Combined Insertion with Subcycling

To further increase the time savings of our problem we combine the dynamic cohesive node insertion and multi-time step subcycling algorithms. As a test case we chose a beam discretized into $800$ equal segments of length = $1.0$ $m$. Subcycling is applied to the left and right regions with the subcycling parameter ${\it m}=10$, as shown in Figure 3.22. Cohesive nodes are dynamically inserted at the $150,000th$ time step ($3750$ $s$), into the middle $200$ nodes, with the simulation being run for $300,000$ time steps ($7500$ $s$) using a $\Delta t= 0.025$ $s$.

Figure 3.22: Test case for dynamic insertion with subcycling.

Figure 3.23: Velocity profile of node $400$ of dynamic cohesive node insertion at time step $150000$ ($3750$ $s$) with nodal subcycling using ${\it m}=10$.

From Table 3.3 we can see that the combined method, using dynamic insertion with subcycling, is more efficient for the individual internal and cohesive force subroutines, although the overall savings is minimal. This low time savings is due to the costly implementation of the subcycling algorithm as well as the increased number of nodal updates of the displacements, velocities and accelerations in the main code.

Table 3.3: Timing results for dynamic cohesive node insertion at time step $150,000$ ($3750$ $s$) with nodal subcycling using ${\it m}=10$. CPU time saving (in %) is given in parentheses.

Subroutine	Reference Case [s]	Combined Case, ${\it m}=10$ [s]
$R^\textrm{co}$	14.32	9.16 ( 36%)
$R^\textrm{in}$	27.33	15.93 ( 42%)
$Total$	117.80	114.57 ( 3%)