This paper presents an extension to the Geometric Multi-Scale Finite Element Method (GMsFEM) developed by Casadei et al. to predict the dynamic response of heterogeneous materials and structures. The proposed approach introduces elements enriched by the natural modes over their own domain. When heterogeneities are present, the auxiliary fine-scale mesh from GMsFEM is used to calculate the modes numerically. The enrichment scheme is also chosen in such a way that it automatically satisfies continuity across boundaries. The computational efficiency of the method is compared to that of traditional finite element formulations through selected benchmark problems.
Modelling axial vibration in windings of power transformers