Invariant and consistent redundancy by large admissible perturbations

Abstract

Structural perturbation theory has been developed over the past 16 years to relate two structural states modeled by the same Finite Element (FE) model but described by different values of the design variables. Relating an intact/damaged (initial) structure to a limit state structure produces the reserve/residual redundancy. Invariant and consistent redundancy, redundancy functions, and injective mappings are defined and related to the design variables. General perturbation equations are derived to relate the two states and produce failure surface equations. Individual and joint failure points are identified and redundancy is computed without linearization of failure surfaces, enumeration of failure paths, trial and error, or repeated FE Analyses (FEAs). This is achieved by large admissible perturbations using a prediction-correction algorithm and postprocessing FEA results of the initial structure only. The latter may differ from the limit state structure in stiffness, mass, geometry, or response by as much as 100-300% depending on the size of the FE model. Structural perturbation theory treats discrete and continuous structures as the FE method does; modeling of the structure as a simplified system of components is not needed. To introduce this new approach to redundancy, modal dynamic and static deflection failure criteria are used in the elastic range. Numerical applications on a beam, a small, and a large offshore tower are used to test the method. Future developments and impact to design are discussed as the new methodology introduces an alternative to systems reliability and stochastic FE.