正交各向异性加筋板屈曲分析方法研究

Study on the buckling algorithm of orthotropic stiffened plate

为简化正交各向异性加筋板屈曲分析,本文将筋条位移场用其所在位置的板的位移表达, 建立加筋板总势能,通过离散位移场,利用最小势能原理,推导出基于里兹法的正交各向异性加筋板屈曲分析控制方程,采用Matlab进行求解。基于本文推导的方程对单筋和三筋加筋板在不同压剪比下的屈曲荷载和模态进行分析,得到与Abaqus基本一致的结果。加筋板的屈曲荷载随着筋条数增加明显增大;压剪比为1∶1时,各阶屈曲荷载均最小;随着位移函数阶数提高,本文算法计算精度提高,但相应的计算量也显著增大。

In order to simplify the buckling analysis of an orthotropic stiffened plate,the displacement of the stiffeners is expressed by the displacement of the plate at their positions,and the total potential energy of the stiffened plate is established in this paper.Through discrete displacement field and using the Principle of Minimum Potential Energy,the governing equation of buckling analysis of the orthotropic stiffened plate based on Ritz method is derived and solved in Matlab.Based on the equations derived in this paper,the buckling loads and buckling modes of the stiffened plates with a single stiffener and three stiffeners under the application of different compression-shear ratios are analyzed,and the results are basically consistent with those from Abaqus.The buckling loads of the stiffened plates increase obviously with the increase of the number of stiffeners.When the compression-shear ratio is 1∶1,each order buckling load is the lowest.With the increase of displacement function order,the result of this algorithm is more accurate,but the corresponding computation also increases significantly.