流固耦合问题中的附连水质量研究

THE ADDITIONAL WATER MASS IN SOLID-LIQUID COUPLING PROBLEM BY FEM

导弹在水下运行时受到水流,波浪和冲击波等流体动力的激励时弹体将产生振动,其周围流场亦将发生变化,这种流场的变化反过来使结构受到的流体动力激励发生变化,使弹体形成新的振型,这样便形成反馈的流体-结构相互作用的流固耦合问题。在用有限元解决此类问题时,原有的动力方程中将出现附连水质量项,所以对如何运用有限元法解决附连水质量的计算是十分有意义的。本文利用变分原理推导出三维流场中附连水质量的一般公式,并给出二维及三维单元的具体表达式,可供流固耦合问题分析选用。

When a missile is moving in a water body, it will vibrate due to the dynamic effects of the water, as the flow, the wave and the shock wave of the water, which will feed back onto the elastic missile. The vibration changes the condition around the missile, which also effect the vibration of the missile, thus a coupling system of liquid and structure is formed. When we solve this kind of problem by FEM, an additional water mass matrix in the old equation is appeared. Thus it becomes necessary to calculate this additional water mass matrix by FEM. In this paper, based on the variational principle, the equation for calculating this additional water mass is deduced, and the equation for 2D and 3D elements are also given.