A proof of equivalence of two force methods for active structural control

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.