基于EEP法的杆系结构裂纹损伤识别有限元自适应求解研究

The crack damage detection of frame structure is one of the central challenges in the research field of structure engineering, in which damage detection based on frequencies is the inverse problem of free vibration. The adaptive approach of finite element method (FEM) and finite element method of lines (FEMOL) for one- and two-dimensional eigenproblems respectively were proposed based on Element Energy Projection (EEP) method, which had succeeded in a series of free vibration problems for beams, moderately thick plates and moderately thick shallow shells with the EEP method for error estimation and the error-averaging method for mesh refine. The mature adaptive approach for free vibration problems have paved the way for its further application in adaptive analysis of damage detection problems. The expected goal is to establish adaptive FEM strategy for accurate damage detection of cracks location, size and number. The analysis patterns of adaptive inverse and subspace iteration for free vibration of damage frame structure and adaptive Newton iteration of damage detection will be established by introducing the spring model for crack, EEP method and error-averaging method. The error between computed frequencies and actual frequencies decreasing and cracks residuals reducing gradually using both of the adaptive and Newton methods are the novel technologies. The proposed methodology in this study is expected to be characterized by accurate and efficient algorithm and reliable application for crack damage detection of variable cross-section and curvilinear frame structure, and hence possesses great potential of being a superior and competitive adaptive approach in theoretical and practical aspects.

杆系结构的裂纹损伤识别是结构工程领域的重要研究课题，基于频率的损伤识别是自由振动这一结构特征值问题的逆问题。申请人建立了基于单元能量投影(EEP)法的一维有限元和二维有限元线法特征值问题的自适应求解方法，对多种梁、板、壳等自由振动的精确求解取得成功，其中误差估计的EEP超收敛算法和网格细分的均差法显示出很强的求解效力。自由振动问题的成功求解，使得挑战损伤识别问题成为可能。本项目旨在建立基于频率的杆系结构裂纹位置、大小、数目等损伤信息精确识别的有限元自适应方法，引入裂纹模拟的弹簧模型、EEP法和均差法，解决含损伤杆系结构自由振动求解的自适应逆幂(子空间)迭代和多裂纹损伤识别的自适应Newton迭代等求解模式问题，形成频率解答和实测频率之间误差不断减小、裂纹损伤信息渐趋准确的技术路线。本项目将构建精确高效的损伤识别求解算法，并发展适于变截面、曲线型杆系结构的计算技术，具有理论意义和实用价值。

杆系结构的裂纹损伤识别是结构工程领域的重要研究课题，基于频率的损伤识别是自由振动这一结构特征值问题的逆问题。杆系结构分析经过杆件计算、常规整体集成，其中主要的各类型杆件计算成为本项目研究的重点。本项目建立了基于频率的杆件裂纹位置、大小、数目等损伤信息精确识别的有限元自适应方法，引入裂纹模拟的弹簧模型、EEP法、SPRD法和网格细分方法，解决了含损伤杆系结构自由振动求解的自适应逆幂(子空间)迭代和多裂纹损伤识别的自适应Newton迭代等求解模式问题，形成频率解答和实测频率之间误差不断减小、裂纹损伤信息渐趋准确的技术路线。本项目构建了精确高效的损伤识别求解算法，并发展适于变截面、曲线型杆系结构的计算技术，具有理论意义和实用价值。近期，本项目裂纹梁损伤识别问题的自适应有限元法已推广应用到岩体压裂裂纹扩展的自适应求解研究中，是具有创新性的后续研究课题。