Assignment 3
Objective : To answer the given questions by performing the required steps and get the results as requested.
Procedure : The answers of the questions are given in order as follows :
1. To change the run time to 55 ms change the parameter below /RUN/FIRST_RUN/1/ to 0.055.
2. To have a minimum of 25 steps and maximum of 60 steps change the second parameter under /ANIM/DT to 0.055/25 = 0.0022 & 0.055/60 = 0.000916 respectively as shown in the two images.
3. Run the simulation as is without changing anything.
4. Plot the energy error and mass error for base simulation.
As we can see by the end of the simulation at 60s the energy error is -11% meaning 11% energy has been artificially added in this simulation. Mass error remains constant at 0.1659e-3. While this energy error is not desirable it is barely acceptable as it is below 15%.
5. The simulation is by default run using q4 elements giving rise to a lot of energy error which do not properly integrate the elements while calculating for the stress at the nodes. The plots are as shown below.
Total energy v/s Hourglass energy :
Internal Energy :
Contact Energy :
Rigid wall forces :
The forces are majorly present in the x-direction as that is the axis wherein load is being applied.
6. Changing all the element properties to the recommended ones :
Now the simulation is rerun.
7. Choosing QEPH elements we can immediately see a drop in energy error.
At the end of the simulation too the energy error is only of the order of 0.1%. This result is desired as it is almost close to 0.
The same plots are repeated for the second simulation.
Total energy v/s Hourglass energy :
As we can see the total energy plot is a much straighter line indicated the total energy of the system remains constant.
Internal Energy :
Contact Energy :
Rigid wall forces :
8. The difference in results is very noticeable between both the simulations.
Pattern of deformation :
Given below is the deformation occuring using Q4 elements. As we can see the elements deform in a very unusual manner and there are many straight surfaces in the middle of the tube where the object starts to kink. The elements do not deform as though they are connected to each other and deform randomly and separately.
.
Given below is the deformation occuring in the second simulation using QEPH elements. As we can see the elements behave as though they are connected better than the previous example and we see lesser unusually straight elements in the middle of the bending region. The whole mesh behaves as one and deforms in a natural manner.
Hourglass energy : Given below are plots of hourglass energy using the following elements.
Q4 :
QEPH :
As we can see there is a major difference in the Hourglass energy in the second case and it remains contstant throughout the simulation unlike the first one which increases as the simulation progresses.
This increase in Hourglass energy is directly proportional to the decrease in total energy of the system as explained in the graphs below :
Q4
QEPH
For a simulation to be accurate the toal energy must remain fairly constant as the simulation progresses and that is the case when we use QEPH elements.
Timestep : For an accurate simulation we need the timestep to remian fairly constant and deviate less from the critical timestep value:
Q4
QEPH
As we can see in QEPH the timestep remains fairly close to a certain critical value unlike Q4 where it drops off to a certain value and remains at that till the end of the simulation.
Energy Graphs : Given below are the plots of the total energy, internal energy, hourglass energy and kinetic energy of both the simulations.
Q4
QEPH
As we can see in the sond simulation the toal energy of the system remains conserved and the hourglass energy also remains constant. Meanwhile the kinetic energy and internal energy curves are like mirror images of each other with one gaining what the other is losing. However in the second case the result is more accurate due to negligeble energy error.
9. As discussed above there is a significant change in result with using QEPH elemetns as compared to the default setting shell elements. The QEPH gives us a more accurate result due to lesser energy error and hourglass formation. It also proves to be a better compromise between cost and quality than Q4 elements. The results in the seond simulation are also improves by using Ismstr = 2 which gives better calculation for large strain deformation with better small strain formation result as opposed to Ismstr = 1 which is good only for small strain calculation.
Meanwhile Ithick = 1 is better as it takes into account change in thickness as compared to the other option whihc does not and Iplas = 1 which makes the material behave plastically after the yield point of the material has been crossed giving more accurate results for larger strain deformations.
Attached below is a google drive link for both simulations Q4(final) and QEPH(final2) if required: