端部受斜撞击作用悬臂梁的弹塑性动力响应模式

基于大变形动力控制方程并利用有限差分离散分析,研究了斜撞击作用下弹塑性悬臂梁的动力响应．通过对屈服函数以及弯矩、轴力在动力响应过程中分布规律的分析,阐明了斜撞击下恳臂梁的弹塑性动力响应模式和斜撞击的轴向分量对变形机制的影响．研究表明,弹塑性响应过程可划分为四个阶段,对应的变形模式为：“压缩塑性区扩展”模式,“广义移行塑性铰”和“压缩塑性区收缩”混合模式,“驻定塑性铰”模式,“弹性自由振动”模式．与刚塑性分析所假定的两相变形模式比较,弹塑性应响分析证实了响应早期的瞬态轴向压缩模式和梁根部“驻定塑性铰”模式的存在性,肯定了刚塑性分析所假定变形模式的主要特征．斜撞击的轴向分量在撞击发生的瞬时主导了梁的变形,使梁呈现同承受横向冲击明显小同的变形规律．随着响应的深入,轴向分量迅速衰减,其对截面屈服的贡献非常微弱,由横向分量引起的弯曲挠动在大部分时间内主导和控制梁的变形．数值计算结果表明,斜撞击载荷的质量、撞击速度和角度是影响梁动力响应的重要因素．

ELASTIC-PLASTIC DYNAMICAL RESPONSE MECHANISM OF A CANTILEVER BEAM SUBJECTED TO OBLIQUE IMPACT AT ITS TIP

By employing large deformation governing equations expressed in the form of finite difference,thedynamical responses of elastic,perfectly plastic cantilever subjected to an oblique impact at its tip are numerically studied.Through analyzing the instantaneous distribution of the yield function,bending moment and axial force during early time response,the elastic-plastic deformation mechanism and the influence of axial component of oblique impact on the dynamical response of cantilever beam are discussed.It is shown that the deformation mechanisms of an elastic-plastic cantilever subjected to an oblique impact consists of four phases,i.e."Expanding compressed plastic region"mode;"Generalized traveling plastic hinge" and "shrinking plastic region"mixed mode;"Stationaryplastic hinge"mode and "Elastic vibration"mode.As compared with the rigid,perfectly plastic approach,this approach can capture the same primary features of deformation mechanisms.This analysis confimed the existence of the mode of shriking plastic region and the stationary hinge mode that do not appear in the rigid-perfectly plastic approach.It is also found that the beam's deformation is mainly controlled by the axial component of oblique impact in the early phase of dynamic response,and the deformation mechanism is obviously different from the case of transverse impact.With the further development of response,the axial component attenuates rapidly and gives negligible contribution to the yielding of the beam cross-section.At the same time,the bending moments along the cantilever develop gradually and dominate the beam's deformation.The numerical results indicate that themass,impact speed and oblique angle are the important factors that influence the elastic-plastic dynamical response of a cantilever beam.