Multi-Scale Methods for Structural Dynamics

多尺度伽辽金方法将用于研究结构/建筑系统，其中响应具有多空间和多时间尺度的特征。对于这类结构问题，响应通常由频谱的中间部分主导，本文将其称为中频动态分析。对于多时间尺度结构动力问题，将发展新的时空离散化方法。对于时间离散，将引入快时尺度和慢时尺度的概念。所需的时间步长仅依赖于慢时间尺度，因此，大时间步长可以用于高频问题。为了满足时间步长要求的空间对应，还将开发有限谱单元和有限波单元。这些发展的方法将应用于建筑系统和充液壳结构的非线性动力屈曲。

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.