- 摘 要
-
（北京市建筑設(shè)計研究院有限公司， 北京 100045）
［摘要］建筑結(jié)構(gòu)線性屈曲分析是一類典型的廣義特征值問題，可用于評估結(jié)構(gòu)的穩(wěn)定安全度，并可從屈曲模態(tài)判斷結(jié)構(gòu)的薄弱環(huán)節(jié)，用于優(yōu)化結(jié)構(gòu)布置；另外，屈曲分析也可用于構(gòu)件長度系數(shù)的分析，其結(jié)果可直接用于鋼構(gòu)件的設(shè)計與驗算，因此屈曲分析在結(jié)構(gòu)設(shè)計中具有廣泛的實際意義。在具體計算中，由于幾何剛度不具備正定性，屈曲分析與振型計算存在顯著差異，甚至經(jīng)常出現(xiàn)正負(fù)屈曲因子共存的情況，其收斂性弱于一般振型分析，采用傳統(tǒng)算法有時會顯著變慢甚至出現(xiàn)計算困難，而采用與屈曲荷載相關(guān)的Ritz向量法，則可顯著改善收斂速度和求解精度。算例表明，該算法可快速計算任意指定荷載下的大量屈曲模態(tài)，對于負(fù)屈曲因子的情況具有良好的適應(yīng)能力。目前，該方法已集成到北京市建筑設(shè)計研究院有限公司自主研發(fā)的結(jié)構(gòu)設(shè)計軟件Paco中，取得了良好的應(yīng)用效果。
［關(guān)鍵詞］屈曲分析； 幾何剛度； Ritz向量法
中圖分類號：TU375文獻(xiàn)標(biāo)識碼：A文章編號：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
作者簡介：武云鵬，博士，高級工程師，Email：wuyunpeng@biad.com.cn。
