Keywords: modelling, simulation, adaptive structures, piezoelectric composites.

Since the first experimental proof of electronic passive (shunted) and active vibration damping of optical bar-like structures using attached piezoelectric patches, a quarter of century ago [1], researches on adaptive structures have received much attention, as attested by the numerous reviews [2,3,4], bibliography [5], surveys [6,7,8] and assessments [9,]. Careful analysis of this literature indicates that piezoelectric materials are the most used as actuators and sensors. Hence, modelling and simulations of adaptive structures and composites with surface-bonded or embedded (integrated) piezoelectric patches or layers have received a lot of investigations in particular during the last decade. They were first based on engineering uncoupled analytical and numerical approaches that mimic the classical techniques used in elastic structures and composites [,4,7]. Then, rapidly, rigorous mathematical analyses and difficulties to reproduce some experimental tests have shown that these simplified methods are not sufficient and can even lead to erroneous results [2,3,9].

This contribution has then the objective to present and discuss current trends, during the last half decade, in modelling and simulation of adaptive structures and composites. For this, multi-physics theoretical formulations are first described for thermo-electro-mechanical media in the form of fundamental equations and associated advanced variational principles. Then, current research interests in analytical and numerical modelling of adaptive structures and composites are surveyed; focus is made on exact and closed-form analytical solutions, and on finite element numerical models. Common benchmarking and simulation practices are also discussed. Finally, some identified future directions for this continuously growing multidisciplinary research field are outlined.

From the current trends survey, it was noticed that:

• Exact solution developments have focused on beam and plate structural elements.
• Closed-form solutions for shear-mode piezoceramics were not yet developed for shells or with the combined state space-asymptotic technique method.
• Finite element (FE) developments are currently concentrated on ESL, HSDT, and plate models; all proposed FE have focused on the use of extension- mode piezoelectric materials; thus, no plate or shell FE developments have been proposed for the shear-mode ones. Also, multi-physics FE models are still limited to the thermo-electro-elasticity.
• The other numerical approaches have also concerned only extension-mode piezoelectric materials. Besides, no numerical developments have been made recently with the boundary element or meshless methods.

These remarks on the current trends can motivate new or further research on the highlighted presently active topics in modelling and simulation of adaptive structures and composites. Additional future research directions for this growing research filed are listed in the corresponding section.

1

Forward, R.L., "Electronic damping of vibrations in optical structures", Applied Optics, 18, 690-697, 1979. doi:10.1364/AO.18.000690

2

Saravanos, D.A., Heyliger, P.R., "Mechanics and computational models for laminated piezoelectric beams, plates and shells", Applied Mechanics Reviews, 52, 305-320, 1999. doi:10.1115/1.3098918

3

Gopinathan, S.V., Varadan, V.V., Varadan, V.K, "A review and critique of theories for piezoelectric laminates", Smart Materials and Structures, 9, 24-48, 2000. doi:10.1088/0964-1726/9/1/304

4

Tauchert, T.R., Ashida, F., Noda, N., Adali, S., Verijenko, V., "Developments in thermopiezoelectricity with relevance to smart composite structures", Composite Structures, 31-38, 2000. doi:10.1016/S0263-8223(99)00070-7

5

Mackerle, J., "Smart materials and structures: FEM and BEM simulations - a bibliography (1997-1999)", Finite Elements in Analysis and Design, 37, 71-83, 2001. doi:10.1016/S0168-874X(00)00018-4

6

Ahmadian, M., DeGuilio, A.P., "Recent advances in the use of piezoceramics for vibration suppression", Shock and Vibration Digest, 33, 15-22, 2001. doi:10.1177/058310240103300102

7

Benjeddou, A., "Advances in piezoelectric finite element modelling of adaptive structural elements: a survey", Computers and Structures, 76, 347-363, 2000. doi:10.1016/S0045-7949(99)00151-0

8

Benjeddou, A., "Advances in hybrid active-passive vibration and noise control via piezoelectric and viscoelastic constrained layer treatments, Journal of Vibration and Control, 7, 565-602, 2001. doi:10.1177/107754630100700406

9

Benjeddou, A., "Modelling of piezoelectric adaptive beam, plate and shell structures: some developments and results", in "Proceedings of the Sixth International Conference on Computational Structures Technology", Topping, B.H.V., Bittnar, Z., (Editors), Civil-Comp Press, Stirling, UK, 2002.

10

Benjeddou, A., "Piezoelectric and viscoelastic constrained layer-based vibration control: numerical developments and performance evaluation", in "Proceedings of ACTIVE 2002", Southampton, UK, 2002.

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