Comparative study of shell element formulations in a Finite Element model and it s effect on the accuracy of results

Comparing the simulation results of the base setup and improved shell element properties.

Objective :

The objective of this project is to simulate the given model by assigning both default elemental properties and recommended elemental properties and comparing the results obtained from the two simulation cases.

Procedure :

1. As instructed, the run time is changed to 55 ms and the animation interval is changed to provide 40 animation steps for both the cases.

2. Then, the engine file is imported as solver deck and the simulation is started by clicking Tools> RADIOSS.

3. For the recommended case, after importing the engine file, in properties section in the model browser, for the components having the property PROP/SHELL, input the recommended element properties and run the simulation again.

4. After both the simulations are completed, navigate to the folder where the output files are stored and open “Element_Formulation-Shell-3_assignment_0001.out” file using notepad to check for energy errors.

The characteristics of a good simulation with less error in result are as follows :

1. Energy error should be less than -15%. The credibility of results is most likely to be high if the energy error is close to 0%

2. The credibility of results increases as the energy error approaches 0%. But there will always be some energy error in a model.

3. The kinetic energy is maximum at first and then starts decreasing.

4. The Internal energy is zero at first if there are no pre stressed components in the model. The internal energy gradually increases

5. There are no dramatic changes in total energy and it remains more or less constant.

6. The hourglass energy is less than or equal to 10% of Internal energy.

Ways to identify hourglass effect in a simulated model :

1. Check the element type from engine file. If first order reduced integration elements are used, there might be uncontrolled or untreated hourglass effect in the model.

2. Coarse meshes may also cause hourglass effect.

3. Very large energy error from engine file can point towards hourglass effect

4. Visual identification from the simulated model by plotting contour of hourglass energy to check areas and maximum magnitude of hourglass energy

5. Plotting a graph of hourglass energy can help verify the presence or absence of hourglass mode.

Normal Case :

Graphs :

Observations :

1. While an acceptable energy error is close to -0.1%, the energy error in the base simulation is -10.3%, which proves that the FE simulation has not been set up properly and the results are most likely to be in inaccurate or wrong.

2. In the provided model, as the element properties are set to default, reduced integration first order element property is used while solving.

3. Reduced integration along with a coarse mesh has led to the development of hourglass effect which caused erratic displacements and deformation which obviously led to misleading and erroneous results.

4. From the plot of the hourglass energy graph, it can be learnt that considerable amount of hourglass energy is recorded (6.301E+06 Joules) which is more than 10% of internal energy.

5. Also from the total energy graph, it can be observed that there is a drastic and noticeable decrease in total energy viz. 6.33E+06 Joules while the total energy in a good simulation will be more or less constant.

6. The time taken to run the simulation was 55.23 seconds.

Recommended Case :

Observations :

1. The energy error in the model was -0.1% which is the ideal value for a good FE model and hence an indicator for a good simulation involving optimal setup conditions.

2. In this case, the recommended properties used for the elements are as follows

3. The Ishell= 24 (QEPH) property means improved reduced integration elements will be used in the model and hence the hourglass effect is controlled or treated at a material level.

4. The plot of hourglass energy shows no hourglass energy in this case as specific algorithms compensate for the hourglass formation at a material level.

5. From the total energy graph, it can be observed that there is only a gradual and slight decrease in total energy (5.66E+04 Joules)

6. The time taken to run the simulation was 58.34 seconds.

Result :

Suggested modifications were made to the model’s engine file, the simulations were run, various outputs were examined and results from both the cases are presented with the help of graphs and animations.

The results from the simulations are as follows

Normal case :

Resultant Normal Force:      4.91 E+04 kN

Resultant Tangential Force: 5.36 E+03 kN

Internal Energy:                  1.931E+07 Joules

Contact Energy:                   9.323E+03 Joules

Hourglass Energy:                6.301E+06 Joules

Total Energy:                        4.498E+07 Joules

Recommended Case :

Resultant Normal Force:      6.498E+04 kN

Resultant Tangential Force: 2.192E+04 kN

Internal Energy:                  1.975E+07 Joules

Contact Energy:                   3.479E+03 Joules

Hourglass Energy:                0 Joules

Total Energy:                        6.125E+07 Joules

Learning Outcome :

1. By simulating both the models and comparing various characteristics like energy error, hourglass energy, etc. It is established that the first case was not set up properly to provide the most accurate results.

2. From the energy error of the normal model, it is evident that the inaccuracy is primarily induced by the hourglass effect.

3. While the normal model’s simulation was done quicker due to certain assumptions like Constant thickness throughout the simulation and radial return for faster stress calculation, the simulation’s accuracy was compromised because the above implemented assumption cannot simulate the exact conditions occurring in the real world.

4. Because in reality, there is always a thickness or cross section change when a material is loaded. When a material starts yielding, its cross section changes according to the type of loading.

5. Hence a simulation taking into factors such as changing thickness, hourglass treatment, full geometric non-linearity with possible small strain activation etc. will give the most accurate results.

6. As a result, the second case (Recommended Case) gives the most accurate results.

7. On comparing results from both the cases, it was found that there are drastic variations in the output quantities.

8. The drastic variation and improved accuracy in recommended case is due to hourglass treatment, taking into account geometric nonlinearities and thickness change.

9. The time taken to run the recommended case simulation was more because of the QEPH element formulation, thickness change compensation and Iterative method to calculate stress values and it is 5.6%  more than the time taken to run the normal case simulation.

10. Even though the simulation time increased by a very small margin, it provided results of highest accuracy. Hence the recommended case must always be preferred while running a simulation.

Conclusion

The given objectives were completed successfully and the steps, observations are documented. Concepts like hourglass mode, energy error, error validation, energy balance, mass balance and simulation verification were learnt and implemented to find out the most appropriate shell element properties that provide the most accurate results.

Google drive link -

https://drive.google.com/open?id=14eTlWNf3V_9xNThhvkLZSfEPy1IOvq83