基于高斯曲率极值点的桥梁结构损伤识别方法

Damage identification method of bridge structures based on Gaussian curvature extremum points

目前中小桥梁日常安全巡检存在对检查人员依赖性高、缺乏可量化的科学依据等不足。针对这些问题,本文提出了一种利用高斯曲率极值点对结构进行损伤识别的方法。将桥面视为受弯弹性薄板,根据弹性薄板的弯曲理论得到了在荷载作用下结构刚度变化与桥面弯曲程度(高斯曲率)的理论关系,并由此推导了高斯曲率对结构刚度损伤的敏感程度公式。通过有限元建立了一座简支T梁模型,并在主梁肋板上设置不同高度、不同位置和不同数量的裂缝来模拟结构刚度损伤。计算了在自重作用下,裂缝高度、位置、数量与桥面高斯曲率变化的关系。分析结果表明,桥面的高斯曲率分布清晰地映射了结构的刚度分布,高斯曲率极值点明确地指征了桥梁的损伤位置。借力三维激光扫描等全息现代测量技术,本文的研究成果为高效量化的桥梁结构损伤识别提供了有效的分析手段。

Aiming at the shortcomings of the current small and medium-sized bridges in the daily safety inspections, such as high dependence on inspectors and lack of quantifiable scientific basis, a method for damage identification of structures using Gaussian curvature is proposed. The bridge deck is regarded as a flexural elastic thin plate. According to the bending theory of the elastic thin plate, the relationship between the structural stiffness change and the bridge deck bending degree, Gaussian curvature, is obtained and verified by numerical examples. A simple supported T-beam model is established in the finite element, and different heights, different positions and different numbers of cracks are set on the web of the main beam to simulate the structural stiffness damages. The height, position and quantity of the cracks are calculated under the action of self-weight. The analysis results show that the stiffness distribution of the structure can be clearly seen through the Gaussian curvature of the bridge deck, and the cracks in the structure can be accurately identified by extremum points of Gaussian curvature. With the help of modern holographic measurement techniques such as 3 D laser scanning, the research results provide an effective analysis means for the efficient and quantified damage identification of bridge structures.