受冲击作用弹塑性圆板动力响应的弹性效应

ELASTIC DEFORMATION EFFECTS ON DYNAMIC RESPONSEOF A ELASTIC-PLASTIC CIRCULAR PLATE UNDERIMPULSIVE LOAD

利用有限差分离散微分方程进行计算分析,研究冲击载荷作用下弹塑性圆板的早期动力响应,通过对瞬态径向弯矩分布规律的细致分析,阐明弹塑性固支圆板响应过程中弹性效应对其变形历史的影响.研究表明:弹塑性响应过程可划分为八个阶段,对应的变形模式为:“单铰圆模式”,“双铰圆模式”,“五铰圆模式”,“四铰圆模式”,“三铰圆模式”,“双铰圆模式”,“双驻定铰圆模式”,“弹性振动模式”.与刚塑性分析所假定的三相的变形模式比较,弹塑性响应分析证实了固支边界“驻定塑性铰圆”的存在性.虽然刚塑性分析所假定的第一相位移响应模式并不存在,但第二相和第三相响应模式则得到了证实.由于这两相及相应弹塑性分析的两个阶段持续时间都较长,因而也肯定了刚塑性分析所假定变形模式的主要特征.弹性效应对于板内“移行铰圆”的影响比较大,它不但使“移行铰圆”出现“回退”现象,还使得“移行铰圆”的个数增加到三个;对于圆心处的“塑性铰圆”,弹性效应则使得它的符号出现由负向到正向的反复变化.因此,弹性效应对弹塑性板的变形历史影响十分明显.

By employing the finite difference method to numerically solve the governing differential equation in its discrete form, the dynamic response is studied for an elastic, perfectly-plastic (e-p-p) clamped circular plate subjected to impulsive loading. The elastic effects on the deformation mechanism of the plate are discussed through carefully analyzing the instantaneous distribution of the radial bending moment during early time response.It can be seen from the present analysis that the deformation mechanisms of an impulsively loaded elastic-plastic plate consist of eight phases, i.e. 'Single plastic hinge-ring' mode; 'Double plastic hinge-ring' mode; 'Five plastic hinge-ring' mode; 'Four plastic hinge-ring' mode; 'Three plastic hinge-ring' mode; 'Double plastic hinge-ring' mode; 'Double stationary plastic hinge-ring mode; 'Elastic vibration' mode. Through a comparison with the three phase's deformation mode obtained by using rigid, perfectly-plastic (r-p-p) approach, the 'stationary plastic hinge-ring' mode at the clamped boundary is verified by e-p-p analysis. The second phase and the third phase in r-p-p analysis can also be observed in the present e-p-p analysis while the first phase is not found. Since the duration of response of the second and third phase in the r-p-p analysis and the corresponding phase in e-p-p analysis is relatively long, the primary feature of the deformation mechanisms are accordant for both of the analysis methods.The elastic effects not only result in the 'travelling plastic hinge-ring' moving back and forth but also make its number increase to 3. In addition, also as the elastic influence, the sign of the 'stationary plastic hinge-ring' at the center of the plate changes alternately from negative to positive. Therefore, the elastic effects on the deformation history of the impacted plate are significant.