用“膜力因子法”分析简支刚塑性圆板的大挠度动力响应

在板的变形过程中,当其挠度与厚度同量级时,膜力的作用与弯矩的作用同样重要;当其挠度超过厚度甚至接近板的面内尺寸的量级时,相对于弯矩的作用,膜力的作用是更主要的。本文发展了一种基于能量平衡的简便的“膜力因子法”,有效地解决了当板的挠度达到厚度量级时弯矩和膜力联合作用问题;用这种方法并结合塑性膜阶段的分析成功地求解了简支刚塑性圆板在冲击载荷作用下的大挠度塑性响应问题。所得结果与Florence实验结果符合良好,比已有理论近似结果有所改进。

ANALYSIS OF THE LARGE DEFLECTION DYNAMIC RESPONSE OF SIMPLY-SUPPORTED CIRCULAR PLATES BY THE "MEMBRANE FACTOR METHOD"

Based on the energy equilibrium, a new procedure called Membrane Factor Method is developed to analyze the dynamic plastic response of plates with deflections in the range where bending moments and membrane forces both are important. The final deflection of a simply-supported circular rigid plastic plate loaded by a uniformly distributed impulse is obtained. In comparison with other approximate solutions, the present method is found to be simplier and the results in better agreement with the corresponding experimental values recorded by A. L. Florence.