3. 2D Element Formulation

OBJECTIVE: To compare the results of the base case simulation and improved shell element properties case simulation.

CASE 1: Base Simulation

Procedure:

• The rail file from the prevous assignment has to be imported to hypermesh.

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

• For changing the run time to 55ms, go to the model tree, under the cards collector, Select ENG_RUN card, change the Tstop value from 60 to 55.

• For changing the animation steps to 40: before that to have 40 animation steps, the frequency should be Run time/Animation steps = 55/40 =1.375
• Now, go to the model tree, under cards collector, Select ENG_ANIM_DT and change the Tfreq value from 1 to 1.375.

• Now to run the base simulation, go to analysis tab and select Radioss option and edit the options tab as "-nt 4" and save the simulation in a new folder.
• After analysis, you can find the .out file and the .h3d file of the simulation in the new folder.
• Now that the simulation is done, We open the .out and the h3d file from the new folder to do the energy error and the mass error checks
• 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, 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 Results of the simulation, i.e, the Displacement and the von misces contours and the plots of the internal energy, hourglass energy, contact energy, total energy and the rigid wall forces are shown below:

RESULTS:

CASE 2: Changing the shell elements properties to recommended properties

 Recommended Properties:

• To modify the properties of the shell elements, go to the properties card and select a property and change its values to the recommended settings. 
• The shell elements properties are modified to recommended property values:

• For changing the run time to 55ms, go to the model tree, under the cards collector, Select ENG_RUN card, change the Tstop value from 60 to 55.

• For changing the animation steps to 40: before that to have 40 animation steps, the frequency should be Run time/Animation steps = 55/40 =1.375
• Now, go to the model tree, under cards collector, Select ENG_ANIM_DT and change the Tfreq value from 1 to 1.375.

• Now to run the simulation with the recommended properties, go to analysis tab and select Radioss option and edit the options tab as "-nt 4" and save the simulation in a new folder.
• After analysis, you can find the .out file and the .h3d file of the simulation in the new folder.
• Now that the simulation is done, We open the .out and the h3d file from the new folder to do the energy error and the mass error checks
• 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, 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 Results of the simulation, i.e, the Displacement and the von misces contours and the plots of the internal energy, hourglass energy, contact energy, total energy and the rigid wall forces are shown below:

RESULTS:

CONCLUSIONS:

When recomended properties are changed from the base values, simulation results shows that

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

Hourglass Energy:

• Hourglass energy modes are nonphysical, zero-energy modes of deformation that produce zero strain and no stress. Hourglass modes occur only in under-intetgrated (single integration point) solid, shell, and thick shell elements.
• In a shell element which have a number of integration points, for reduced computation effort, a reduced integration which uses a single integration point is used. In such cases, the deformation mode from the analysis results will be false. This is called hourglass phenomenon. 
• This is just a non physical zero energy mode which leads to excessive element distortions. The more structured and less distorted your elements are, the better the results.

This problem can be reduced by,

1. mesh refining
2. Viscous Damping
3. Increasing stiffness