基于构件层次的铰接杆系结构几何稳定性讨论

考察构件刚度和构件撤除对杆件系统几何稳定性的影响.从常规结构稳定理论的角度审视铰接杆件系统几何稳定性问题.基于结构稳定的能量准则和刚度矩阵的构成分析,重新考察了Maxwell准则和平衡矩阵准则的充分必要性.解释了构件零刚度和构件撤除对体系几何稳定性影响的一致性.利用自应力矩阵的特性,提出并证明了一种快速识别杆系结构中“必需杆”的方法.一种多根构件撤除后体系几何稳定性的判别准则进而被发展.该判别准则的数值效率体现在仅利用原结构平衡矩阵一次分解后的信息,杆件撤除后体系平衡矩阵的秩可通过两小规模矩阵秩之间的关系来表示.

DISCUSSION ON GEOMETRICAL STABILITY OF PIN-BAR ASSEMBLIES AT MEMBER LEVEL

The geometrical stability of pin-bar assemblies and the effects of bar stiffness are reinvestigated from the viewpoints of conventional structural stability theory.Based on the energy criterion of structural stability and the constitution analysis of stiffness matrix,sufficient and necessary conditions of Maxwell rule and Equilibrium Matrix rule are discussed.The equivalence of zero bar stiffness and removal of the same bar to the geometrical stability is explained theoretically.By utilizing the properties of self-stress matrix,a technique for quickly distinguishing "necessary bars" is proposed.Further,a criterion to determine geometrical stability of pin-bar structures after removal of multiple bars is developed.This criterion is effective since it only depends on the matrix information obtained by one-time decomposition of the equilibrium matrix of original configuration.The rank of equilibrium matrix of updated assembly can be determined from a relationship between the ranks of two small-scale matrices.