The following sections provide additional details about defining integration time step, automatic time stepping, and damping.
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). A time step that is too small wastes computer resources. To calculate an optimum time step, adhere to the following guidelines:
Resolve the response frequency. The time step should be small enough to resolve the motion (response) of the structure. Because 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. For the Newmark time-integration scheme, using approximately twenty points per cycle of the highest frequency of interest results in a reasonably accurate solution; that is, if f is the frequency (in cycles/time), the integration time step (ITS) is given by ITS = 1/(20
f). Smaller ITS values may be required if acceleration results are needed.The following figure shows the effect of ITS on the period elongation of a single-degree-of-freedom spring-mass system:
Notice that 20 or more points per cycle results in a period elongation of less than one percent.
For the HHT time-integration method, the same guidelines for time step should be applied. Note that if the same time step and time-integration parameters are used, the HHT method will be more accurate compared to the Newmark method.
Alternately, you can use the midstep residual criterion to select time step size. If you do, the response frequency criterion is disabled by default. You have the option to enable the response frequency criterion along with the midstep residual criterion. (See item 6 below.)
Resolve the applied load-versus-time curve(s). The time step should be small enough to "follow" the loading function. The response tends to lag the applied loads, especially for stepped loads, as shown in Figure 5.3: Transient Input vs. Transient Response. 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 surfaces. 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 acceleration results are needed. For the mode-superposition method, N must be at least 7 to ensure stability.
You can use fewer than 30 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 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 for a discussion of element size.
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.
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 intermediate 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 issue the MIDTOL command to select 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 analysis. 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.
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 gives the added advantage of incrementing the loads appropriately and retreating to the previous converged solution (bisection) if convergence is not obtained. You can activate automatic time stepping with the AUTOTS command. (For more information on automatic time stepping in the context of nonlinearities, see Nonlinear Structural Analysis.)
Although it seems like a good idea to activate automatic time stepping for all analyses, there are some cases where it may not be beneficial (and may even be harmful):
Problems that have only localized dynamic behavior (for example, turbine blade and hub assemblies), where the low-frequency energy content of part of the system may dominate the high-frequency areas
Problems that are constantly excited (for example, seismic loading), where the time step tends to change continually as different frequencies are excited
Kinematics (rigid-body motion) problems, where the rigid-body contribution to the response frequency term may dominate
Many transient dynamic analysis settings can be automatically set by the program
based on the intended application. When you specify an application type on the
TINTP command, the program automatically defines the
time-integration constants (GAMMA parameter on
TINTP) and several solver settings. Listed below are the
application-based settings you can choose from.
Impact Simulation
Use the command TINTP,IMPA if the intended application is an
impact simulation and you do not want any numerical dissipation. The program follows
the time-integration method that you specify via the TRNOPT
command (Newmark or HHT) and sets GAMMA = 0, resulting in
no numerical dissipation.
High Speed Simulation
Use the command TINTP,HISP if the intended application is a
high speed simulation. The program follows the time-integration method that you
specify via the TRNOPT command (Newmark or HHT) and sets
GAMMA = 0.005, resulting in a small numerical
dissipation.
The Impact Simulation (IMPA) and High Speed Simulation (HISP) options result in little or no energy dissipation. Therefore, it might be hard to achieve convergence under these settings. However, they can accurately capture the dynamic response of a structure. For example, the IMPA and HISP options are recommended in the following cases: analyzing high frequency vibrations in a structure; and studying the wave propagation in a structure during impact.
Moderate Speed Simulation
Use the command TINTP,MOSP if the intended application is a
moderate speed simulation. The program follows the time-integration method that you
specify via the TRNOPT command (Newmark or HHT) and sets
GAMMA = 0.1, resulting in a moderate numerical
dissipation which helps to achieve convergence without significant energy loss. This
setting can be used for most transient dynamic simulations.
Low Speed Simulation
Use the command TINTP,LOSP if the intended application is a low
speed simulation. The program follows the time-integration method that you specify
via the TRNOPT command (Newmark or HHT) and sets
GAMMA = 0.414, resulting in a high numerical
dissipation. The automatic time incrementation is changed such that only one point
per cycle is required per integration time step, therefore allowing use of much
larger time increments.
For the LOSP option, the mid-step convergence check is ignored, overriding the MIDTOL command. The impact constraints for contact elements defined using KEYOPT(7) = 4 are also ignored. These settings help to achieve convergence and larger time increments in a nonlinear transient dynamic simulation. However, because of the higher numerical dissipation, the LOSP option is recommended for low-speed applications where the high frequency vibrations of structures are not of interest; for example, simulating metal forming processes like rolling or extrusion.
Quasi-Static Simulation
Use the command TINTP,QUAS if the intended application is quasi-static. For this option, the program uses backward Euler time-integration. The high numerical dissipation in this time-integration scheme can help to achieve convergence in some problems that are quasi-static in nature but fail to converge in a static analysis. This option is valid for any physics type as well as coupled-physics elements.
Similar to the program default for ANTYPE,STATIC, the loads are ramped by default (KBC,0). The automatic time incrementation does not try to maintain any minimum points per cycle, therefore allowing use of much larger time increments. The mid-step convergence check is ignored, overriding the MIDTOL command. The impact constraints for contact elements defined using KEYOPT(7) = 4 are also ignored.
Applications that can benefit from using the QUAS option include: buckling dominated simulations; models that may display temporary rigid body modes; and simulations that have a snap-through event, causing instability.