Assignment 3-2D Element Formulation Challenge

AIM:

1. The aim is to run the simulation on crash beam model with base simulation and improved shell element properties
2. Change the elemental properties as mentioned below and check whether the results are acceptable then compare the results with the base simulation.
3. Study the output of both the simulation by plotting Rigid wall forces and Energies like internal energy, Hourglass energy, Contact energy and Total energy.

Parameters	Comment
Ishell =24	QEPH 4 nodes shells are 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 set to 5 for accuracy bending.
Ithick=1	Thickness change is taken into account for accuracy.
Iplas=1	Iterative plasticity for good accuracy.

Element formulation:

• There are so many elements that we use in radioss to get the desired results. And these elements are categorized by the element formulation technique, which consists of the same elements but varies with respect to some parameters such as type of integration within the element, cost, etc. Based on this element formulation, we can specify the type of elements to be used in our simulation. These are explained below.   

In general, there are 3 types of elements. Based on dimensions. They are:

• 1D elements: Which include Springs, Trusses, Beams.
• 2D elements: This includes shell elements like quads(4-noded), Trias(3-noded).
• 3D elements: This includes solid elements such as Tetra, Hexa elements.

2D Element formulation: -

• Before going to the 2D shell element formulation, an important parameter should be discussed. Which is named "Hourglass".

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

Hourglass is basically a kind of deformation that is produced during the simulation in certain shell elements that have not been integrated appropriately. As a result, stress is not produced in these elements and this reduces the accuracy and true response of the structure during the simulation. This effectively results in incorrect displacement results with unrealistic representations of the simulated part.

How to reduce hourglass?

There are two ways to control hourglass formation. One is via Perturbation method and the other is through Physical Stabilization. It is important to deploy the right method based on the conditions of the simulation.

Perturbation is deployed by Q4 elements (`I_(shell)`= 1, 2, 3, 4) and involves introducing an opposing force to stabilize whichever node it detects potential hourglass formations. This opposing force produces energy and that's known as 'hourglass energy'. As mentioned before, this method fails for large rotation and elastic loading-unloading cycles. In addition to that, it uses a simple under integrated method and this takes lesser time and computational power but that comes at the cost of accuracy.

This is why the Physical Stabilization method is the best method since it can be used in any case. This method is deployed by QEPH elements (Ishell">IshellIshell = 24) and involves introducing an artificial stiffness. As a result, shell elements are controlled from a material level and in addition to that, they use an improved under-integrated method that provides the best compromise between computational cost and accuracy.

Procedure:

Case -1 (Without assigning the recommended parameters in the property): -

• Initially, after opening the Altair HyperWorks desktop software, the user profile should be selected. And the user profile to be selected is "Radioss" . Because for performing the analysis. 

• The next step is to import the given rad file (starter file). This is done by clicking on import, selecting the solver deck in it. After selecting the solver deck, a pop-up appears. In which the given rad file is browsed and by clicking on import, the model with respect to that rad file is imported. 

• After importing the model

• As the model is in wireframe mode to view it properly, an option named "shaded elements with mesh lines" is enabled. After enabling it, the given model.

• The next step is to assign the time step value in the card named "ENG_RUN". As mentioned in the question, the run time or time step is 55 ms. This value is entered in the parameter named "Tstop".

• The next step is to select the number of animation steps required. As mentioned in the question, the number of animation steps can be between 25 to 60. In this challenge, the number of animation steps selected is 40.
• Now to calculate the Tfrequency for a run time as 55 ms with respect to the 50 animation steps.
• The formula used: Tfreq = Time step ÷Number of animation steps

                              = 55÷40

                              = 1.375

• Therefore, the Tfreq is 1.375.
• This value is entered in the parameter named "Tfreq" in the card named "ENG_ANIM_DT"

• These values are entered just to perform the simulation.
• As in this case, the results are obtained without assigning any properties to the given components. The parameters in the property card are taken the default values.

• The next step is to run the simulation. For doing that, the "radioss" option is used in the "Analysis" panel 

• After entering into the radioss panel, initially, the file should be saved in some folder using "save as", and in the options, it is recommended to be written as "-nt 4" as shown in the image below. This means assigning the task to 4 cores in the system, to perform the simulation faster. It depends upon the process of our computer (it has a quad-core processor, then it should be taken as 4. If the system has an octa-core processor, then it is taken as 8). And "nt" means "number of threads". Then click on "Radioss", in order to run the simulation.

• The next step is to verify the assigned values such as Tfreq, Tstop in the engine rad file (00001.rad) in notepad. 

• The next step is to verify the required number of animation files are obtained in the file location that is specified at the beginning. As the specified number of animation steps is 40. The obtained number of animation steps is 41. 

• The next step is to check the obtained values for energy error, internal energy, total energy, mass error from the engine output file (00001.out). 

• In the same file, when it is scrolled down to last, the maximum values are seen as shown in the image below. From the figure, the obtained maximum values are energy error: -10.3%, Internal energy: 0.1928E+08 gm^2/s^2, Kinetic energy: 0.3569E+08 gm^2/s^2.

Note: The acceptable tolerance for energy error is -15% to +5%. 

• Then click on "results" as shown in the HyperWorks Solver View tab, in order to have a new window. After opening a new window, it automatically switches to HyperView from Hypermesh. It shows to import the h3d file and click on Apply . In order to view the simulation.

• After importing the h3d file, it appears as shown in the image below.

• Then, the next step is to enable the contour. This is done by selecting the contour.

• The next step is to select the various parameters such as the way to view as von-misses, selecting the components, selecting the averaging method, then click on apply at the end 

• After applying that, run the simulation. The simulation appears as shown in the below animation.

                               

• The next step is post-processing, this is done by obtaining the various graphs for the above simulation. In order to view what is happening within the component (Rail). This is done by switching to Hypergraph 2D .

 

• After switching to the hypergraph 2D, the first graph to be plotted is chosen to obtain the rigid wall forces. So, the various parameters such as the parameter to be on Y-axis (Rigid wall force), the component to be on Y-axis (Total resultant force) which indicates the term be in the graph are chosen and then click on "Apply".
• The obtained rigid wall force graph appears as shown in the image below. The reason for the rigid wall force is dropping from the top is, Initially the rigid wall force acts within the rail component. At that time, the rigid wall force will be maximum, which is indicated as the starting point of the curve. Slowly that force is observed by the adjacent elements, which leads to the decrease of force (results in falling of curve). And this curve again raises up because the rail component is getting contact with the rigid wall. In this way, rigid wall faces fluctuating

• The next step is to plot the graph that indicates some various important parameters such as Internal energy, Kinetic energy, Contact Energy, Total energy, and Hourglass energy. Those parameters are selected and applied from the Hypergraph 2D.   

•  The obtained graph appears as shown in the image below. The reasons for the behavior of the obtained curves are:

Kinetic energy (KE):

• We know that the formula for kinetic energy is 1÷2mv^2
• Since the velocity is applied to the component, there will be a high velocity at the beginning. This velocity decreases with respect to the time, due to the deformation within the rail component. 
• So, the kinetic energy is directly proportional to the velocity. That is the reason why, the kinetic energy drops gradually, as shown in the graph below.

Internal energy(U):

• We know that the formula for internal energy is obtained from the first law of thermodynamics. This depicts the change in internal energy is equal to the difference of the heat transfer into the system(Q) and work(W) done by the system.
• Mathematically, U = Q - W
• let us neglect the heat transfer here because the heat transfer is not calculated by the solver (Because Thermal analysis is not done). Now, Work done (W) is the product of force and displacement. The internal energy depends upon the displacement mush here. In the beginning, there is no displacement within the component, that’s why the internal energy starts from zero(origin). when it is subject to acceleration there will be a displacement. As the displacement increases, the internal energy increases, that’s why there is a raise internal energy curve, as shown in the graph below.

Contact Energy:

• The obtained graph for contact energy appears as shown in the graph below. Initially, there will be no contact between the rail component and rigid wall. And also, there is no contact within the component, that’s why the curve starts from origin. And gradually, it reaches the peak because of more contact within the elements of the component due to the deformation. And it drops down as shown in the image below. It raises slowly again to some extent because there will be a contact between the component and the rigid wall. And due to this contact between the wall and the contact takes place, again and again, there will be a regulation in the curve as shown in the graph below.

Hourglass energy: 

• As the recommended properties are not specified in this case, there will be a deformation of elements with respect to the strain is not recorded. Which depicts that, the elements undergo an hourglass effect. And there will be no physical stabilization. So, to balance the energy, artificial energy is required. That is hourglass energy. So, there is a lot of hourglass energy needed. So, the hourglass energy starts from the origin and goes on increasing, as shown in the graph below.

Total energy:

• We know that Total energy is the sum of kinetic energy and potential energy. As there is no potential energy plotted here, the kinetic energy is taken into account. The total energy is directly proportional to kinetic energy. As the kinetic energy decreases, the total energy also decreases, 

Case 2 (With assigning the recommended parameters in the property): -

• In this case, the properties which are recommended in the question are entered. The procedure is the same as in case-1 till entering the parameters in the property cards. After entering the recommended properties, the property card.

 

Note: Save this new file in another location. In order to have the entire animation files, engine output files separately with respect to the first case. To compare the results.

• After doing the analysis through the radioss option in the analysis panel, the verification is done to check the required number of animation files are obtained or not.
• Then the engine output file is opened to view the various parameters such as kinetic energy, Internal energy, energy error, etc. 
• These values are much less when compared to the obtained values in case-1 which depicts the improvement.

 

• The obtained simulation, with respect to von-misses view, appears as shown in the animation below.

 

• The next step is post-processing, in this process, various graphs are obtained. In order to see the changes in the result with respect to case-1. The process of obtaining the graphs is the same as in case-1.
• The obtained rigid wall force graph appears as shown in the image below. The graph appears as similar to that of case-1. And there is some improvement in the graph.

 

• The next graph consists of parameters such as Internal energy, kinetic energy, contact energy, total energy, Hourglass energy as shown in the image below. The graph seems to be somewhat similar in the aspects of kinetic energy, internal energy. But there will be a small rise in total energy, and the hourglass energy is zero. 

 

Note: The same system of units should be used in all cases.

Hourglass energy

• As the deformation starts increasing the hourglass energy increases gradually because the Default elemental property I;e 0- DEF SHELL has a single integration point and the hourglass is managed with perturbation method by slightly changing the material properties thus it makes to increase the hourglass energy.
• Where as in improved elemental property I;e QEPH-4 the hourglass energy is zero because the property of the element has improved 4 noded under integration points and it has physical hourglass stabilization property it thus it avoids the hourglass completely in this case.

    

Total energy

• The total energy for the default element property varies. At the initial stage when the load is applied, energy will be at its maximum and decreses as the material starts to deform this is due to the energy error in the simulation where the error was found to be varying from 0 to -10.3% .
• The total energy was found to be constant throughout the simulation for the improved elemental property simulation because the energy errors were negligible and close to 0 (found to be 0 to -0.1%) due to the accuracy of this property it’s always preferred in explicit analysis.

• Results

Comparison between the results of case-1 & case-2: -

Basis for comparison	Case-1	Case-2
Obtained maximum energy error	-10.3%	-0.1%
Obtained maximum kinetic energy	0.3563E+08	0.4376E+08
Obtained maximum Internal energy	0.1932E+08	0.1750E+08
Hourglass energy	Varying hourglass energy	Constant hourglass energy
Reason for hourglass energy	The elements don’t have physical stabilization (Due to the default values in the property cards).	The elements have physical stabilization (Due to the assigning of recommended values in the property cards).
The requirement of hourglass energy	requires hourglass energy to the energy balance.	No hourglass energy is required to balance the energy.
Results	The results are less accurate	The results are accurate

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 (`I_(shell)`= 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).

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.

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.

Learning Outcomes

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 of the 2^nd case are much higher and different than 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 reduced hourglass formation drastically due to the introduction of the physical stabilization method that is deployed by QEPH elements.