Modal Methods for Contact Analysis and Contact Force Reconstruction
Problems of dynamic contact require an extraordinary number of solution iterations with very small time step and are—even in the age of massively parallel computing—a major impediment to efficient computational simulation of dynamics. To address this issue, we consider a modal approach to the contact problem: we consider a displacement basis that consists of eigen-modes for the problem where there is no contact and of eigen-modes from the situation where contact is enforced. A numerical experiment employing this approach is performed for the case of a vertically oriented elastic rod bouncing on a rigid horizontal surface. Numerical results show, and compared to an exact solution, demonstrate that this mixed basis approach is capable of capturing the dynamics of the system in both contacting and non-contacting states. Reaction forces are recovered from modal coordinates. Because of this a problem where a finite number of modes is used to approximate a wave solution, there are of course spurious high frequency responses. The general character of the reaction force of the exact solution is obtained through judicious filtering.
KeywordsModal Contact Force reconstruction Discontinuous basis functions Non-smooth systems