## Best Practices to define Time Step in Transient Analysis

Transient response analysis is used to calculate the response of a structure where the loads and responses are time-dependent.

In short terms, transient systems are solved according to the equation of motion: One of the main inputs for this type of analysis is the time step of the solution through the TSTEP card. In this article, we will cover best practices to define the parameters in TSTEP and understand how they can impact the accuracy of the solution, running time and file storage.

## TSTEP Parameters

The TSTEP card defines parameters for control and intervals at which a solution will be generated and output in transient analysis. In this article, we will discuss the three main inputs for this card:

N - Number of time steps of value DT#.

DT – Time Increment

N0 – Skip factor for output. N0i-th step will be saved for output.

Example

To run a certain model for 10s with outputs for every 0.5s, TSTEP should be defined as:

N = 20

DT = 0.5

The total time will be N x DT. Regarding N0 definition:

Using N0 = 1, the outputs will be at 0.0s, 0.5s, 1.0s, 1.5s, 2.0s, 2.5s, etc.

Using N0 = 2, the outputs will be at 0.0s, 0.5s, 1.5s, 2.5s, 3.5s, 4.5s, etc.

## Guidelines for DT definition

Defining the time increment correctly can be the key to the accuracy of the solution, running time and saving disk space. Keep the following rules in mind:

• Keep DT constant if possible. If DT is changing, the equation must be re-decomposed, which may be a time-consuming operation.
• The smaller the value of DT, the more accurate the integration will be.

• However, it may be time effective for a large model to decrease DT at a time of critical interest (say under impulsive loading) and increase it later. Normally it will take a few runs to tune the model overall, and the effectiveness of this technique can be investigated.
• The time step chosen should be sufficiently small to capture the highest frequency of interest in the response.

• For example, if this value is 100 Hz, each time period is 0.01s (1/100Hz). We recommend having at least 10 steps per period. Therefore, DT = 0.01/10 = 0.001s.
• The frequency content of the applied load should also be taken into consideration. Doing an FFT of the time signal can help to understand the frequency content. We recommend having at least 10 steps per period.
• If you are using test data as input, make sure to follow the data sample rate when defining DT. N0 can help to reduce the results file size in this case.
• The total duration should be sufficient to ensure the response has reached steady state and is decaying in a predictable manner, as shown in figure a. Figure b is not recommended.  For short-duration events, such as half-sine shock, the time of loading will be on the order of 10ms to 50ms. The decay time will be dependent on the frequency content of the structure and the amount of damping. The lowest significant frequency (first eigenvalue) needs to be checked to ensure enough decay time has been allowed. An overall rule for the total time would be 5 to 10 times the event duration, to ensure the capture of the long-period motion.