Reduced Order Modeling with Local Enrichment for the Nonlinear Geometric Response of a Cracked Panel

Abstract

High-speed flight vehicles operating in extreme environments are likely to undergo significant nonlinear dynamic deformation. The accurate response and life predictions of such structures require methods that enable direct time integration over long portions of flight trajectories, and also require the ability to resolve local stress concentrations. The approach proposed here takes root in displacement-based reduced order modeling to allow for direct time integration. The reduced order models (ROMs) are built using first a ROM constructed over the uncracked structure, whose global basis is augmented with localized enrichment basis functions that are constructed to capture the localized impact of a crack on the displacement field of the structure. The enrichment bases are built using a 3D generalized finite element model defined only in the region of the crack itself. Detailed stress information can also be extracted from the 3D fracture model. The proposed approach is demonstrated on a cracked flat cantilevered blade model, and the benefits of coupling the global basis functions and the localized enrichment bases are demonstrated.