（北京市建筑设计研究院有限公司， 北京 100045）

［摘要］建筑结构线性屈曲分析是一类典型的广义特征值问题，可用于评估结构的稳定安全度，并可从屈曲模态判断结构的薄弱环节，用于优化结构布置；另外，屈曲分析也可用于构件长度系数的分析，其结果可直接用于钢构件的设计与验算，因此屈曲分析在结构设计中具有广泛的实际意义。在具体计算中，由于几何刚度不具备正定性，屈曲分析与振型计算存在显著差异，甚至经常出现正负屈曲因子共存的情况，其收敛性弱于一般振型分析，采用传统算法有时会显著变慢甚至出现计算困难，而采用与屈曲荷载相关的Ritz向量法，则可显著改善收敛速度和求解精度。算例表明，该算法可快速计算任意指定荷载下的大量屈曲模态，对于负屈曲因子的情况具有良好的适应能力。目前，该方法已集成到北京市建筑设计研究院有限公司自主研发的结构设计软件Paco中，取得了良好的应用效果。

［关键词］屈曲分析； 几何刚度； Ritz向量法

中图分类号：TU375文献标识码：A文章编号：1002-848X(2017)18-0105-05

Research and engineering application of structural linear bucking analysis algorithm

Wu Yunpeng, Han Bo, Zeng Qiang, Miao Qisong

(Beijing Institute of Architectural Design, Beijing 100045, China)

Abstract:The linear buckling analysis of building structure is a kind of typical generalized eigenvalue issue, which can be used to evaluate the stability of structure and can be used to judge weak parts of the structure based on buckling mode to optimize the structural arrangement. In addition, the buckling analysis can also be used for the analysis on component length factor, and the results can be directly used for the design and checking of steel components, so the buckling analysis has a wide range of practical significance in the structural design. In actual calculation, because the geometric stiffness does not have positive definite property, buckling analysis and vibration calculation have significant differences, and there is even sometimes coexistence of positive and negative buckling factors. Moreover, the convergence is weaker than the general vibration analysis, and the convergence speed is sometimes significantly slowed down and even the calculation is difficult when adopting traditional algorithm. However, if Ritz vector method related to buckling load is used in structural buckling analysis, the convergence speed and the solution precision can be improved obviously. Examples show that the algorithm can quickly calculate a large number of buckling modes under any given load, and has good adaptability for the case of negative buckling factors. At present, the proposed method has been incorporated completely into Paco which is a program for structural design independently developed by Beijing Institute of Architectural Design, and satisfied effect has been achieved.

Keywords:buckling analysis; geometric stiffness; Ritz vector method

作者简介：武云鹏，博士，高级工程师，Email：wuyunpeng@biad.com.cn。