高层空间框架结构动力分析的超级元子结构模型

A Super Finite Element Substructure Model forDynamic Analysis of High Rise Spatial Frames

本文将超级元和子结构的思想相结合,根据框架结构的变形特点,建立了高层空间框架结构动力分析的超级元子结构模型。模型中将楼面划分为子结构,在总结构层次将各子结构假想为二维连续体后用超级元来描述,而在子结构内部仍用经典有限元三维梁单元模拟。据此,框架梁位于同一超级元内,而框架柱连接不同的超级元。通过假设子结构内部结点自由度与总结构结点自由度的位移关系,得到超级元的质量矩阵以及框架梁和框架柱的单元刚度方程。该模型中空间框架结构的动力和非动力自由度均有大幅度的缩减,而刚性楼面假定可以进一步减少计算量。最后通过一幢30层钢筋混凝土空间框架结构的动力特性分析验证本文理论的正确性和适用性。

By combining super finite element(SFE)with substructure, a SFE-substructure model was proposed for dynamic analysis of high rise spatial framed structures in accordance with their deformation characteristics. In the model, each floor structure was taken as an independent substructure, which was considered as a 2-dimensional continuum simulated with a SFE at global level and was still modeled as a framed structure composed of 3-dimensional beam elements at local level. In this way, a beam was located in the same SFE, while a column connected different SFEs. With an assumption of the displacement relation between global and local degrees of freedom within the same substructure, the mass matrix of SFE was obtained and the stiffness equations of beams and columns were derived as well. Both the dynamic and non-dynamic degrees of freedom of the model are hence largely reduced and the usual assumption of rigid diaphragm can be employed to reduce computational effort further. Finally the dynamic analysis of a 30-storeyed reinforced concrete space frame was performed to validate the model.