Distributed indeterminacy evaluation of cable-strut structures: formulations and applications

The indeterminacy evaluation is an effective method for system identification; it can predict the mechanical behaviors of flexible structures in the primary design. However, the conventional indeterminacy evaluation based solely on geometry and topology has neglected the influence of material properties on mechanical behavior and the contribution of each component to the total indeterminacy. To address these issues, a distributed indeterminacy evaluation taking account of the effect of component stiffness was carried out with a view to providing reasonable interpretations and feasible applications for two concepts, i.e., the distributed static indeterminacy (DSI) and the distributed kinematic indeterminacy (DKI). A unified method for the DSI is proposed, and a comparative analysis between this and an existing method revealed that the proposed method has a wider range of applicability and is essentially identical in the kinematically determinate case. It can be concluded that since the DSI is representative of symmetric properties, a simple but efficient grouping criterion can be established which can improve the efficiency of the specific force finding method entitled double singular value decomposition (DSVD). On the other side, an evaluable method for the DKI is proposed suggesting that DKI is a useful indicator for the assessment of nodal mobility and can provide a feasible solution to the form transforming study.中文概要题目索杆结构分布式不定数分析:推导和应用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。