Assignment 3-2D Element Formulation Challenge

Assignment 3-2D Element Formulation Challenge

Objectives: -

Perform the simulation on the given model with default properties and change the properties. Compare both CASE 1 & CASE 2. Also, give a detailed explanation of hourglass energy.

Recommended properties:

Parameters		Comment
Ishell =24		QEPH 4 nodes 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		The 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.

Procedure: -

CASE 1:

1. Firstly, import the .rad file.

2. Now, edit the file. For that, go to the cards folder and edit the ENG_RUN.

Change the run time to 55 ms in Tstop.

Change the number of animation steps during simulation to a minimum of 25 and a maximum of 60. So, we put 45 animation steps.

Frequency = 1/time

f = 1/t

Put the value in above equation,

f = 1/55

f = 0.01818 Hz

Multiply frequency by 45

f = 0.01818 × 45

f = 0.818 Hz

Now, edit ENG_ANIM_DT & put Tfreq = 0.818Hz

After that, go to analysis and select radios.

Upload .rad file and put -nt 4 in options, then press Radioss.

Wait for a minute to complete the entire procedure.

1. The Energy error range is between -15% to +5%, and we obtain -10.3% which is an acceptable range.

Now, the job is completed. Press Result.

Press apply and see the animation.

After that, open the model in contour mode.

Hourglass energy is range between Min. -2.871E+01 to Max. +2.284E+04. As shown in the above animation.

Now, open the Hypergraph 2D to view the graph and open the assignmentT01 file.

CASE 2

In case 2 assign the Recommended properties:

Parameters		Comment
Ishell =24		QEPH 4 nodes 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		The 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.

Now, open the property and put all the above-given values.

After that, go to analysis and select radios.

Upload .rad file and put -nt 4 in options, then press Radioss.

Wait for a minute to complete the entire procedure.

1. The Energy error range is between -15% to +5%, and we obtain -3.8% which is an acceptable range.

Now, the job is completed. Press Result.

Press apply and see the animation.

After that, open the model in contour mode.

Hourglass energy is range between Min. -9.957E+01 to Max. +3.653E+04. As shown in the above animation.

Now, open the Hypergraph 2D to view the graph and open the assignmentT01 file.

Comparison of CASE 1 & CASE 2

	CASE 1	CASE 2
1. Energy Error	-10.3%	-3.8%
2. Kinetic Energy	0.3563E+08	0.3967E+08
3. Internal Energy	0.1932E+08	0.1932E+08
4. Hourglass Energy	Min. -2.871E+01 Max. 2.284E+04	Min. -9.957E+01 Max. 3.653E+04
5. Mass Error	0.1659E-03	0.1659E-03
6. Von mises stress	3.500E+02	3.500E+02

Energy Error: -

• If the error is negative, it means that some energy has been dissipated.
• In the case of under integrated elements (Belytschko shells, solids with 1 integration point),
• Hourglass Energy can explain a negative Energy Error since it is not counted in the energy balance. The normal amount of Hourglass energy is about 10% to 15%.
• If the error is positive, there is an energy creation.
• In the case of using QEPH shell formulation or fully integrated elements, the Energy Error can be slightly positive since there is no Hourglass energy and the computation is much more accurate. An error of 1% or 2% will be acceptable.

Hourglass Energy: -

Hourglass is the weird mode of deformation that occurs under integrated elements and no stresses will be produced. This can affect solution accuracy by varying the structure’s true response. This leads to inaccurate stress, strain, and deflection results. For an under-integrated element, displacements and forces may exist for each node of the element. If the sum of all these forces and displacements gives null strain and stress on the integration point of the element, then that element fails to calculate stiffness for certain modes of deformation. At this stage, we say the element has entered into the hourglass. Soon after this as the element failed to calculate stiffness, the element will behave weirdly. There are ways to control hour glassing and in the subsequent units, we will discuss it.

Hourglassing Due to Reduced Integration: -

• Reduced integration can lead to non-physical zero-energy modes, called hourglass modes
• Two methods used to control the formation of hourglassing:
• Perturbation (Q4 Elements)
• Physical Stabilization (QEPH Elements)

Hourglass Perturbation Control Method: -

Perturbation method Ishell=1,2,3 or 4 (Q4)

• The hourglass deformation is detected with the relative motion (velocity) of the nodes.
• When hourglassing is detected, a force is applied to the node to stabilize the deformation.
• This force is defined according to the element stiffness (Young modulus, yield stress, plastic tangent)
• This force introduces artificial energy (named hourglass energy)

Perturbation method Ishell= 24 (QEPH)

• Hourglass yield depends on the natural yield
• Hourglass loading stiffness depends on the natural tangent modulus
• The hourglass treatment is done at the material level

Hourglass Control Methods Comparison: -

• The Q4 (Belytshko & Tsay) elements may have bad behavior in case of large rotation and distortion and case of elastic load-unloading cycles.

• The QEPH elements give accurate results in the case of loading and unloading, even if there is hourglass mode deformation.

What About Hourglass Energy?

The normal value for hourglass energy:

• 10% to 15% of the total energy when using under integrated elements (Belytschko shells, solids with 1 integration point)

• Hourglass Energy is not counted in Energy Error, so negative energy error can occur High hourglass energy in case:
• Under integrated elements without optimized parameters. To avoid high hourglass energy:
• Set recommended parameters for the property definition.
• Fully integrated elements. Or
• HEPH for solid elements.
• QEPH for shell elements (HEPH & QEPH can result in a slightly positive energy error, 1 to 2%).

Hourglass Modes: -

Hourglass modes are element distortions that have zero strain energy. The 4-node shell element has 12 translational modes, 3 rigid body modes (1, 2, 9), 6 deformation modes (3, 4, 5, 6, 10, 11), and 3 hourglass modes (7, 8, 12).

Figure 1. Translational Modes of Shell

Along with the translational modes, the 4-node shell has 12 rotational modes: 4 out of plane rotation modes (1, 2, 3, 4), 2 deformation modes (5, 6), 2 rigid body or deformation modes (7, 8) and 4 hourglass modes (9, 10, 11, 12).

Figure 2. Rotational Modes of Shell

Result: -

As we see the difference between CASE 1 & CASE 2, there will be lots of changes in Energy error and Hourglass energy. Others are the same value in both CASE 1 & CASE 2.

Learning Outcomes: -

1. We learn about how to analyze the file using radioss.
2. We learn about how the energy error and hourglass energy change the model values.
3. We learn about how to perform animation with different methods like Von mises and Hourglass energy in contour mode.
4. Also, we learn about how to plot the graph of internal energy, kinetic energy, hourglass energy, total energy, contact energy, and time step.

Conclusion: -

In this challenge, we check the difference between CASE 1 & CASE 2 how the energy error and hourglass energy affect the model with the same run time and animation steps.