均匀受压矩形管的屈曲后板组效应研究

本文根据势能驻值原理,建立了均匀受压矩形管的大挠度弹性屈曲理论,用于分析屈曲后相邻板件间的相互约束作用,即屈曲后板组效应。该方法通过引入拉格朗日乘子,使系统总势能取驻值的同时,形函数能满足一系列基本的,但非完备的边界条件;在此基础上采用增量法将非线性方程组线性化,从而确定给定荷载下矩形管的受力状态及变形。由于系统总势能是以解析式的形式给出,且仅需取有限的级数项就可达到满意的精度,故该半解析法具有计算效率高的特点。目前许多国家的钢结构设计规范中,在计算受压板件的有效宽度时,常采用板组约束系数来考虑板组效应。由于有效宽度法本身考虑了板的屈曲后强度,而约束系数多数却是建立在小挠度弹性屈曲理论上的,故有必要分析板件的屈曲后板组效应。本文详细讨论了矩形管的屈曲后板组效应,并与小挠度理论给出的计算结果进行比较,得出了均匀受压矩形管屈曲后板组效应减弱的结论。

Study on Postbuckling Plate Assembly Effect of Rectangular Tube under Uniform Compression

Based on the energy principle,the large deflection plate theory of box section under uniform compression was established.The energy method was applied to analyze the restraining action exerted by adjacent plate element in the same section,which is called plate assembly effect(PAE) in the stage of postbuckling.By introducing Lagrange multiplier,the assumed deformation functions,which were expressed in Fourier series,can satisfy the essential but not necessarily the natural boundary conditions when the potential energy of system takes the stationary value.The incremental method was then applied to linearize the equations and thus the stress state and deformation of box section were determined under a given load.Since the procedure is semi-analytical in the sense that all the energy formulations are derived analytically,and only a few terms of series are required to produce a result with satisfying precision,this method is very efficient.In many update steel structure codes,the restraining coefficient is often adopted in effective width approach to taken PAE into account.The effective width approach utilize the reserved strength of postbuckling,while the restraining coefficient is derived on the small deflection plate theory,it is necessary to study PAE of postbuckling.PAE of box section was fully discusses,and the results were compared with small deflection theory.It is concluded that the plate assembly effect of box section under uniform compression is weakened in the stage of posbuckling.