Abstract
In the present paper the method of shape control of structures is applied to the following problem. Given a three-dimensional elastic body with sources of self-stress acting in the background, how do we have to distribute these sources within a subdomain of the structure in order to control the deformation of this subdomain. In the first part we present a solution for given disturbances, such as body forces and surface tractions, for which an open-loop strategy is sufficient. In the second part we assume the time variation of the disturbances unknown; hence, a closed-loop strategy has to be applied. We design distributed sensors and actuators to be collocated to each other. This allows us to use a simple PD controller to ensure the stability of the closed-loop system. In the third part we discuss the application of discretely acting actuators and sensors to approximate the distributed ones. This is especially important in practical applications. Finally, numerical results for a cantilever beam are presented. Results are excellent with respect to the goal of controlling the deformation within a subsection of the beam. Copyright © 2005 John Wiley & Sons, Ltd.
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