathematics and its Applications 29. North-Holland Publishing Co., Amsterdam (2000).
  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.
  6. P.G. Ciarlet and P. Destuynder, A justification of the two-dimensional linear plate model. J. Mécanique 18 (1979) 315–344.
  7. C. Collard and B. Miara, Two-dimensional models for geometrically nonlinear thin piezoelectric shells. Asymptotic Anal. 31 (2002) 113–151.
  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. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  9. G. Duvaut and J.-L. Lions, Inequalities in Mechanics and Physics, Grundlehren der mathematischen Wissenschaften 219. Springer-Verlag, Berlin (1976).
  10. I. Ekeland and R. Temam, Convex Analysis and Variational Problems, Classics in Applied Mathematics 28. SIAM, Philadelphia (1999).
  11. I. Figueiredo and C. Leal, A piezoelectric anisotropic plate model. Asymptotic Anal. 44 (2005) 327–346.
  12. I. Figueiredo and C. Leal, A generalized piezoelectric Bernoulli-Navier anisotropic rod model. J. Elasticity 85 (2006) 85–106. [CrossRef] [MathSciNet]
  13. R. Glowinski, Numerical Methods for Nonlinear Variational Inequalities. Springer-Verlag, New York (1984).
  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).
  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]
  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]
  17. T. Ikeda, Fundamentals of Piezoelectricity. Oxford University Press (1990).
  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).
  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]
  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.
  21. J.-L. Lions, Perturbations singulières dans les problèmes aux limites et en contrôle optimal, Lecture Notes in Mathematics 323. Springer-Verlag, Berlin (1973).
  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. [CrossRef]
  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]
  24. B. Miara, Justification of the asymptotic analysis of elastic plates. I. The linear case. Asymptotic Anal. 9 (1994) 47–60. [MathSciNet]
  25. M. Rahmoune, A. Benjeddou and R. Ohayon, New thin piezoelectric plate models. J. Int. Mat. Sys. Struct. 9 (1998) 1017–1029. [CrossRef]
  26. A. Raoult and A. Sène, Modelling of piezoelectric plates including magnetic effects. Asymptotic Anal. 34 (2003) 1–40.
  27. N. Sabu, Vibrations of thin piezoelectric flexural shells: Two-dimensional approximation. J. Elast. 68 (2002) 145–165. [CrossRef]
  28. A. Sene, Modelling of piezoelectric static thin plates. Asymptotic Anal. 25 (2001) 1–20.
  29. R.C. Smith, Smart Material Systems: Model Development, Frontiers in Applied Mathematics 32. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2005).
  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]
  31. M. Sofonea and El-H. Essoufi, Quasistatic frictional contact of a viscoelastic piezoelectric body. Adv. Math. Sci. Appl. 14 (2004) 613–631. [MathSciNet]
  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.
  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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.