CAJ | 학술논문

研究了结构损伤与系统矩阵秩变化之间的对应关系，以此为基础提出一种损伤识别方法。首先分析了结构损伤所引起的系统矩阵秩的变化，然后利用结构损伤前后的静力响应方程，推导了柔度扰动量的限定秩解计算公式，再结合柔度扰动新方法计算结构各单元损伤参数，据此确定损伤位置及损伤程度。研究表明，损伤前后结构静力位移差向量之间必然存在着线性相关性，因此，施加静力荷载的组数并非越多越好，而是只要大于柔度扰动矩阵的秩即可。由该方法所获得的柔度扰动量的限定秩解，是一种理论上的精确解，以它为基础可以获得很高精度的损伤识别结果。以桁架结构为例对所提方法进行了验证，结果表明了本文方法的可行性。
연구료결구손상여계통구진질변화지간적대응관계，이차위기출제출일충손상식별방법。수선분석료결구손상소인기적계통구진질적변화，연후이용결구손상전후적정력향응방정，추도료유도우동량적한정질해계산공식，재결합유도우동신방법계산결구각단원손상삼수，거차학정손상위치급손상정도。연구표명，손상전후결구정력위이차향량지간필연존재착선성상관성，인차，시가정력하재적조수병비월다월호，이시지요대우유도우동구진적질즉가。유해방법소획득적유도우동량적한정질해，시일충이론상적정학해，이타위기출가이획득흔고정도적손상식별결과。이항가결구위례대소제방법진행료험증，결과표명료본문방법적가행성。
The static response-based structural damage identification methods have received much attention in civil engineering field in recent years.A static rank analysis of a structure’s system matrix method was presented here for structural damage identification using its static response data and the matrix rank analysis theory.Firstly,the rank varying of a structure’s system matrix due to its damage was analyzed and then a limited rank solution formula of structural flexibility perturbation was developed.With the flexibility change determined,the elemental damage parameters were calculated by using the new flexibility perturbation method.According to the elemental damage parameters,the damage position and damage level were determined.Being different from the existing detection techniques,using the presented method could directly compute the damage parameters with the incompletely measured static data.The efficiency of the proposed method was demonstrated with a numerical example.The effect of measurement of noise on damage detection performance of the proposed method was also investigated.The results showed the good efficiency and stability of the proposed method for the identification of damage of a structure with more than one element.For the case with 3% and 10% noise,the prediction obtained was also reasonable.