含缺陷的固支梁在阶跃载荷作用下塑性动力响应的完全解

COMPLETE SOLUTIONS FOR DYNAMIC PLASTIC RESPONSE OF CLAMPED IMPERFECT BEAMS SUBJECTED TO STEP LOADING

本文分析了含两个对称缺陷的固支梁在阶跃载荷作用下的刚塑性动力响应,给出了不同载荷幅值区段的响应模式,求得了完全解,指出在结构参数和缺陷参数与外载之间存在着比较复杂的关系。表现在结构的响应模式高达十几种。它们可能是双自由度的三铰(整体五铰)模式,也可能是单自由度的双铰(整体三铰)模式。但是当载荷幅值很高时,都会出现一种固定的三铰模式。另一方面,在缺陷处通常存在一个塑性铰,这种现象反映了缺陷造成的应变集中效应。

The paper examines the dynamic response of a rigid-plastic clamped beam with two symmetric imperfections about the mid-span cross-section when subjected to step loading.The complete solutions corresponding to different magnitude of loading have been obtained.It is found that there are quite a complicated relations among the para- meter of structure,location of the imperfection and the magnitude of external loading because the response modes reach up to more than ten kinds.For half span,they may be three-hinge mechanisms of two degree of freedom(five hinge for whole span),or double-hinge mechanisms of one degree of freedom(three hinge for whole span).Ho- wever,when magnitude of the loading exceeds a certain level,one kind of three-hinge mechanisms will appear.On the other hand,a plastic hinge usually forms at the cross section where the imperfection or crack exists.Obviously,this indicates a concentra- tion of strain localized by the imperfection or crack.