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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。
Linear buckling analysis of building structure is a kind of typical generalized eigenvalue problem, which can be used to evaluate the stability and safety of the structure. The buckling mode can be used to judge the weakness of the structure and optimize the structural layout. In addition, buckling analysis can also be applied to the component Length coefficient analysis, the results can be used directly for the design and checking of steel components, so buckling analysis in the structural design has a wide range of practical significance. In the concrete calculation, there is a significant difference between buckling analysis and mode shape calculation because of the lack of positive definite geometric stiffness, and even the coexistence of positive and negative buckling factors often occurs. The convergence is weaker than the general mode shape analysis. Slow or even computationally difficult, and using Ritz vector methods associated with buckling loads can significantly improve convergence speed and accuracy. The examples show that this algorithm can quickly calculate a large number of buckling modes under any given load, and has good adaptability to the case of negative buckling factor. At present, the method has been integrated into Paco, a self-developed structural design software developed by Beijing Institute of Architectural Design and Research Co., Ltd., and has achieved good application results.