Study of Mass Scaling using LS-Dyna

OBJECTIVE:

To use mass scaling to reduce the runtime of the given model. The simulation should satisfy the objectives stated below.

1. The limit on mass scaling is 8% and the mass scaling should not hinder the stability of the model.

2. Optimisation of both DT and TSSFAC has to be done.

3. Histogram should be plotted to compare the runtime with mass scaling trials.

4. The model has to be run using implicit analysis and it should be compared with the results obtained in explicit analysis.

PROCEDURE:

1. Open LS-Dyna Manager. Run the given .k file as it is without making any changes. The following runtime is obtained. The parameters given in the file is shown in the figure below.

Without mass scaling, the estimated total run time obtained is 14 hours 6 mins.

2. Now, keeping the tssfac as 0.9, increment the dt2ms value in a specific interval steps. The results obtained for various runtime is shown below.

For tssfac=0.9 and dt2ms= -4.5E-05

The estimated total runtime obtained is 13 hours and 4 mins.

For tssfac=0.9 and dt2ms= -5.5E-05

The estimated total run time obtained is 11 hours 56 minutes which is lesser compared to the earlier case. This is because some mass has been added and this has been reflected in the percentage increase of 0.01.

This is process is iterated till percentage mass added becomes 8%. This is the upper limit given in the problem statement.

For tssfac=0.9 and dt2ms= -6.5E-05

The estimated run time obtained is 10 hours 21 minutes with a total mass percentage increase of 0.0578%

For tssfac=0.9 and dt2ms= -7.5E-05

The estimated run time obtained is 8 hours 45 minutes with a total mass percentage increase of 0.372%

For tssfac=0.9 and dt2ms= -8.5E-05

The estimated run time obtained is 7 hours 43 minutes with a total mass percentage increase of 1.5872%

For tssfac=0.9 and dt2ms= -9.5E-05

Here, the estimated run time obtained is 7 hours 15 minutes with a total mass percentage increase of 4.3136%

For tssfac=0.9 and dt2ms= -1.05E-04

Here, we observe that the percentage increase has become 10.748% which is out of the limit. Hence, no mass should be added after this. This indicates the end of case 1. 

3. For the next case, the tssfac is changed to 0.8, increment the dt2ms value in a specific interval steps same as the earlier case. The results obtained for various runtime is shown below.

For tssfac=0.8 and dt2ms= -3.5E-05

The estimated total runtime obtained is 15 hours and 28 mins without any increase in mass percentage.

For tssfac=0.8 and dt2ms= -4.5E-05

The estimated total runtime obtained is 14 hours and 42 mins without any increase in mass percentage.

For tssfac=0.8 and dt2ms= -5.5E-05

The estimated total run time obtained is 13 hours 25 minutes which is lesser compared to the earlier case. This is because some mass has been added and this has been reflected in the percentage increase of 0.01.

This is process is iterated till percentage mass added becomes 8%. This is the upper limit given in the problem statement.

For tssfac=0.8 and dt2ms= -6.5E-05

The estimated run time obtained is 11 hours 4 minutes with a total mass percentage increase of 0.0578%

For tssfac=0.8 and dt2ms= -7.5E-05

The estimated run time obtained is 10 hours 21 minutes with a total mass percentage increase of 0.372%

For tssfac=0.8 and dt2ms= -8.5E-05

The estimated run time obtained is 8 hours 28 minutes with a total mass percentage increase of 1.5872%

For tssfac=0.8 and dt2ms= -9.5E-05

Here, the estimated run time obtained is 7 hours 22 minutes with a total mass percentage increase of 4.3136%

For tssfac=0.8 and dt2ms= -1.05E-04

Here, we observe that the percentage increase has become 10.748% which is out of the limit. Hence, no mass should be added after this. This indicates the end of case 2. 

4. For implicit analysis, the following *CONTROL_IMPLICIT cards are activated and the timestep for the simulation is kept as 1. The model is run using the LS-Dyna manager. The cards are shown in the figure below.

RESULTS AND DISCUSSION:

The trend observed for various values of TSSFAC and DT2MS is shown in the figure below.

From the above values, the least run time is 7 hours 15 mins for mass addition of 4.3136%. But our upper value is 8%. Thus, the time interval is further splitted up in this region and it is simulated again. This is shown below.

For tssfac=0.9 and dt2ms= -9.60E-05

The estimated run time obtained is 10 hours 41 minutes with a total mass percentage increase of 4.682%

For tssfac=0.9 and dt2ms= -9.70E-05

The estimated run time obtained is 9 hours 22 minutes with a total mass percentage increase of 5.0775%

For tssfac=0.9 and dt2ms= -9.80E-05

The estimated run time obtained is 9 hours 6 minutes with a total mass percentage increase of 5.4995%

For tssfac=0.9 and dt2ms= -9.90E-05

The estimated run time obtained is 8 hours 19 minutes with a total mass percentage increase of 5.9481%

For tssfac=0.9 and dt2ms= -1.00E-04

The estimated run time obtained is 8 hours 55 minutes with a total mass percentage increase of 6.4233%

For tssfac=0.9 and dt2ms= -1.01E-04

The estimated run time obtained is 8 hours 40 minutes with a total mass percentage increase of 6.9297%

For tssfac=0.9 and dt2ms= -1.02E-04

The estimated run time obtained is 7 hours 35 minutes with a total mass percentage increase of 7.4771%

For tssfac=0.9 and dt2ms= -1.03E-04

The estimated run time obtained is 7 hours 21 minutes with a total mass percentage increase of 8.0660%

For tssfac=0.9 and dt2ms= -1.04E-04

The estimated run time obtained is 7 hours 36 minutes with a total mass percentage increase of 8.8759%.

The tabulated results are shown below.

The histogram obtained is shown below.

The simulation is stopped at time step scaling factor (TSSFAC) of 0.8 because on scaling down time step further results in increased run time. This can be observed from the above values. For the same mass added, the run time is more for TSSFAC of 0.8 when compared to 0.9. Thus, reducing the TSSFAC further to 0.7 does not yield any reduction in run time when compared to 0.9. Thus, optimum value of TSSFAC is 0.9

For implicit analysis, the total run time cannot be expected. This is because implicit solver considers global equilibrium at each and every time step. Also, non-linearity plays a major factor in the iteration involved. Since, these values can be computed only at the time of the simulation it won't be possible to predict the value at the start of the simulation. So, run time is not shown.

Note:

1. The estimated total time obtained in the simulation is a rough estimation. The actual values would be lesser than the values shown here. Practically, it would not be possible to run the simulation completely for each and every case. So, this value is taken for comparison.

2. The estimated total time differs from system to system. This is because it is dependent on the configuration of the system and the running applications at the time of the simulation. So, consistency in the run time cannot be expected.

3. Adding mass increases the density of the material which inturn reduces the value of speed of sound. This reduces the timestep as the timestep is inversely proportional to speed of sound.

CONCLUSION:

From the added mass, the minimum run time is obtained for TSSFAC-0.9 and added mass of 7.477%. The estimated run time obtained is 7 hours 35 minutes.

For implicit analysis, it won't be possible to compare with explicit analysis due to the reasons mentioned the results and discussion part.

The objectives of the given challenge is satisifed.

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