Damping of Blind Insertion

The nodal oscillations resulting from blind insertion must be minimized in order to obtain an accurate solution. One known method of minimizing general oscillations is to remove some energy from a system through the use of linear damping, as discussed in Chapter 2.

Figures 4.10 and 4.11 show the result of applying linear damping on the dynamically inserted cohesive elements for the ``horizontal'' and ``mixed'' cases. From trial and error the optimal damping coefficients for insertion at $t = 2500 \Delta t$ and $5000 \Delta t$ are $\eta = 3.8$ and $\eta = 4.4$ for the "horizontal" case, and $\eta = 2.4$ and $\eta = 4.3$ for the ``mixed'' case, respectively. From the figures, we can see that linear damping does minimize the oscillations after some initial time, although, our experimentation has shown that if the coefficient is too large, the solution can diverge from the reference solution.

Figure 4.8: Normalized separation of the tracking node for "horizontal" blind insertion at the $0th$ ($0.0$ $s$), $2500th$ ($1.0$ $s$) and $5000th$ ($2.0$ $s$) time step.
Figure 4.9: Normalized separation of the tracking node for "mixed" blind insertion at the $0th$ ($0.0$ $s$), $2500th$ ($1.0$ $s$) and $5000th$ ($2.0$ $s$) time step.

Figure 4.10: Normalized separation of the tracking node for "horizontal" blind insertion with damping at the $0th$ ($0.0$ $s$), $2500th$ ($1.0$ $s$ with $\eta = 3.8$) and $5000th$ ($2.0$ $s$ with $\eta = 4.4$) time step.
Figure 4.11: Normalized separation of the tracking node for "mixed" blind insertion with damping at the $0th$ ($0.0$ $s$), $2500th$ ($1.0$ $s$ with $\eta = 2.4$) and $5000th$ ($2.0$ $s$ with $\eta = 4.3$) time step.