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目的:针对预张力索杆体系,将构件刚度与体系判定相结合,提出分布式静不定和分布式动不定的计算方法,使体系分析从“系统”层面向“构件”层面延伸。创新点:1.推导出具有广泛适应性的分布式静不定公式,并证明与原有方法的内在关系。2.首次提出分布式动不定数学公式。3.给出分布式不定数的物理意义及潜在的应用。方法:该方法在平衡矩阵理论基础上,采用奇异值分解法分别求解相互正交的两类单元变形量和两类节点外荷载模态;在排除整体刚体位移模态后,利用该正交性,求解分布式静不定和动不定。结论:1.该方法能克服已有方法中的奇异性问题,具有普遍性,可适用于动定及动不定结构。2.作为结构双对称性的代表,分布式静不定数可被用作一个简单而有效的分组准则;该准则能提高二次奇异值找力法(DSVD)的效率并能为设计师提供更多的初始预应力设计可能性。3.揭示分布式静不定与结构重要性及结构敏感性间的关系。4.分布式动不定数可被用作节点可动性的一个基本指标。
OBJECTIVE: According to the pre-tensioned cable system, combining the stiffness of components with the judgment of the system, a distributed static uncertainty and distributed uncertain computing method are proposed to extend the system analysis from the “system” level to the “component level” . Innovative points: 1. Derive a widely distributed static deterministic formula, and prove the inherent relationship with the original method. For the first time, a distributed and uncertain mathematical formula is proposed. 3. Given the physical significance of distributed indefinite numbers and potential applications. Methods: Based on the equilibrium matrix theory, the singular value decomposition method was used to solve the two types of element deformations and the two types of node external load modes respectively. After excluding the overall rigid body displacement modalities, , Solve the static and uncertain distributed. Conclusion: 1.This method can overcome the singularity problem in the existing methods and is universal, which can be applied to dynamic and dynamic structures. 2. As a representative of the symmetry of the structure, the distributed static indeterminate number can be used as a simple and effective grouping criterion; this criterion can improve the efficiency of the second singular value seeking method (DSVD) and can provide designers with more More initial prestress design possibilities. 3. Uncover the relationship between distributed static uncertainty and structural importance and structural sensitivity. 4. Distributed uncertainty can be used as a basic indicator of node mobility.