Multi-scale Galerkin methods will be developed for the study of structural/building systems in which the response is characterized by multiple-spatial and multiple-time scales. For this type of structural problems, the response is often dominated by the middle part of the frequency spectrum, which in this proposal is referred ta as medium frequency dynamic analysis. New temporal and spatial discretization methods will be developed for the multi-time scale structural dynamic problems. The concept of fast and slow time scales will be introduced for the temporal discretization. The required time step is shown to be dependent only on the slow time scale, and therefore, large time step can be used for the high frequency problems. To meet the spatial counterpart of the requirement on time step requirement, finite-spectral elements and finite wave elements will also be developed. These developed methods will be applied to building systems, and nonlinear dynamic buckling of fluid-filled shell structures.
