索结构找力的扩展广义平衡矩阵奇异值分解法  

Force finding of cable structures based on singular value decomposition of expanded generalized equilibrium matrix

作　　者：朱忠义[1] 白光波[1] 周忠发[1] ZHU Zhongyi;BAI Guangbo;ZHOU Zhongfa(Beijing Institute of Architectural Design,Beijing 100045,China)

机构地区：[1]北京市建筑设计研究院有限公司,北京100045

出　　处：《建筑结构学报》2023年第4期118-128,共11页Journal of Building Structures

基　　金：北京市建筑设计研究院有限公司创新发展资金科研项目(2020-059)。

摘　　要：预应力是维持索结构稳定性、形成刚度和承载能力的核心要素。考虑结构几何对称性等因素求解预应力模态,是获取索结构可行预应力的必要条件。通过对平衡矩阵的含义进行再阐释,引出广义平衡方程和广义平衡矩阵的概念。将广义平衡矩阵与平衡矩阵结合,形成索结构的扩展广义平衡矩阵。通过对扩展广义平衡矩阵进行奇异值分解,即可得到符合预定分布模式的预应力模态。针对3个典型算例,采用所提出的方法求得了满足工程需求的可行预应力模态。研究表明:通过指定合理的预应力分布模式,采用扩展广义平衡矩阵奇异值分解法,仅需一次奇异值分解即可得到可行预应力模态,找力过程简洁、直接;预应力分布模式可根据需要灵活设定,易于得到符合设计意图的可行预应力模态。The prestress plays a major role in stabilizing the cable structure as well as in forming its stiffness and load-bearing capacity.To obtain a feasible prestress for cable structure,it is a necessity to find the prestress modes considering multiple factors such as the geometric symmetry.The meaning of the equilibrium matrix is reinterpreted,after which the concept of the generalized equilibrium equation and the generalized equilibrium matrix are introduced.The expanded generalized equilibrium matrix is then derived by combining the equilibrium matrix with the generalized equilibrium matrix.The prestress modes,which conform to the predetermined prestress pattern,can be obtained by the singular value decomposition(SVD)of the expanded generalized equilibrium matrix.The feasible prestress modes for three examples are calculated using the proposed method.The results show that the method,provided with a proper prestress pattern,offers a simple and direct force-finding process in which the SVD is performed only once to calculate the feasible prestress mode.The prestress pattern can be determined flexibly as required,thus making it easier to find the feasible prestress mode that meets the design idea.

关 键 词：索结构 找力 广义平衡方程 扩展广义平衡矩阵 奇异值分解 可行预应力模态 

分 类 号：TU394[建筑科学—结构工程] TU311