The accuracy of the transient dynamic solution depends on the integration time step: the smaller the time step, the higher the accuracy. A time step that is too large introduces an error that affects the response of the higher modes (and hence the overall response). On the other hand too small a time step size wastes computer resources.
An optimum time step size can depend on several factors:
Response frequency: The time step should be small enough to resolve the motion (response) of the structure. Since the dynamic response of a structure can be thought of as a combination of modes, the time step should be able to resolve the highest mode that contributes to the response. The solver calculates an aggregate response frequency at every time point. A general rule of thumb it to use approximately twenty points per cycle at the response frequency. That is, if f is the frequency (in cycles/time), the integration time step (ITS) is given by:
ITS = 1/(20f)
Smaller ITS values will be required if accurate velocity or acceleration results are needed.
The following figure shows the effect of ITS on the period elongation of a single-DOF spring-mass system. Notice that 20 or more points per cycle result in a period elongation of less than 1 percent.
Resolve the applied load-versus-time curve(s). The time step should be small enough to "follow" the loading function. For example, stepped loads require a small ITS at the time of the step change so that the step change can be closely followed. ITS values as small as 1/180f may be needed to follow stepped loads.
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 faces. Otherwise, an apparent energy loss will occur and the impact will not be perfectly elastic. The integration time step can be determined from the contact frequency (fc) as:
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 velocity or acceleration results are needed. See the description of the Predict for Impact option within the Time Step Controls contact Advanced settings for more information.
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.
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.
After calculating the time step sizes using the above guidelines, you need to use the minimum value for your analysis. However using this minimum time step size throughout a transient analysis can be very inefficient. For example in an impact problem you may need small time step sizes calculated as above only during and for a short duration after the impact. At other parts of the time history you may be able to get accurate results with larger time steps sizes. Use of the Automatic Time Stepping procedure lets the solver decide when to increase or decrease the time step during the solution.