Dynamic reanalysis of structures with geometric variability and parametric uncertainties via an adaptive model reduction method

In this paper, a model reduction method is proposed for the dynamic reanalysis of structures with geometric variability and parametric uncertainties. Geometric variability is introduced by distorting the finite element meshes for some substructures via arbitrary shape functions. Parametric uncertainties are also considered to describe local variations of the stiffnesses of the substructures. The proposed approach involves expressing the substructure transformation matrices using interpolated matrices of Craig–Bampton component modes together with matrices of enrichment vectors. These enrichment vectors are parameter-independent and, as such, they only need to be computed once. This, as a result, leads to reduced substructure models which can be quickly updated to reanalyze structures with geometric and parametric changes. The accuracy and numerical efficiency of the proposed approach are highlighted through numerical experiments.