相似理论及其在板壳屈曲分析中的应用研究进展

Review for Similitude Theory and Its Applications in Analysis of Plate and Shell Buckling

因受试验设备、场地和经济等条件的影响,对大型板壳结构开展原型结构屈曲试验比较困难。因此,利用相似理论进行缩尺模型设计,对于大型板壳屈曲模型试验研究具有重要意义。首先,对相似理论的发展和主要内容进行回顾,并对主要的屈曲相似分析方法,包括量纲分析法、控制方程法和能量法的原理及特点进行了介绍与比较。其次,根据方法的不同,对板壳屈曲相似分析研究进展进行总结与评述。量纲分析法是最早也是目前仍应用于板壳结构屈曲相似理论研究的一种方法。基于板壳屈曲控制方程和方程解的相似变换方法应用较为广泛,其相似条件具有明确的物理意义。着重介绍了基于结构体系总能量的相似分析法,该方法已应用于含缺陷加筋板壳的屈曲相似分析,并得到了一些有益的结论。最后,讨论了相似理论在板壳屈曲研究中面临的问题和难点,并展望了需要研究的方向。

Due to the influence of test equipment,site and economy,it is difficult to carry out the prototype buckling test of large plate and shell structures.Therefore,the scale model design is great significance for the buckling model test of large plates and shells based on similitude theory.Firstly,the development and main contents of similitude theory were reviewed.The characteristics of dimensional analysis method,similitude theory applied to governing equations and energy method were discussed.Secondly,the research progress of the application of similitude theory for the buckling analysis of plates and shells was summarized.Dimensional analysis is one of the earliest and still applied methods to the buckling similitude theory of plate and shell structures.The similarity transformation method based on the governing equations and solutions of plate and shell buckling is widely used,and its similitude condition has clear physical significance.The similitude method based on the total energy of structural system was mainly introducted,which has been applied to the buckling similitude analysis of stiffened plates and shells with imperfections,and some useful conclusions are obtained.Finally,the problems and difficulties of the similitude theory study of plate and shell buckling were discussed,and the research directions were prospected.