基于改进应变能法的无环索弦支穹顶拉索重要性评价

李雄彦; 刘人杰; 邹瑶; 薛素铎; 王超

doi:10.13206/j.gjgSE20041903

基于改进应变能法的无环索弦支穹顶拉索重要性评价

doi: 10.13206/j.gjgSE20041903

1. 北京工业大学空间结构研究中心, 北京 100124;
2. 烟台大学土木工程学院, 山东烟台 264005

基金项目:

The authors gratefully acknowledge the supports from the National Natural Science Foundation of China (51778017, 51878014) and Beijing Natural Science Foundation (8172011).

详细信息

作者简介:
李雄彦：刘人杰,Email:liurenjie2011@163.com

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出版历程
- 收稿日期: 2020-04-19

Importance Evaluation for Cables in the Loop-Free Suspen-Dome Based on an Improved Strain Energy Method

1. Spatial Structures Research Center, Beijing University of Technology, Beijing 100124, China;
2. School of Civil Engineering, Yantai University, Yantai 264005, China

Funds:

The authors gratefully acknowledge the supports from the National Natural Science Foundation of China (51778017, 51878014) and Beijing Natural Science Foundation (8172011).

摘要

摘要: 基于上部网壳总应变能变化量峰值和上部网壳杆件应变能变化率标准差提出一种改进应变能法，用于评价无环索弦支穹顶不同部位的拉索重要性。改进应变能法采用上部网壳总应变能变化量峰值作为主要评价指标，其目的是表征断索后上部网壳的最不利状态且避免断索导致的下部预应力索杆体系应变能损失对以结构总应变能为指标的评价结论的干扰。改进应变能法采用上部网壳杆件应变能变化率标准差作为辅助评价指标的目的是考虑上部网壳不同部位应变能变化的分布情况。
以含有三层无环索预应力索杆体系的直径100 m的无环索弦支穹顶为例。首先，建立结构有限元分析模型，通过施加预应力和外荷载得到无环索弦支穹顶的荷载态。然后，基于荷载态采用杆件瞬时移除技术完成断索模拟，采用中心差分积分模式的修正拉格朗日列式增量解法求解断后无环索弦支穹顶的杆件内力时程和节点位移时程。同时，基于杆件内力时程和节点位移时程，求得上部网壳每根杆件的应变能时程。最后，在此基础上，求得上部网壳总应变能时程和上部网壳杆件应变能变化率标准差。如果某部位断索后发生了结构连续倒塌，则该位置拉索的重要性排在首位或并列排在首位；如果未发生结构连续倒塌，则根据不同部位断索后的上部网壳总应变能变化量峰值和上部网壳杆件应变能变化率标准差为指标评价不同部位拉索的重要性。比较上部网壳总应变能变化量峰值，当断索后上部网壳总应变能变化量峰值越大，则该部位的拉索重要性越高；当上部网壳总应变能变化量峰值较为接近时，应补充比较上部网壳杆件应变能变化率标准差：上部网壳杆件应变能变化率标准差越大，拉索重要性越高。
结果显示：无环索弦支穹顶的所有拉索预应力乘以相同倍数后以及所有拉索的截面面积乘以相同倍数后，采用以结构总应变能作为评价指标的拉索重要性评价结论会随预应力倍数和截面面积倍数的变化发生明显变化。这种现象的主要原因是下部预应力索杆体系应变能下降而上部单层网壳应变能上升，导致结构总应变能变化规律复杂。基于改进应变能法，采用上部网壳总应变能变化量峰值和上部网壳杆件应变能变化率标准差作为评价指标，则拉索重要性评价结论不随预应力倍数、截面面积倍数和上部网壳形式的变化而变化，避免了下部预应力索杆体系应变能下降带来的干扰，且可以有效区分不同部位的拉索重要性。
研究表明：基于结构总应变能指标的拉索重要性评价方法不适用于无环索弦支穹顶，提出的改进应变能法可以有效评价无环索弦支穹顶不同部位拉索的重要性。基于改进应变能法分析发现：最外层预应力索杆体系中索力较大，断索的不对称变形导致不同部位拉索的重要性略有区别，拉索的中间段的重要性略小于其余各段；其余各层的索力远小于最外层，不同部位拉索的重要性没有明显区别。不同层预应力索杆体系之间，最外层的拉索重要性最高，向内依次降低。分析中还发现，断索部位附近的网壳杆件应变能变化较为明显，而距离断索部位较远的网壳杆件受到的影响很小；断索仅对无环索弦支穹顶的局部有影响，对结构主体的影响不大。
- 空间结构 /
- 弦支穹顶 /
- 无环索弦支穹顶 /
- 拉索重要性 /
- 应变能
Abstract: Combining the peak change of the total strain energy of the reticulated shell and standard deviation of the strain energy change rates of all reticulated shell members, an improved strain energy method for evaluating the importance of the cables in the loop-free suspen-dome is proposed. Taking two 100 m-span loop-free suspen-domes as examples, the central difference method is employed to calculate the dynamic response and obtain the time history of internal forces and displacements in seven cable-rupture schemes in each model. The peak change of the total strain energy of the reticulated shell and standard deviation of the strain energy change rates of all the reticulated shell members are calculated according to the dynamic response. The results show that the importance ranking results by current strain energy method varies with magnitudes of cross-sectional areas and pre-tension levels of the cable-strut system. The importance ranking results by improved strain energy method is stable and only determined by the location of the cable. It is concluded that the improved strain energy method is reasonable in evaluating the cable importance of the loop-free suspen-dome. It is also found that an outer cable layer is more important than an inner cable layer, and cables in a layer share approximate the same importance. The reticulated shell members with increased strain energy are mostly distributed near the ruptured cable, and members that are far away from the ruptured cable are less affected.
- spatial structures /
- suspen-dome /
- loop-free suspen-dome /
- importance of cable /
- strain energy

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