柔性预张力结构的刚度解析和评价理论研究

Structural rigidity is the kernel for the in-service performance evaluation of flexible tensile structures, such as cable net and cable dome, due to their special mechanisms in structural configuration. A new idea is put forward in this proposal to evaluate the structural rigidity of an existing flexible tensile structure by emphasizing the monitoring of so-called “required stiffness”, and motivates sequential theoretical topics. The analytical theory of structural rigidity will be primarily studied to differentiate the contribution respectively from linear elastic stiffness and geometrical stiffness, as well as to quantitatively describe the contribution of member’s elastic stiffness and pretension to the structural global stiffness. A numerical approach will be further developed to separate the required stiffness, which dominantly resists the structural deformation caused by the main loadcases, from the structural global stiffness. Thus, the evaluation of in-service structural rigidity performance can basically focus on the required stiffness. For adapting to the direct dynamic detection of structural stiffness, an analytical method will be established to solve those structural eigenmodes which can effectively reflect the properties of the required stiffness, and the corresponding method of optimal sensors layout will also be studied. A method will be developed to identify the damage of the required stiffness based on the measured structural modal parameters. By means of analytical theory of structural rigidity, further theory will be put forward to guide the analysis for the recover or compensation of structural rigidity deficiency.

由于结构构成机理的特殊性，结构刚度是索网、索穹顶等柔性预张力结构在役期性能评价的核心内容。本项目提出了一种以需求刚度为监测重点的在役期柔性预张力结构刚度性能评价新思路并开展相关的理论研究。以刚度解析理论研究为出发点，目的是能够在结构层面区分线弹性刚度和几何刚度的贡献大小，且能定量描述构件自身弹性刚度和预张力对结构整体刚度的贡献。研究数值方法用于从结构整体刚度中分离出抵抗结构主控荷载变形的需求刚度分量，并以此作为评价在役期结构刚度性能的重点。为配合动力方法对结构刚度的直接检测，研究最能体现需求刚度的结构特征模态的解析方法，并发展相应的传感器优化布置理论。研究基于实测结构模态参数识别结构需求刚度损伤的方法，进而利用刚度解析理论提出能指导结构刚度缺陷修复和补偿的理论方法。

由诸多因素引起的预张力偏差容易导致在役期内柔性预张力结构的刚度发生退化。因此，对此类结构进行刚度监测是工程中面临的重要问题。本项目提出了一种以关键刚度为监测重点的在役期柔性预张力结构刚度性能评价新思路。通过刚度解析分离出了对主控荷载所引起变形起主要抵抗作用的刚度分量，将其定义为重点监测的关键刚度。理论上阐明可通过监测少量模态（目标模态）的参数变化来评价结构关键刚度的变化。建立了目标模态集合的扩展方法以考虑预张力偏差引起的模态变化。提出了阶跃激励荷载的优化方法来增大结构振动响应中目标模态的能量占比，进而提高密频区域内目标模态的识别精度。为保证在役期内实际结构关键刚度的监测精度，提出了面向实际结构目标模态测试的策略，并给出了一种基于贡献模态的振型扩展方法。建立了实际结构关键刚度评价的位移指标，并且分别从静力位移测试和动力模态测试的角度给出了实际结构位移的监测方法。对于结构关键刚度出现损伤的情况，提出了一种基于模态修复的刚度补偿方法并给出了一种补张拉索的优选策略。通过数值分析和模型试验，验证了本研究所提出的目标模态测试理论、刚度性能评价方法和刚度补偿策略的有效性。