结构撞击响应的一种弹性模型及其精细求解

AN ELASTIC MODEL AND ITS PRECISE SOLUTION FOR STRUCTURAL IMPACT RESPONSE

在弹性撞击问题的经典有限元解法中,通常将靶体和撞击物独立考虑。该文基于把靶体和撞击物看成一个整体的思想,将撞击问题转化为振动问题,进而对于考虑和不考虑接触刚度的情况,分别使用有限元法建立了结构撞击问题的弹性模型,得到了离散后的动力微分方程,并利用精细积分方法给出了问题的动态响应解。算例表明所用方法能够滤去低阶有限元导致的虚假高频模态;另外,精细积分法还具有受时间步长限制小、精度高和无条件稳定等特点。

In classical finite element method concerning of elastic impact problem, the target and the impacting body are often separately considered. Based on the view of regarding the target and the particle as one integrated system, the impacting system is transformed into a vibration problem. For the case considering or not considering the contact stiffness, the dynamic models are established for vibration systems respectively using finite element method, and the dynamic differential equations are obtained. Then the precise integration method is introduced to solve the time response. The numerical examples show that one of the most important advantages of the proposed method is that the false high frequency modes can be filtered. Furthermore, the precise integration method has other characteristics such as unconditional stability, high accuracy and few limits to time step selection.