Keywords: piezoelectric, smart beam, linear analysis, layer-by-layer.

Technological developments in aerospace engineering have created new avenues of research, particularly in the areas of health monitoring, vibration and shape control of flexible structures using the concept of smart or intelligent structures. Under external loading, conventional structures deform in a passive manner with no control over the configuration of the deformed state. Whereas in smart structures, the structural deformation is continuously monitored and controlled (using distributed sensors and actuators) to achieve the desired configuration of the deformed state of the structure. In principle, distributed sensing and actuation can be implemented by embedding piezoelectric material in the structure. Essentially three types of physical behaviour exist in a piezoelectric crystal. These are thermo-elasticity, piezoelectricity and pyroelectricity.

A survey of the literature on smart structures indicates that there are two distinct lines of research, namely:

1. One dealing with the fundamental formulation of the constitutive and equilibrium laws applicable to structures subjected to thermal, electrical and mechanical loading under the title of electro-thermo-elasticity.
2. Studies related to application of smart materials for static and dynamic control of structures which usually assume the electro-elastic laws either in the decoupled or coupled form.

In general it has been observed that the key difference between actuation and sensing of a smart beam has not been clearly brought out in the literature, particularly with regard to distribution of interfacial shear stress between the piezo layer and the host structure.

The objectives of the present study are:

1. Formulation of the governing equations for coupled electro-thermo-elasticity for a continuum model.
2. Analysis of the interfacial stress distribution in a smart beam under actuation and sensing using layer-by-layer finite element model.
3. Analysis of a piezo beam developing a step like transverse deformation, under an external electrical loading along the longitudinal direction.

The important observations of the study can be summarised as:

1. It is shown that layer-by-layer finite element modeling effectively captures the continuity of shear stress across the interface between piezo-layers and the metallic material.
2. The nature of shear stress distribution across the interface between the piezo material and the host structure exhibits different trends for sensing and actuation cases.
3. It is shown that a piezo beam under an electric field along the span shows an interesting step like transverse deformation. It is envisaged that this concept can be used to develop a switch in a MEMS device.

In brief a general electro-thermo-elastic formulation has been developed for the analysis of smart structures from the laws of conservation. Based on this formulation a layer-by-layer finite element model has been developed using variational principle. The present study clearly shows that the layer-by-layer finite element modeling effectively captures the continuity of shear stress across the interface between piezo-layers and the metallic host material. The key difference between actuation and sensing of a smart beam, having single and multiple piezo patches, has been identified particularly with regard to the variation of shear stress along the span at interfaces between piezo patch and the core. The influence of electric field along the span of a piezo cantilever beam has been studied.

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