Abstract
This paper gives a proof of equivalence between two existing force methods (FM) for structural analysis: The Integrated Force Method (IFM) and a force method based on singular value decomposition (SVD) of the equilibrium conditions here named as SVD-FM. Recently, these methods have been employed to design and control active structures. Actuation is employed to counteract the effect of external loading by modifying internal forces and the external geometry in order to meet strength and serviceability requirements. Both IFM and SVD-FM offer an effective way to estimate the combined effect of external loading and that of actuation. Generally, the SVD-FM has a lower degree of computational complexity with respect to the IFM, the more so as the structure static indeterminacy increases. However, the IFM has a more intuitive formulation that is preferable pedagogically and it is of value for future extensions to kinematically indeterminate configurations and to geometric non-linear cases.
Highlights
Active structural control through integrated sensing and actuation has been investigated and experimentally tested to reduce the structure response under extreme loading events such as strong winds, earthquakes and unusual crowds [1, 2, 3, 4]
The Integrated Force Method (IFM) has a more intuitive formulation that is preferable pedagogically and it is of value for future extensions to kinematically indeterminate configurations and to geometric non-linear cases
The work presented in this paper shows that the IFM and singular value decomposition (SVD)-force methods (FM) are equivalent
Summary
Active structural control through integrated sensing and actuation has been investigated and experimentally tested to reduce the structure response under extreme loading events such as strong winds, earthquakes and unusual crowds [1, 2, 3, 4]. Recent studies [16, 17] have investigated structural adaptation through large shape changes In this case the structure is designed to be controlled into a shape that is optimal to counteract the effect of the external load. A non-elastic strain can be thought of as caused by the action of actuators and it has been referred as eigenstrain [26, 13] Another force method that has been used for control of adaptive structures was first presented in the work of Pellegrino and Calladine [27, 28]. The self-stress basis can be obtained through singular value decomposition (SVD) of the equilibrium conditions This method, which is here referred as SVD-FM, has been generalized to structural systems with static as well as kinematic indeterminacies.
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