Assignment 3-2D Element Formulation Challenge

OBJECTIVE:

• To Run the simulation with the default property card {CASE:1}
• Changing the property card {CASE:2} and run the simulation.
• Comparing the result of CASE:1 & CASE:2

THEORY:

HOURGLASS

• Hour glassing is an artificial deformation that can occur in some types of finite element models. It typically occurs in shell and solid elements and is caused by numerical instability. Hour glassing is characterized by a type of deformation where the elements seem to bulge out in the center and contract at the edges, resulting in an hourglass shape.
• Hour glassing can occur due to various reasons such as incorrect element formulation, material properties, or boundary conditions. It can also occur due to an inadequate mesh or time step size.
• Hour glassing can lead to inaccurate results in finite element analysis, especially in dynamic simulations. Therefore, it is essential to take appropriate measures to prevent or minimize hour glassing in finite element models.
• Various techniques can be used to prevent or minimize hour glassing, such as selecting the appropriate element formulation, adjusting the material properties, using a suitable mesh, and controlling the time step size. Another common technique is to apply an hourglass control to the model, which is a numerical method used to counteract hour glassing by introducing additional forces to the nodes of the affected elements.

METHODS TO CONTROL THE HOURGLASS:

1.) Perturbation method (Viscous method):

• This method is generally used for the elements with Ishell: 1,2,3,4 or Q4 elements.
• The process how this method work is: When the hourglass deformation occurs---> There will be some damping applied, which is 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 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.
• Recommended for high velocity or high strain rate problems. Example: Involving high explosives.
• A huge amount of hourglass energy is generated.

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

Shell Element Formulation

• Q4 Element:

• It is represented in the RADIOSS solver by an entity named "Ishell(1,2,3,4)".
• It is an under(or) reduced-integrated element. Because it has only 1 integration point for an element.
• Usually Ishell:1, 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.
• But 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 to each node.
• It is represented in the RADIOSS 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. But 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 RADIOSS solver by an entity named "Ishell:24".
• This type of element is 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.

Key parameters in /PROP/SHELL:

• Ishell: -To select the element formulation for 4-noded shell elements.
• Ish3n: -To select the element formulation for 3-noded shell elements.
• N: - To choose the number of integration points through the thickness
• Ismstr: - To specify whether the strain formulation is small or large.
• Iplas: - To choose method for the calculation of post-yield strain.
• Ithick: - To determine if the thickness is constant under load or if the element thins

PROCEDURE/STEPS:

• Import the model

Here we import the Model in RADIOSS {solver deck}.

Our Model will appear in Hyper mesh GUI

• Assigning time step Value

Now for this we go to ENG_RUN card >> and in Tstop is 55ms as per given.

Tstop is simulation time or Final time for run [t] .

• Changing the number of animation steps

• Here we have minimum 25 and maximum of 60.
• We take 40
• T{freq.} = TIME STEP/NUMBER OF ANIMATION STEP.

= 55/40

= 1.375.

{CASE: 1}

• property card parameter

In the property card every parameter property is by default for CASE:1

• Simulation

Now we will run the simulation by using Tool Analysis >> Radioss >> Edit the card as per figure below.

Click Radioss and simulation starts running after some time, it will show JOB IS COMPLETED

• Checking energy error and mass error:

we need to check the output of simulation in 0001.out file

Condition for acceptable result

• The error {Energy} must be less than – 15 % at the end of computation (-5% for a good model setup).
• The error {mass} must be less than 2%.

So, from out put data our both the condition is satisfy we go for plots.

Plots

• Rigid wall Force:

• Internal Energy:

• Hourglass Energy:

• Contact Energy

• Total Energy:

{CASE:2}

• property card parameter

• Simulation

Checking energy error and mass error:

we need to check the output of simulation in 0001.out file

• Here we have Energy Error -0.1% which is good as previous.
• The mass Error is 0.1659e-03 this one is also good as previous.

Plots

• Rigid wall Force:

• Internal Energy:

Hourglass Energy:

Contact Energy:

Total Energy:

COMPARISON {CASE:1} & {CASE:2}

CONCLUSION

Here we have Learn

• How to carry out simulation
• How to set property card
• How to use hypergraph for 2D plots.
• Role of hourglass and how to Counter Hourglass effect.

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Thanks & regards,

DEVESH KASHYAP