Active Shape Control of Smart Structures

Intelligent materials have become a focal point for ongoing research and development due to the distinct advantages offered by these materials over conventional materials. These advantages have resulted in the application of smart materials in many areas including health monitoring, vibration control, shape control, noise suppression and damage mitigation, to name a few. This research is concerned with the use of intelligent materials, in particular both piezoelectric and shape memory alloy materials, as actuators to achieve active structural shape control. 

Exact analytical solutions have been formulated for optimal voltages for the shape control of linear piezoelectric composite laminated cantilever beams, considering shear deformation and the contribution of stiffness of the actuators. The formulation incorporates upper and lower bounds on the voltages as these voltages are constrained due to cost and material constraints. Several shape control problems of laminated beams were solved which include symmetric and asymmetric beams with two sided and one sided piezoelectric patch actuator configurations.

Figure 1: Shape control of laminated beam with piezoelectric patch actuators.


Figure 2: Shape control using embedded SMA wire actuators.ol of laminated beam with piezoelectric patch actuators.

All the studies reported so far on the shape control of piezoelectric beams were based on the linear behavior of piezoelectric materials. The nonlinear behavior of piezoelectric materials is significant for high electric fields and hence a model incorporating nonlinear behavior is required to exploit the actuation capacity in the nonlinear range. The shape control of composite laminated beams with nonlinear piezoelectric patch actuators was thus investigated. The governing electromechanical coupled equations for nonlinear material behavior were developed for a general three dimensional structural element using Gibbs free energy formulation. Nonlinearity was accounted for in the analysis by incorporating enough number of nonlinear terms in the Gibbs free energy expression. A finite element model was developed for the beam with piezoelectric actuators using a modified bilinear four node quadratic element. The expression for the actuation voltages required for shape control was then obtained by minimizing an error function, which is a measure of the area between the achieved and desired shape. The final system of coupled equations was solved by an iterative finite element procedure. Numerical results were obtained for several piezoelectric patch configurations on beams with various boundary conditions. Results show the significance of nonlinear effects in the shape control of beams with piezoelectric actuators. 
Among the intelligent materials used for sensing and actuation, shape memory alloys (SMA) have received much attention due to their distinctive properties. Its one- or two-way shape memory effect can generate significant force by temperature change. In view of the large actuation force that SMA can generate, the use of embedded SMA wires as actuators for the shape control of beams was investigated. In the design of SMA wires embedded in a host structure, it is first necessary to derive a mechanics interaction model between the host material and embedded SMA wire. Integral equations for the displacement distribution along the interface of SMA wire and host structure were derived, and solutions were developed using the Kelvin elastic solution and the distribution of shear and normal stresses along the interface of SMA wire and host structure. The phase transformation of SMA material is divided into five consecutive phases and detailed description of the behavior of the embedded SMA wire in every phase was discussed. Validity of this model was investigated by comparing the results from the present model with those obtained by the finite element analysis. Two types of problems in shape control, namely to determine (1) the deformation given the configuration of SMA actuators and (2) the configuration of the SMA actuators given the desired deformation, were investigated using the proposed computational schemes.