Integration Methods

Activating the command: Setup Model Setup Parameters Advanced Integration tab

The information on this page applies to the following analysis types except if indicated:

• Mechanical Event Simulation (MES)
• Static Stress with Nonlinear Material Models
• MES Riks Analysis

There are three suggested integration methods available for a nonlinear stress analysis. These can be selected in the Time integration method suggested for type of analysis drop-down box in the Integration tab. (Notes: MES stands for mechanical event simulation, NLS is nonlinear static, and LS is linear static.)

• The General: MES, NLS option allows for the damping of high frequencies without loss of temporal integration accuracy. This option is also appropriate for many nonlinear static problems, when performed using MES. (The General option is not available for analysis types of Static Stress with Nonlinear Materials or MES Riks.)
• The Static: NLS, LS option is the classical Newmark method. It allows for high frequency damping but at the cost of some temporal integration accuracy. The loss of accuracy is generally not important in static problems, since the results are the end-state, not the time history. It should be noted that a time integration method is needed for static problems because pseudo time is used to solve such problems.
• The Static II: NLS option uses the Wilson-Theta method. It is used for nonlinear static analyses. This option reverts to the Static: NLS, LS option if any brick elements in the model do not enforce compatibility.

General MES, NLS Integration Method

If you are using the General: MES, NLS integration method, you must specify a value in the Parameter for (MES) integration method field. Valid input values are 0 and 1, with 1 being the default value:

• A value of 1 filters out high-frequency vibrations and noise, and is shown to yield more stable solutions (easier convergence).
• A value of 0 will capture more high-frequency effects. These effects may be of interest, but they may also be extraneous high-frequency vibrations (noise) and may make convergence more difficult.

Note: For the purpose of this discussion, the terms high frequency and low frequency are defined relative to the capture rate. If the capture rate of the analysis is sufficient to produce around eight or more data points per cycle at the resultant vibration frequency of the structure, the integration parameter (0 or 1) will likely have little effect on the analysis results. In this case, the results can be considered to be low frequency effects relative to the capture rate, and they will not be filtered out. However, if the default integration parameter of 1 is used, and if the analysis capture rate produces around five or fewer data points per vibration cycle, then the deformation and stress results will likely be significantly attenuated (over-damped). In this case, the frequency of vibration can be considered to be high relative to the capture rate, and the high-frequency effects will be filtered out.

Tip: When expected high-frequency effects (that you wish to see in the results) are not captured, it is preferable to first increase the capture rate, rather than to change the integration parameter from 1 to 0. The capture rate was clearly not optimal. For reasonable accuracy, you should have approximately ten or more resultant data points per vibration cycle of the structure.

Tip: When performing drop tests, an integration parameter of 0 will typically result in more accurate impact time and impact velocity results compared to a parameter of 1. Other analyses involving similar free-body motion (such as the simulation of projectile motion) will also likely follow the theoretical time and velocity results more accurately when a parameter of 0 is used.

Static: NLS, LS (Classical Newmark Integration Method)

If you are using the Static: NLS, LS integration method, you must specify values in the First parameters for (LS) integration method and Second parameters for (LS) integration method fields. These parameters will be used as follows:

• For conditional stability, it is necessary that: , where P2 is the second parameter and P1 is the first parameter.
• Whenever the values P1 = 0.5 and P2 = 0.25 are not used, the accuracy of the analysis is diminished, but the stability of a high frequency event is increased. For example, an object impacting a wall using (0.5, 0.25) will not penetrate the wall, but will be very unstable. If values like (0.7, 0.4) are used, then there will be minor penetration (loss of accuracy), but a stable rebound will occur.
• The choice of which parameter values to use is up to you. Testing has shown that (0.60, 0.31) and (0.7,0.4) often give desirable results.
• Based on the above considerations, it is possible to discern what the effect of increasing these parameters is: the higher they are, the more the high frequencies are filtered. For a problem for which high frequencies dominate, increasing parameters above (0.5, 0.25) is not appropriate. The only way to determine if the high frequencies are important is to run the same problem using different parameter combinations and examine how the results change.

Static II: NLS (Wilson-Theta Integration Method)

If you are using the Static II: NLS integration method, 1.40 will be used as the First parameter for (LS) integration method value. The parameter values cannot be user-specified.

This integration scheme “centers” the equilibrium balance at a time just beyond the next time step.

Tip: Although a time integration method may be labeled as static, the equations used in the integration method are also applicable to dynamic situations.