基于能量流动网络的杆系结构易损性

Vulnerability of Frame Structures Based on Energy Flow Network

本文从杆系结构的能量流动网络入手,通过折减杆件刚度模拟结构构件受到的损伤,建立了描述结构能量流动网络变化的两个矩阵——结构的流动能量变化矩阵、留驻能量变化矩阵,并由此构造出衡量二者综合变化的结构能量综合变化矩阵。该矩阵同时考虑了杆件受到损伤后对结构其他部分的影响以及结构的其他部分受到损伤后此杆件自身受到的影响,通过对其进行范数计算确定杆件的重要性排序。类比链式法则,由确定的最重要杆件序列的重要性系数确定结构的易损性指标。算例中对连续梁、并联结构、一榀框架和三铰刚架进行了分析,结果表明,本文计算方法的合理性以及应用于结构健康监测等领域的可行性。

Based on the network of energy flow in frame structures,three matrixes of energy change are constructed due to reduction of member stiffness： matrix of change of energy flow,matrix of change of stored energy and matrix of change of structural energy.By calculating the matrix of change of structural energy,the effects both on the structure when a member is damaged and on the member itself when other portion of the structure is damaged,are considered.Then the index of member importance is determined.By analogy to the chain law in calculus,the index of vulnerability of a structure is defined on the importance indexes of a series of the most important members.As demonstration,a continuous beam,a parallel structure,a frame and a three-hinged frame are analyzed.The results which show that the presented method is reasonable and can be used in other fields in structural engineering such as health monitoring.