Extended Integrated Force Method for the analysis of prestress-stable statically and kinematically indeterminate structures

This paper presents a new force method to predict the structural response of statically and kinematically indeterminate systems that can be stabilized through prestress, i.e. prestress-stable structures. This new force method, here named Extended Integrated Force Method (IFME), extends the existing Integrated Force Method (IFM) which is only applicable to the analysis of kinematically determinate systems. The product force concept is adopted and incorporated into the IFME to model the effect of infinitesimal mechanisms. This makes the IFME capable of dealing with cases in which the external loads contain components that cannot be taken by the system in its initial configuration. As the original IFM, the IFME bypasses the well-known concept of redundant forces and basis determinant structure of the Standard Force Method (SFM) by taking the internal forces as the independent variables which are obtained simultaneously. A proof is provided to show that, when the product force is not included in the formulation, the IFME reduces to the IFM for kinematically determinate systems and it also reduces to another force method based on singular value decomposition of the equilibrium matrix which is here named SVD-FM. Compared to the better known Displacement Method (DM), the IFME is a suitable alternative and it offers a deeper insight into the structure response which is decoupled into an extensional and an inextensional part for prestress-stable kinematically indeterminate systems. Numerical examples are carried out to test accuracy and effectiveness of the IFME on kinematically indeterminate structures with multiple self-stress states and mechanism modes. Application of the IFME to active structural control of kinematically indeterminate systems is also discussed through a numerical example.