弹性杆自接触问题数值模拟的一类罚函数方法

A Penalty Function Approach for Simulating the Self-contact of a Slender Elastic Rod

弹性杆自接触问题的数值计算的一个困难是弹性杆出现自接触时,拓扑结构发生变化。为了解决此问题,引入静电斥力作为惩罚函数,通过对电荷强度的调节,实现接触的"软着陆",从而较好地解决了弹性杆的穿越和拓扑结构变化带来的困难。通过引入Cosserat方程的四元数表示和弹性杆接触集合的检测方法,完善了计算方法的设计。

A computational difficulty in simulating a slender elastic rod with self-contacts is the change of its topological structure at the contact point set. To solve the problem, an artificial electric static repulsion is introduced as the penalty factor in numerical simulation. By adjusting the intensity of the repulsion, the contact can be achieved smoothly so that the difficulty can be solved. We also introduce a quaternion ex- pression of the Cosserat model and a test criterion of the contact set to imnrove the mlmPrienl ~nnrr~,-h