摘要
提出了采用k-means聚类算法对动力相似自由度进行自动集结的模型降阶方法。考虑动力荷载空间分布,给出了根据模态参与系数选取原模型重要模态的方法,并讨论了次要方向自由度舍弃的方法。根据重要模态中各自由度振型值的相似性,应用聚类算法对自由度进行自动分类,从柔度矩阵元素的定义入手推导了结构矩阵显式条件下柔度法降阶的统一表达式,并证明了降阶模型的正定性、对称性及正交关系。最后通过一榀40层混凝土框架结构模型由240自由度降阶为8自由度的算例,说明了柔度法降阶的有效性及降阶模型评判指标的合理性。
A model reduction method by which the concentration of dynamical similar DOFs is auto-conducted with k-means clustering algorithm is proposed.Considering the space distribution of the dynamic loads,the method to select important modes of original model based on modal participation factor is proposed,and the omission of DOFs in the secondary directions is discussed.According to the similarity of the mode shape values in important modes the DOFs are auto-clustered using clustering algorithm.Starting from the definition of the entries in flexibility matrix,the flexible reduction common formula is induced with the explicit original model,and the positive definiteness,symmetry and orthogonality relationship of the reduced matrices are proved.At last,an example reducing a 40-storey concrete frame containing 240 DOFs to a model containing 8 DOFs shows the efficiency of the reduction method and the reasonability of the assessment indices.
出处
《计算力学学报》
EI
CAS
CSCD
北大核心
2012年第2期236-241,248,共7页
Chinese Journal of Computational Mechanics
基金
国家自然科学基金(90815030)资助项目
关键词
结构动力学
模型降阶
模态分析
聚类算法
structural dynamics
model reduction
modal analysis
clustering algorithm
