Mechanical APDL Structural Analysis Guide

3. Resolve the contact frequency. In problems involving contact (impact), the time step should be small
   enough to capture the momentum transfer between the two contacting surfaces. Otherwise, an apparent
   energy loss will occur and the impact will not be perfectly elastic. The integration time step can be de-
   termined from the contact frequency (fc) as:

c c= π

where k is the gap stiffness,m is the effective mass acting at the gap, and N is the number of points

per cycle. To minimize the energy loss, at least thirty points per cycle of (N = 30) are needed. Larger

values of N may be required if acceleration results are needed. For the mode-superposition method,

N must be at least 7 to ensure stability.

You can use fewer than thirty points per cycle during impact if the contact period and contact mass

are much less than the overall transient time and system mass, because the effect of any energy

loss on the total response would be small.

4. Resolve the wave propagation. If you are interested in wave propagation effects, the time step should
   be small enough to capture the wave as it travels through the elements. See Build the Model (p. 110) for
   a discussion of element size.


5. Resolve the nonlinearities. For most nonlinear problems, a time step that satisfies the preceding guidelines
   is sufficient to resolve the nonlinearities. There are a few exceptions, however: if the structure tends to
   stiffen under the loading (for example, large deflection problems that change from bending to membrane
   load-carrying behavior), the higher frequency modes that are excited will have to be resolved.


6. Satisfy the time step accuracy criterion. Satisfaction of the dynamics equations at the end of each time
   step ensures the equilibrium at these discrete points of time. The equilibrium at the intermediate time
   is usually not satisfied. If the time step is small enough, it can be expected that the intermediate state
   should not deviate too much from the equilibrium. On the other hand, if the time step is large, the inter-
   mediate state can be far from the equilibrium. The midstep residual norm provides a measure of the
   accuracy of the equilibrium for each time step. You can use the MIDTOL command to choose this criterion.
   See the MIDTOL command description for suggested tolerance values. See also Midstep Residual for
   Structural Dynamic Analysis in the Mechanical APDL Theory Reference.

After calculating the time step using the appropriate guidelines, use the minimum value for your ana-
lysis. By using automatic time stepping, you can let the program decide when to increase or decrease
the time step during the solution. Automatic time stepping is discussed next.

Caution

Avoid using exceedingly small time steps, especially when establishing initial conditions.

Exceedingly small numbers can cause numerical difficulties. Based on a problem time scale

of unity, for example, time steps smaller than 10-10 could cause numerical difficulties.

5.6.2. Automatic Time Stepping

Automatic time stepping, also known as time step optimization, attempts to adjust the integration time
step during solution based on the response frequency and on the effects of nonlinearities. The main
benefit of this feature is that the total number of substeps can be reduced, resulting in computer resource
savings. Also, the number of times that you might have to rerun the analysis (adjusting the time step
size, nonlinearities, and so on) is greatly reduced. If nonlinearities are present, automatic time stepping

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Transient Dynamic Analysis