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CivilComp Proceedings
ISSN 17593433 CCP: 86
PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 6
Structural Displacement Tracking by Eigenstrain Actuation: Computational and Experimental Validations H. Irschik^{1}, M. Krommer^{1}, M. Nader^{2}, Ch. Zehetner^{2} and M. Zellhofer^{2}
^{1}Institute for Technical Mechanics, University of Linz, Austria
H. Irschik, M. Krommer, M. Nader, Ch. Zehetner, M. Zellhofer, "Structural Displacement Tracking by Eigenstrain Actuation: Computational and Experimental Validations", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", CivilComp Press, Stirlingshire, UK, Paper 6, 2007. doi:10.4203/ccp.86.6
Keywords: displacement tracking, shape control, eigenstrain, smart structures, piezoelectric actuation.
Summary
In the classical framework, structural mechanics deals with the computation of displacements and stresses, which are produced by a given set of loadings, such as imposed forces, imposed boundary conditions and imposed initial conditions. The solution of such direct problems has been brought to a high art, particularly in the linear theory of elastic structures. In the present paper, we treat a problem, which is inverse to the classical direct framework of structural mechanics, and which we call the displacement tracking problem: we seek for a control actuation, which, when being subjected together with some imposed transient force loading, produces a desired (prescribed) displacement field in a linear elastic structure. In our study, special emphasis is made on upon smart structures, i.e. on a control actuation by eigenstrains induced via piezoelectric or thermal actuators, or via analogous effects, such as magnetostriction or prestress.
The strategy followed in the present study is to seek for analytical solutions of the displacement tracking problem, assuming that no constraints are present with respect to the spatial and timewise distribution of the control actuation, the latter being assumed to be distributed throughout the structure. A feedforward control situation is treated, in which both, the structural parameters as well as the imposed loadings are known as functions of space and time. The corresponding analytical solutions for distributed actuators afterwards serve as a starting point for the design of suboptimal discrete actuator nets. Our analytical solution, in which we derive in the framework of the linear theory of elastodynamics, can be summarized as follows: the actuation stresses due to the distributed control eigenstrains must satisfy certain quasistatic equilibrium conditions, where auxiliary bodyforces and auxiliary surface tractions are to be taken into account. The latter auxiliary loading can be directly computed from the imposed loading and from the desired displacement field to be tracked. Hence, despite the fact that we are dealing with a dynamic problem, a straightforward computation of proper actuator distributions can be performed in the framework of quasistatic equilibrium conditions only. After having presented a proof of the above stated analytical solution, we give a short review of the previous contributions of our group, mainly concerning structural shape control, i.e. the case of zerodisplacement tracking [1,2,3]. We then present an exemplary numerical validation of our analytical solution for displacement tracking by means of finite element computations. The presented analytical solution finally is used as a suitable starting point for the actuator design, in the case where restrictions with respect to the spatial applicability and the intensity of actuation have to be taken into account. Here, we report on an experimental verification in the laboratory, using a framed structure, which is equipped with a net of piezoelectric actuator patches. References
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