基于类平衡矩阵的桁架构件重要性计算方法  

Component Importance Evaluation Method of Truss Structures Based on Class-balance Matrix

作　　者：周雅[1] 王方[1] 蔡建国 冯健[1] ZHOU Ya;WANG Fang;CAI Jianguo;FENG Jian(Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education(Southeast University),Nanjing 210096,China)

机构地区：[1]混凝土及预应力混凝土结构教育部重点实验室(东南大学),江苏南京210096

出　　处：《湖南大学学报（自然科学版）》2023年第5期22-28,共7页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(51822805,51878147,U1937202)。

摘　　要：为简化构件重要性系数的计算过程,提高计算效率,以基于刚度的构件重要性判断方法为基础进行数学推导,提出一种基于类平衡矩阵的空间结构重要构件的快速判断方法,并进行算例验证.结果表明,当铰接杆件体系的各杆件线刚度近似相等,且不考虑结构应力刚化作用或应力刚化所贡献的刚度很小时,整体切线刚度矩阵仅与类平衡矩阵相关,构件重要性系数可直接利用类平衡矩阵的奇异值进行计算.通过算例验证,类平衡矩阵的重要性构件判断方法与基于刚度的重要性构件判断方法计算结果一致,说明所提方法是一种切实可行的快速计算方法.To simplify the computational process and improve the calculation efficiency,a fast evaluation method of component importance coefficients based on the quasi-balanced matrix,which was derived from the stiffness-based component importance evaluation method,was proposed for spatial structures.By transforming the balanced matrix,the quasi-balanced matrix containing the length information of components was obtained.When the linear stiffness of each component was approximately equal and the effect of structural stress stiffening was not considered,the global tangential stiffness matrix was simplified,and the component importance coefficients were ex⁃pressed only including the quasi-balanced matrix.The singular value decomposition of the quasi-balanced matrix was carried out,and the mathematical relation between the eigenvalues of the stiffness matrix and the singular values were established.Taking the product of singular values as a response,the expression of the component importance coefficient was modified so as to calculate it.Through case study on three truss examples,it was proved that the cal⁃culation results of the evaluation method of component importance coefficients based on the quasi-balanced matrix are consistent with the stiffness-based evaluation method,which shows that the proposed method is a practical and fast calculation method.

关 键 词：切线刚度 刚度矩阵 类平衡矩阵 构件重要性 重要性系数 

分 类 号：TU323.4[建筑科学—结构工程]