预张力索杆体系分布式静不定与动不定分析

针对预张力索杆体系,将构件刚度与体系判定相结合,提出了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.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.所提出的方法克服了已有方法中的奇异性问题,具有普适性,能广泛地适用于动定及动不定结构;揭示了分布式静不定与结构重要性及结构敏感性间的关系,以及分布式动不定与节点可动性间的关系.通过2组算例,说明了该方法在预张力索杆体系中的应用,并证明了其有效性和正确性.

Analysis of Distributed Static and Kinematic Indeterminacy of Pre tensioning Cable Strut Systems

Abstract： An analytical approach to the distributed static and kinematic indeterminacy taking into account the stiffness as well as the topology and geometry was developed for pre tensioning cable strut systems, making it possible to identify the structural system in terms of every component rather than the whole system. Based on the equilibrium matrix theory, the singular value decomposition (SVD) method was adopted to calculate two pairs of orthogonal modes, i.e., the modes of compatible/ incompatible elongations and the modes of compatible/ incompatible loads. Due to the orthogonality that indeed avoids the singularity problem, the proposed approach was applicable to kinematically determinate structures and even kinematically indeterminate structures. It is shown that the distributed static indeterminacy is closely related to the structural robustness theory based on the importance indices and the structural sensitivity theory, while the distributed kinematic indeterminacy can reveal the nodal mobility in every equilibrate configuration. Besides, an algorithm was developed to implement this approach and two examples of cable strut system were presented to demonstrate its robustness and accuracy.