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The main objective of this article is to present an overview of the modelling that has been proposed by various workers in the field of smart or intelligent structures. Before the main discussion on the various models, some background information will be presented in relation to intelligent structures and the types of adaptive materials that are available. Although there are several categories of materials that can be implemented in intelligent structures, this article will focus on models that use piezoelectric materials as sensors and/or actuators (S/A). The modelling of the intelligent structures can be categorised in terms of the structural configuration (e.g., rod composites, fibre composites, monolithic structures, etc.) and also according to the type of modelling whether by finite element modelling or by analytical exact solutions. Models in this field of work had incorporated concepts from different background including three-dimensional linear elastic theory and dielectric theory to give rise to the linear piezoelectric model. Rules of Mixture and methods for calculating effective properties of fibre composites were extended to include piezoelectric fibre composite models. Classical Laminated Plate Theory was also adopted in laminated composite models where some laminae were piezoelectric materials. Exact solutions were applied to simple models and illustrated the potential of using piezoelectrics. Finite element techniques were used for more complicated problems that included complex geometries, nonlinear behaviour and dynamic control of the structure. The difference between induced strain and actuation strain is usually not addressed when using FE techniques, instead the piezoelectric strain can be regarded as an equivalent external force/moment or incorporated into the strain energy. In regard to control algorithms, the most common form applied by investigators in this field seems to be the negative velocity feedback control with single input and single output and some included linear quadratic control. More advanced control algorithms such as using multiple input and multiple output or even neural networks are less established.

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A theoretical formulation to model composite smart structures in which the piezoelectric actuators and sensors are treated as constituent parts of the entire structural system is presented here. The mathematical model is based on a high order displacement field coupled with a layerwise linear electric potential. This model is developed for a composite beam structure using Hamilton's variational principle and is facilitated by the finite element (FE) formulation. The generic element implemented in the FE analysis is a two-noded Hermitian - 2(n+1) layerwise noded element for an n-layered beam. The variational principle led to a derivation that could include dynamic analysis but the present work will only focus on the static beam structure. This formulation in general will enable the modeling of vibration and shape control applications. Comparison of numerical results from this formulation with previous works, including three configurations - non-piezoelectric, actuator and sensor configurations, showed a high to a reasonable degree of correlation. The effects of varying actuator locations and orientations on the deflection and curvature of the beam were also studied.

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