结构鲁棒性评价中的构件重要性系数

IMPORTANCE COEFFICIENTS OF COMPONENTS IN EVALUATION OF STRUCTURE ROBUSTNESS

考虑结构的鲁棒性是保证结构安全、特别是应付突发事件的最重要措施之一。如何对结构的鲁棒性进行定量评价是目前结构工程界最具有挑战性的前沿问题之一。以移除所分析构件前后的结构承载力变化为着眼点,给出一个结构鲁棒性评价中计算构件的重要性系数的新方法。在概念上,综合考虑结构的几何拓扑关系、构件的刚度和强度以及外荷载对结构鲁棒性的影响;在力学意义上,描述已破坏的构件是如何影响剩余结构的,实际上考虑了结构本身的性质与外荷载的共同作用机制;在加载过程中,以结构退化成机构为分析终止点,从一定程度上表现构件重要性与整个结构鲁棒性之间的关系;在算法上,以摄动法建立将构件"概念移除"前后的结构刚度矩阵关系,避开重组刚度矩阵和对其求逆的复杂过程,从而简化运算。最后通过两个满应力设计下的平面桁架结构为例,说明计算的过程,同时通过与已有构件重要性系数指标方法作比较,找到其中的区别和内在联系,论证计算结果的正确性和合理性。

Consideration of structural robustness is one of the most important measures to guarantee the structural safety, especially to deal with unexpected events. How to evaluate the structural robustness quantitatively is one of the most challenging problems in structural engineering. A new method to calculate the importance coefficient of components in structural robustness evaluation is given, which focuses on the change of structure capacity after removing a certain component in the structure. From conception, the structural topological relation, the component stiffness and strength, and the effect of external loads are all considered synthetically. Besides, from mechanics, how the broken component influences the remnant structure are also described, which can be used to explain the physical meaning of the new coefficients. At the same time, from global point of view, the interaction between the structural property and the external load effects is considered. The loading process is completed until the structure becomes a mechanism, to some extent, which helps to establish the relationship between component importance and structural robustness. From algorithm, a method called perturbation is used. It bridges the structural stiffness matrix before removing some component with that after removing, by which the rearrangement and inversion of the structural stiffness matrix can be avoided. Instead, the dimension of the structural stiffness matrix in each stage is only decided by the number of the broken components. The inversion calculation is easy, which only needs to treat some specific large sparse matrices. Finally, as practical examples, two plane trusses are given. Comparing with some existing indexes of component importance, the internal relations between them are found, and the correctness and rationality are also proven.