Motivated by the grave consequences of an aircraft impact into robust engineering structures like nuclear power plants, we investigate the time-dependent reaction force during the impact of a crushing, elongated elasto-plastic missile into a robust elastic target. We derive a set of partial differential equations on a time-dependent domain to describe the impact. The simplest case of a homogeneous, cylindrical aircraft fuselage impacting a rigid target is solved analytically by using conformal mapping. After developing a numerical scheme for the case of an elastic target, we find that a simple dimensionless number, the damage potential, gives an accurate prediction of the impact force. The peak reaction force during the impact is found to exceed the initial impact force by up to 20%; hence the often applied strategy to estimate the peak force as the initial impact force is not a conservative approach. This effect is due to a resonant vibration in both the missile and the target. Predicted and computed parameters at which this counter-intuitive, resonance-like behavior occurs are shown to agree well.

受飞机撞击核电站等坚固工程结构的严重后果的推动，我们研究了在破碎、拉长的弹塑性导弹撞击坚固的弹性目标期间随时间变化的反作用力。我们在依赖于时间的域上推导出一组偏微分方程来描述影响。最简单的均匀圆柱形飞机机身撞击刚性目标的情况是通过使用保形映射来解析解决的。在为弹性目标的情况开发数值方案后，我们发现一个简单的无量纲数，即损坏潜力，可以准确预测冲击力。发现冲击过程中的峰值反作用力超过初始冲击力高达 20%；因此，将峰值力估计为初始冲击力的常用策略并不是一种保守的方法。这种效应是由于导弹和目标的共振造成的。这种违反直觉的、类似共振的行为发生时的预测和计算参数显示出很好的一致性。