Week - 8 Mass Scaling
Aim :
The aim of the project is to study the effect of mass scaling on explicit and implicit analysis to reduce the computational time.
Mass Scaling:
Anytime you add nonphysical mass to increase the timestep in a dynamicanalysis, you affect the results (think of F=m*a). Sometimes the effect is insignificant and in those cases adding nonphysical mass is justifiable. Examples of such cases may include the addition of mass to just a few small elements in a noncritical area or quasi-static simulations where the velocity is low and the kinetic energy is very small relative to the peak internal energy. In the end, it's up to the judgement of the analyst to gage the affect of mass scaling. You may have to reduce or eliminate mass scaling in a second run to gage the sensitivity of the results to the amount of mass added.
One can employ mass scaling in a selective manner by artificially increasing material density of the parts you want to mass-scale. This manual form of mass scaling is done independently of the automatic mass scaling invoked with DT2MS in *CONTROL_TIMESTEP.
When DT2MS is input as a negative value, mass is added only to those elements whose timestep would otherwise be less than|DT2MS|. By adding mass to these elements, their timestep becomes equal to |DT2MS|. An infinite number of combinations of TSSFAC and DT2MS will give the same product, i.e., timestep but the added mass will be different for each of those combinations. The trend is that the bigger |DT2MS| (and the smaller TSSFAC while TSSFAC*|DT2MS|=const), the greater the added mass. In return, stability may improve as TSSFAC is reduced (just as in non-mass-scaled solutions). If stability is a problem with the default TSSFAC of 0.9, try 0.8 or 0.7. If you reduce TSSFAC, you can increase |DT2MS| proportionally so that their product, and hence timestep, is unchanged.
Explicit analysis without Mass scaling Effect:
The above figure shows the given model run without mass scaling effect. The computational time shows for this analysis is 213000 sec (59 hrs and 10 min).
The computational time is more in this analysis. To reduce this we will use the mass scaling effect.
Explicit Analysis with mass scaling effect:
The above figure shows the mass scaling effect parameter by using the control timestep. Here the mass scaling effect varies by altering the tssfac and dt2ms parameter.
Tssfac does not affect the added mass but it affect the timestep.
The above figure shows the effect of mass scaling. It shows computational time is reduced by using the mass scaling effect and the added mass is 0.
By keeping the tssfac 0.9 and varying the dt2ms value to get the mass scaling upto 8% which is shown below.
The above table shows the tssfac for 0.9
It shows that at dt2ms value -1.029e-4 and tssfac 0.9, we get the mass scaling effect as 8% with the low computational time of 47753 seconds( 13 hrs 15 min)
Similarly the same case if we run the analysis for tssfac 0.8 and dt2ms vary. Then we get the result as for dt2ms -1.029e-4 we get 8% of added mass and the computational time increases 55712 seconds (15 hrs 28 min)
The above figure shows the explicit analysis of tssfac 0.8 and the dt2ms -1.29e-4 .
The above table shows the tssfac for 0.8.
From the above two method and compare the table for tssfac 0.9 and 0.8 ,it is shown that tssfac 0.9 gives less computational time compare to other tssfac value and it does not affect the added mass and it affect only the computational time.
Histogram:
Timestep and run time upto 8% mass added for tssfac 0.8 and 0.9 in explicit analysis:
Series 3 tssfac 0.9, series 4 tssfac 0.8.
Since we know the TSSFAC range is 0.5 to 0.9. From the above figure we will get that optimized tssfac 0.9 with dt2ms -1.028e-4 gives less computational time compare to the tssfac 0.8.
Mass scaling effect on implicit analysis:
The given model is convert to implicit analysis by using control implicit general and auto.
The above figure shows the elapsed time for implicit analysis.
Conclusion:
Implicit analysis is unconditionally stable and it is not time dependent problem. It depends on the loadstep. Each load step the solution is converged. It depends upon the termination time provided by user. So it is mostly good for long duration and computationally expensive. So Mass scaling is not give much change in the implicit analysis.
Since the computational time for explicit analysis depends on the timestep and the iteration. To reduce the computational time without affecting the solution and accuracy mass scaling is used. From the result we can have different set of the mass scaling value based on the tssfac and dt2ms.
The range of the tssfac is 0.5 to 1. The ideal value of tssfac is 0.9 where computational time is reduced and the dt2ms value is -1.028e-4 to get the mass percentage of 8% which is the optimized value for this analysis.