中文摘要：

提出一种不需要有限元建模的梁结构损伤定位方法。基于最小秩理论，利用结构损伤前后的静力响应方程，推导了柔度改变量的静力最小秩解计算公式，并据此来定位结构的损伤位置，分析了所提方法相比传统的动柔度损伤定位方法的优势。研究表明，本文所提的柔度扰动量的静力最小秩解，是一种理论上的精确解，避免了动柔度方法中忽略高阶模态所致的不利因素，可以获得比动柔度方法精度更高的损伤定位结果。而且，所提方法不需要建立结构的有限元模型，只需要测量损伤前后结构在施加的静力荷载作用下的部分位移参数即可进行，是一种简便易行的实用方法。以两个梁结构为例对所提方法进行了验证，结果表明了方法的可行性。

英文摘要：

A flexibility difference method based on the minimum-rank solution for locating damage in beam structures has been proposed in this paper. This method is based on the estimation of changes in the flexibility matrix by using the static response data and the minimum rank update theory. The main advantage of using the static data rather than dynamic data is that the static equilibrium equation is solely related to the structural stiffness, and accurate static response data can be obtained rapidly and cheaply. As distinct from the existing minimum-rank methods, the presented method can directly compute the flexibility perturbation using the incomplete measured static data. Moreover, the proposed theory provides an insight to the appropriate number of the applied static loads for structural damage detection. The efficiency of the proposed method is demonstrated by two numerical examples. The results show the good efficiency and stability of the proposed method on the localization of damage. It has been shown that the proposed procedure may be a promising method in structural damage localization.