Assignment 3-2D Element Formulation Challenge

OBJECTIVE:

Comparison of results with base simulation and improved shell element properties using

Recommended properties:

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.

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

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

Create a brief report comparing all the results

Procedure:

case 1: Base simulation

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

• The elements view is set to shaded elems view which displays the elements as follows.

• Changing run time to 55ms:
• In the model tree, under CARDS collector, ENG_RUN card has a Tstop of 60, which is changed to 55.

• Changing animation steps to 40:
• To have 40 animation steps, the frequency should be Run time/Animation steps = 55/40 = 1.375
• In the model tree, under CARDS collector, ENG_ANIM_DT card has a Tfreq of 1.0, which is changed to 1.375.

• The base simulation is run without any modification to element properties using Radioss option under Analysis tab.
• Create a folder to save the rad files in a local directory.

• edit options providing a number of threads as " -nt 4 ".
• After analysis, the.OUT file is viewed to check whether the Energy error and mass error fall within the acceptable range

• The energy error starts from 0% to 10% which is within acceptable range.
• Mass error stays constant throughout the simulation at 0.1659e-03 which is also within the acceptable range.
• Since the error values are acceptable, rigid wall forces, internal energy, hourglass energy, contact energy, and total energy of the simulation are plotted with the help of hypergraph 2-D
• Hyperview is opened to view the simulation (deformation of the crush tube).
• Model and results (h3d file) are loaded from the newly created folder

• The animation shows how the crush tube deforms (displacement)under the action of force.
• To plot the specific graphs, hypergraph 2-d is selected.
• A file named Element_Formulation-Shell-3_assignmentT01 is opened.
• Specified energies are plotted against time on the same plot as shown below:

• From the plot obtained for base simulation without any modification to element properties, the following observations are made:
• Internal energy increases throughout the simulation which is due to the force developed on the tube due to deformation.
• There is a slight increase in hourglass energy throughout the simulation.
• Contact energy remains zero throughout the simulation.
• The total energy of the system has a slight decrease from the start to the end of the simulation.

A new plot is created to plot the rigid wall forces.

Total resultant force and Resultant normal rigid wall forces are plotted against time as shown above.

The rigid wall force curve is of non-linear behavior, which is due to the variation in the force exerted by the crush tube on the wall throughout the simulation.

A contour plot of Hourglass energy is obtained using the contour option under hyperview.

The contour plot of Displacement is obtained using the contour option under hyperview.

case 2:

Changing the shell elements properties to recommended properties

Recommended properties:

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.

The shell elements properties are modified to recommended property values:

• Changing run time to 55ms:
• In model tree, under CARDS collector, ENG_RUN card have a Tstop of 60, which is changed to 55.

• Changing animation steps to 40:
• To have 40 animation steps, the frequency should be Run time/Animation steps = 55/40 = 1.375
• In the model tree, under CARDS collector, ENG_ANIM_DT card has a Tfreq of 1.0, which is changed to 1.375.

• Running the simulation with the newly defined recommended properties using the Radioss option under the Analysis tab.
• Create a folder to save the rad files in a local directory.

• Edit options providing a number of threads as " -nt 4 ".
• After analysis, the.OUT file is viewed to check whether the Energy error and mass error fall within the acceptable range

• The energy error starts from 0% to -0.10% which is within acceptable range.
• Mass error stays constant throughout the simulation at 0.1659e-03 which is also within the acceptable range.
• Since the error values are acceptable, rigid wall forces, internal energy, hourglass energy, contact energy, total energy of the simulation are plotted with the help of hypergraph 2-D
• The file named Element_Formulation-Shell-3_assignmentT01 is opened.
• Specified energies are plotted against time on the same plot as shown below:

• From the plot obtained for simulation after modification to element properties, following observations are made:
• Internal energy increases throughout the simulation which is due to the force developed on tube due to deformation.
• Total energy remains same throughout the simulation.
• Hourglass energy and contact energy remains zero and follows the origin throughout the simulation.

A new plot is created to plot the rigid wall forces.

Total resultant force and Resultant normal rigid wall forces are plotted against time as shown above.

The rigid wall force curve is of a non-linear behaviour, which is due to the variation in the force exerted by the crush tube on the wall throughout the simulation.

Comparison:

Case 1:

Case 2:

RESULT AND CONCLUSION

When recommended properties are changed from the base values, simulation results show that

1. Total Energy remains constant rather than decreasing which is clear from the energy error which went till-10% and now changed to -0.1%.
2. Hourglass energy which was increasing changed to zero throughout the simulation.
3. Contact energy characteristics are the same in both cases.
4. Internal energy is having gradually increasing characteristics in both cases.
5. Rigid wall forces also decreased to a lower value than that of the default value rigid wall force value.
6. Contour plots show that there is a slight increase in the maximum displacement of an element with recommended property values.

Hourglass energy:

• In FEA, the hourglass mode is also known as the "zero energy mode" because the deformation energy of elements under the hourglassing mode is zero. But the hourglass energy is not equal to zero.
• In a shell element that has a number of integration points, for reduced computation effort, a reduced integration that uses a single integration point is used. In such cases, the deformation mode from the analysis results will be false. This is called the hourglass phenomenon.
• This is just a nonphysical zero energy mode which leads to excessive element distortions. The more structured and less distorted your elements are, the better the results.

To solve this problem,

1. Mesh Refining is a solution. Hourglassing is more prone in the coarse mesh.
2. Fully Integrated elements are better though computational time increases vastly and fully integrated elements are prone to shear locking.
3. Providing a small arbitrary stiffness in the mode in which the hourglass deforms. This is only a FEA point of view and in actual physical systems, there is no such stiffness. This is what is called as Built-in hourglass controls.
4. Viscous damping.