阶跃载荷作用下变截面悬臂梁的弹塑性响应模式

Elastic-plastic dynamic response mechanism of a variablecross-section cantilever beam subjected to step load

利用有限差分离散控制方程进行数值分析,研究了阶跃载荷作用下变截面悬臂梁的弹塑性动力响应。通过对不同阶跃载荷作用下,响应各时刻弯矩分布规律的细致分析,清晰地阐明了变截面悬臂梁的弹塑性动力响应模式。研究表明,对于中载工况,整个响应过程只在梁根部形成塑性铰;对于高载工况,响应过程在梁跨中形成塑性铰的基础上,还增加了在半梁左侧存在塑性区、梁的根部存在驻定塑性铰等响应模式。弹塑性响应分析肯定了刚塑性分析所假定的变形模式的主要特征,同时也指出了刚塑性分析模型的不足,因而增进了对于梁的变形机制的认识和理解。

<Abstrcat>Employed the method of finite difference to discrete the governing equation, the dynamic response of an elastic, perfectly plastic variable cross-section cantilever beam subjected to step load was investigated in (pre)sent paper. The elastic-plastic dynamic response mechanisms of the beam subjected to various step loads were discussed meticulously through analyzing the instantaneous distribution of the bending moment during the course of response. It can be seen from the present analysis that only one plastic hinge is formed at the root of beam in the case of moderate load, but in the case of intense load, the mechanism was quite complicated: on the basis of plastic hinge formed at the internal of the beam, the mode of plastic zone at the left part of beam and the mode of stationary plastic hinge at the root of beam were also discovered during the whole dynamic response. The elastic-plastic analysis confirmed the main feature of the dynamic response mechanism supposed by method of the rigid plastic, and meanwhile the shortage of that theory was pointed out.