Assignment 3-2D Element Formulation Challenge

Objective:

The primary objective of this assignment is to compare two simulations with different shell element properties. The comparison would be between the one with default properties and one with the following properties:

Parameters		Comment
Ishell =24		QEPH 4-node shells are the best combination of cost and accuracy.
Ismstr=2		Full geometric nonlinearities (default)with possible small strain formulation activation in RADIOSS Engine.
Ish3n=2		Standard 3 noded shell (C0)with modification for large rotation(default)
N=5		Number of integration points is set to 5 for accuracy bending.
Ithick=1		Thickness change is taken into account for accuracy.
Iplas=1		Iterative plasticity for good accuracy.

Questions:

Comparison of results with base simulation and improved shell element properties

1. Using the crash beam file from the previous assignment, change the run time to 55 ms.

2. Change the number of animation steps during simulation to a minimum of 25 and a maximum of 60.

3. Run the base simulation without any modification to element properties.

4. At the end of the simulation, do the energy error and mass error checks and determine whether the results would be acceptable.

5. If acceptable, Plot rigid wall forces, internal energy, hourglass energy, contact energy, and total energy of the simulations.

6. Change all the shell elements properties to recommended properties, save this as separate, rad files, and run the simulation.

7. Follow steps 5 and 6.

8. Create a brief report comparing all the results from steps 5 and 6 for both simulations.

9. Comment whether there is any change in the results and why there is any change in the result.

What is hourglass deformation and why it needs to be reduced?

Hourglass:

"Hourglass is a deformation, that is noticed when an element is deformed due to the applied load. But the strain energy due to this deformation is not recorded for that element". It is also known as "Zero energy deformation modes" where an element is seen as deformed.

• It indicates instability.
• It is also said to be a non-physical mode of deformation, that occurs in reduced or under-integrated elements & produces no stress.
• Usually, it can be seen in the post-processing stage, where the elements will have a zig-zag formation.

BEFORE HOURGLASS EFFECT

AFTER HOURGLASS EFFECT

METHODS TO CONTROL THE HOURGLASS:--

1. Perturbation method(viscous method)
2. Physical stabilization method (stiffness method)

Perturbation method(Viscous method):-

• This method is generally used for the elements with Ishell: 1,2,3,4 or Q4 elements.

• The process of how this method works is: When the hourglass deformation occurs---> There will be some damping applied, which stabilizes the deformation, which results in controlling the speed of deformation.

• But this damping opposes only the velocity, But not the force. So, the force is introduced, which results in adding some stiffness to the elements. This stiffness helps in controlling the hourglass.

• The force is applied externally, by some other means. But not from an FEA nature. This force constitutes energy called "Hourglass energy", Which is artificial energy(neither Kinetic nor internal energies). It is a loss of both energy types.

• If the hourglass energy is added along with the kinetic energy & Internal energy, A balance system is obtained.

• It is recommended for high velocity or high strain rate problems. Example: Involving high explosives.

• A huge amount of hourglass energy is generated.

Physical stabilization method (stiffness method):--

• In this method, the stiffness is getting added right from the material level. This will have a large effect on our components.

• It is recommended for fewer velocity problems.
• used for QEPH elements.
• A lesser amount of hourglass energy is needed. Because it is going to be controlled before it arises.

Q4 element:

• It is an under(or) reduced-integrated element because it has only 1 integration point for an element.
• It is represented in the radioss solver by an entity named "Ishell(1,2,3,4)".
• Usually Ishell:1, and Ishell:4 elements are used when no more velocities are to be found.
• By default, the solver takes as Ishell:1.
• As it has only 1 integration point, the time required to solve the problem with this type of element is relatively less.
• The cost required to solve this type of element is relatively low.
• However, there will be no accuracy in the results.

QBAT element:

• It is a fully integrated element, Which means it comprises 4 integrated points. Each point is near each node.
• It is represented in the radio solver by an entity named "Ishell: 12".
• Because of these 4 Gaussian integration points, there will be no Hourglass deformation.
• Using this element is not economical. However, the achieved results are more accurate than the remaining Ishell elements of quads.

QEPH element:

• It is an improved under-integrated element with physical hourglass stabilization within itself.
• It is represented in the radio solver by an entity named "Ishell:24".
• This type of element has been mostly used recently. Because of its best compromise between the cost, quality& accuracy in results.
• It is widely used in the automotive industry.

CO element:

• It is a standard co-rotational triangle, with modification for large rotations.
• Usually, it helps in representing the tria elements with the entity named "Ish3n:2".
• It consists of 1 integration point.
• No hourglass deformation.
• Low CPU cost.
• Results may not be accurate.

Import:

• The given rad file is imported to Hyperworks and is displayed below.

 

• We shall be changing a couple of simulation properties by accessing them through Hyperworks. This first question requires us to change the run time to 55 ms. We first need to import the solver deck file in question to RADIOSS.
• For that, we need to go to File > Import > Solver Deck. This brings up the import menu. Here, we can select the file we need to import. The file would be the starter input deck file.
• which is the file that ends with '0000.rad'.
• With the model imported, we can go ahead and change the run time to 55 ms (as required). To do that, we need to proceed to the solver tab in the sidebar. Proceeding to ENGINE_KEYWORDS > RUN > ENG_RUN, we can now edit the properties of ENG_RUN in the small window below the tab.

• The next question requires us to change the number of simulation steps to a minimum of 25 and a maximum of 60. For this, we need to go to the same solver tab and proceed to ENGINE_KEYWORDS > RUN > ANIM > ANIM/DT. We shall be changing this particular attribute's properties.

CASE:1 BASE SIMULATION:

• The next requirement is to run the base simulation. For that, we need to save the current file with edited parameters. This can be carried out via the analysis process.

• For this, we can go to the 'Analysis' section from the bottom panel.
• There, we can select RADIOSS.
• In the next section, we are given the option to save the file before running it in the solver. We can go ahead and give it a different name from the base file to avoid confusion. Clicking 'save as' lets us do that.

• After saving, before running it into the solver, we can activate 'include connectors' and in the options bar, we need to enter "-nt 4" to increase the processing power of the solver (as in to use all 4 cores). After that, we can click 'Radioss' to activate the solver and it processes t the file. We get a solver window that tells us what's going on in the process. It runs for several seconds before finishing and letting us know about completion.

• After accessing Hyperview, we are asked to input the simulation file. For this, we shall be using the h3d file that was generated when RADIOSS processed the starter file. It should be generated in the same folder. After selecting it, we can click 'apply'.

• 

  

• Doing so generates the simulation animation. We can change what is being represented by selecting the 'contour' option in the toolbar.
  

• The next step is to carry out energy error and mass error checks and this is done by analyzing the RADIOSS engine output file. This can be accessed from the same directory as the starter and engine files and is denoted by the '.out' extension. We need to check the file that contains '_0001.out' by using any text editor.
• On opening the file and scrolling down to the end, we can see the final energy and mass error values.

• On opening the file and scrolling down to the end, we can see the final energy and mass error values.

• The final energy error is -10.3%, which is less than the threshold of -15% and is acceptable. Acceptable energy error values are supposed to be between -15% and 10%. The closer to 0 it is, the better.
• With the energy and mass errors deemed acceptable, we can go ahead and plot the graphs. For this, we shall be using the Hypergraph client. We can switch to it using the same client selector option in the toolbar.

Generate the graph for rigid wall forces (Rigid Wall/Rwall Force - 4 RIGID WALL 1 - total resultant force).

we can take a look at the energy graphs (internal energy, hourglass energy, contact energy, kinetic energy, and total energy).

CASE:2 EDITED SIMULATION:

•  For this question, we are to simulate a new case with the recommended shell element properties. We can repeat the process of importing the original solver deck file and change the values of Tstop">Tstop����� , Tstart">Tstart������ &  Tfreq">Tfreq����� in the solver tab.
• After that, we can move to the model tab and go to the properties submenu. The shell properties of the model's components are to be changed so we need to select each of the 'Hat-Section' and 'Close-Out Panel' one by one and change the values in the property window below as shown:

• As specified, Ishell">Ishell��ℎ��� would be 24, Ismstr">Ismstr������ would be 2, Ish3n">Ish3n��ℎ3� would be 2, N would be 5, Ithick">Ithick��ℎ��� would be 1 and Iplas">Iplas����� would be 1. These values are changed for both aforementioned components.
• After they're changed, we need to generate the RADIOSS analysis file again via Analysis > RADIOSS in the bottom panel. We can save it in a different name and assign the same settings as the previous case (option: "-nt 4" and with 'include connectors' checked. The solver file is then generated by clicking Radioss.
• After that, we can switch to Hyperview to generate the simulation. Like last time, we need to pick the h3d file of this case and click apply.

• Having generated the simulation, we can go ahead and carry out energy and mass error checks, again using this particular simulation's RADIOSS output file. This can be accessed from the same directory as the starter and engine files of this simulation and is denoted by the '.out' extension. We need to check the file that contains '_0001.out' by using any text editor.

• As we can see, there is a drastic reduction in energy error, as was evident in the more natural-looking simulation (reduction in hourglass energy).
• Now we can generate the graphs by switching to Hypergraph and selecting this simulation's T01 file. Firstly, the energy graph:

• As we can see, there is almost no hourglass energy and this corresponds with the energy error observation.

• Now we shall generate the graph for rigid wall forces:

• The obvious difference in both simulations is the reduction in hourglass energy. The introduction of QEPH shell formulation (Ishell">Ishell��ℎ��� = 24) In the second case, provides an artificial stiffness to the shell elements and helps counter hourglass formation.
• A result of hourglass reduction is the more 'natural' looking simulation in the second case, with less crumpling.
  
• A reduction in hourglass means a reduction in hourglass energy since an artificial, external force needn't be applied to negate the hourglass formation (as in the case of Q4 elements).

RED DENOTES FOR CASE 2

BLUE- DENOTES FOR CASE 1

• This, in turn, affects the total energy in the system. When recommended settings are applied, with no loss of energy to hourglass energy, the total energy in the system is maintained.

case 1:                                                                                                                                                                 Case 2:

                                               

• The more realistic simulation also resulted in a different resultant force graph that represents the collision events more realistically. The formation of a kink at around 20 ms causes a sudden spike in case 1, whereas in the second simulation, as the QEPH shell formulation is used, there is no sudden spike as the elements are deformed in a much better manner. Understandably, there is a large force at the beginning, which happens at contact and is the same in both cases.

Overall, there have been some obvious differences in results. To summarize:

ATTRIBUTE	BASE SIMULATION	Simulation with recommended properties
ENERGY ERROR	-10.3% WHICH IS ACCEPTABLE	-3.8% A GOOD NUMBER SINCE IT IS ALMOST 0.
TOTAL ENERGY	TOTAL ENERGY REDUCES OVER TIME DUE TO THE INTRODUCTION OF HOURGLASS ENERGY	TOTAL ENERGY IS CONSTANT SINCE THERE IS BARELY ANY HOURGLASS ENERGY
HOURGLASS ENERGY	HOURGLASS ENERGY INCREASES OVER TIME	HOURGLASS ENERGY IS INCREASED BUT LESSER WHEN COMPARED TO (Q4)

RESULTS:

• Two simulations were carried out on the same crush beam using different shell element formulation properties.

• Comparing the results of both cases, it can easily be figured out that there is a big difference in the values of hourglass energy, internal energy, and rigid wall forces.

• Also, the amount and nature of deformation in the 2nd case are much higher and different than in the first case. This deformation is more practical than the base simulation. This improvement is definitely due to changes in the material card and its element properties.

• It was established that using the recommended settings helped reduce hourglass formation drastically due to the introduction of the physical stabilization method that is deployed by QEPH elements.