The application of static shape control was investigated in this thesis particularly for a composite plate configuration using piezoelectric actuators. A new electro-mechanically coupled mathematical model was developed for the analysis and is based on a third order displacement field coupled with a layerwise electric potential concept. This formulation, TODL, is then implemented into a finite element program. The mathematical model represents an improvement over existing formulations used to model intelligent structures using piezoelectric materials as actuators and sensors. The reason is TODL does not only account for the electro-mechanical coupling within the adaptive material, it also accounts for the full structural coupling in the entire structure due to the piezoelectric material being attached to the host structure. The other significant improvement of TODL is that it is applicable to structures which are relatively thick whereas existing models are based on thin beam / plate theories. Consequently, transverse shearing effects are automatically accounted for in TODL and unlike first order shear deformation theories, shear correction factors are not required. The second major section of this thesis uses the TODL formulation in static shape control. Shape control is defined here as the determination of shape control parameters, including actuation voltage and actuator orientation configuration, such that the structure that is activated using these parameters will conform as close as possible to the desired shape. Several shape control strategies and consequently algorithms were developed here. Initial investigations in shape control has revealed many interesting issues which have been used in later investigations to improve shape controllability and also led to the development of improved algorithms. For instance, the use of discrete actuator patches has led to greater shape controllability and the use of slopes and curvatures as additional control criteria have resulted in significant reduction in internal stresses. The significance of optimizing actuator orientation and its relation to piezoelectric anisotropy in improving shape controllability has also been presented. Thus the major facets of shape control has been brought together and the algorithms developed here represent a comprehensive strategy to perform static shape control.
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