线弹性多体接触问题建模方法的研究

A STUDY ON THE MODELING OF LINEAR ELASTIC MULTIBODY CONTACT PROBLEMS

提出了一种线弹性多体接触问题的有限元建模及求解方法。通过静态凝态聚,将增量方程变换为仅与接触边界节点自由度有关的方程以提高其迭代效率。根据4种节点接触状态的相容关系建立接触状态修改准则加速了判断的迭代过程。最后,采用变步长增量求解方法提高了计算效率,并通过经典Hertz接触问题的算例验证了方法的有效性。

In this paper, an approach is developed to model the contact problems of linear elastic multi-boby by using FEM. In order to improve the iterative efficiency the contact increment equations regarding only with the contact nodes are derived from the system increment equations through a technique of static condensation. According to the compatibilities among four contact patterns, a critrion for the amendment of contact pattern is made, with the aid of this criterion, the computation time can be saved. Finally, the variable increment loading is utilized to improve the efficiency and accuracy. As a numerical example, the classical Hertzen problem is used to verify the effectiveness of the method.