Investigate the Effect of Smaller Time Increments

Repeat the simulation with a smaller time increment, and review the change in the nonzero energies and the reaction force.

In general, smaller time increments lead to more accurate results with the expense of additional computation time. However, smaller time increments can result in convergence difficulties in this contact analysis. The inclusion of stabilization in the analysis introduces viscous forces that oppose sudden changes in the model’s configuration.

Stabilization damps the sudden release of elastic energy that accompanies the arrow snapping into place, allowing the static solver to achieve convergence. Therefore, we can compute the insertion force in a relatively quick static analysis by approximating the actual snapping event.

  1. Create a duplicate analysis case for the small time increment case.
  2. Repeat the simulation with an initial and maximum time increment of 0.02s. Enable energy fraction stabilization and use the default values for the energy fraction (2 x 10-4) and the energy ratio tolerance (0.05).

    The physical process of the arrow snapping into place is highly dynamic. By its nature, a static analysis does not include inertia effects; however, with appropriate use of stabilization we can still generate meaningful results. The primary quantity of interest is the peak force required to move the arrow into its final position.

  3. Create a history plot of the same energy variables that you selected previously.
    The figure below shows the nonzero energy output variables with the smaller time increment. With finer time incrementation, ALLCCDW generally becomes smaller because the change in the contact constraint normal direction between increments is less abrupt.

  4. Create history plots of the reaction force in the x-direction (RT) for both the large and small time increment cases, as shown below.




    The maximum time increment allowed with the large time increments is five times larger than with the small time increments. With small time increments, convergence of the global Newton iterations is more difficult to reach because the arrowhead snaps to the stress-free state near the last stage of the analysis. The “back of the head” touches the rear edge of the wall along the way. With large time increments, this contact is avoided completely. The difference is shown as the reaction force in the x-direction becomes negative for small time increments.

    Use static stabilization with care because the associated viscous damping artificially removes energy from the model and may hide errors. This example demonstrates how the proper use of static stabilization can help find a solution efficiently.

  5. Save your work.

Congratulations, you have successfully completed this example!