圆环形薄板大挠度变形有限元分析比较研究

摘要

Annular thin plate is an important part of automobile shock absorber,which belongs to the typical non-linear deformation of large deflection. Traditional calculation method will cause large errors,or complicated cal-culation which can not be used in engineering conveniently. With the aid of and modern engineering analysis software,the large deflection of circular thin plate of different shock absorbers specifications were studied using the method of finite element analysis. According to von Kármán differential equation,combining with Chien per-turbation method,the analytical expression of the large deflection were presented. Undetermined coefficients of the analytical expression were been fitting out. For different situations,such as fixed radial ratio,or inner/out-side diameter,the calculation analysis and error comparison were carried out. Numerical calculation showed that the method is reasonable and reliable,simple and quick,with an error below 3%,and precision is higher,which can meet with the needs of engineering design and analysis.%环形薄板是汽车减振器中的一个重要零件，属于典型的大挠度非线性变形，传统的计算方法要么产生误差较大，或者计算繁琐不利于工程应用。本文借助于现代分析软件，利用有限元分析方法对汽车减振器中不同规格环形薄板的大挠度变形情况进行了研究。根据von Kármán提出的微分方程，结合钱氏摄动法给出了求解大挠曲变形的解析表达式，拟合出了解析式中的待定系数的数学表达式，并针对固定半径比、内/外径等不同情况进行了计算分析和误差比较。数值计算证明，使用的方法合理可靠，求解精度高、简单快捷实用，误差在3％以下，完全可以满足工程设计分析的需要。