耦合有限元物质点法及其在流固耦合问题中的应用

COUPLED FINITE ELEMENT MATERIAL POINT METHOD AND ITS APPLICATION IN FLUID-STRUCTURE INTERACTION

有限元法在求解大变形问题时会遇到网格畸变和时间步长严重减小的问题。物质点法在大变形问题中无网格扭曲问题,且粒子代表了物质流动,无需界面追踪算法。但在小变形问题中,物质点法的精度和效率均低于有限元法。该课题组针对冲击侵彻问题提出的耦合有限元物质点法分别采用有限元法和物质点法模拟小变形和大变形物体,物体间的相互作用通过接触算法实现,既保留了有限元针对小变形问题高精度高效率的特点,又避免了材料大变形给有限元法带来的网格扭曲和时间步长严重减小的问题,还可以自动追踪界面。在流固耦合问题中,固体变形较小而流体变形较大,因此也适合用耦合有限元物质点法求解。该文简要介绍了耦合有限元物质点法的基本原理,并将其应用于流固耦合问题中,取得了较好的效果,表明耦合有限元物质点法是分析流固耦合问题的一种有效的方法。

In large deformation problems, the FEM will encounter mesh distortion and severe time step reduction. On the contrary, the material point method （MPM） does not suffer these difficulties. However, the accuracy and efficiency of the MPM are lower than the FEM in small deformation problems. Recently, a coupled finite element material point method （CFEMP） was proposed by our group to fully take advantages of both the FEM and MPM. In the CFEMP, the FEM and MPM are used to simulate the small and large deformation bodies, respectively. The interaction between two bodies is realized by the contact algorithm. Thus, the high accuracy and efficiency of the FEM is retained, while mesh distortion and severe time step reduction are avoided. The CFEMP is very suitable for the fluid-structure interaction problem, because the structure deforms little but the fluid deforms severely. In this article, the CFEMP is first reviewed briefly and then applied to the fluid-structure interaction problem. The results show that the CFEMP is a powerful tool for modeling fluid-structure interaction problems.