Assignment 3-2D Element Formulation Challenge

OBJECTIVE:

Comparison of results with base simulation and improved shell element properties

Import:

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

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

• 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 model tree, under CARDS collector, ENG_ANIM_DT card have 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 local directory.

• edit options providing 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 aceptable 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, 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

• animation shows how the crush tube deformes (displacement)under the action of force.
• To plot the specific graphs, hyper graph 2-d is selected.
• 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, following observations are made:
• Internal energy increases throughout the simulation which is due to the force developed on tube due to deformation.
• There is a slight increase in hourglass energy throughout the simulation.
• Contact energy remains zero throughout the simulation.
• Total energy of the system has a slight decrease from the start to 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 a non-linear behaviour, which is due to the variation in the force exerted by the crush tube on the wall throughout the simulation.

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

Contour plot of Displacement is obtained using contour option under hyperview.

Changing the shell elements properties to recommended properties

Recommended properties:

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 model tree, under CARDS collector, ENG_ANIM_DT card have a Tfreq of 1.0, which is changed to 1.375.

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

• edit options providing 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 aceptable 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
• 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:

Default

Recommended Properties

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:

• In FEA, the hourglass mode is also known as the "zero energy mode" because deformation energy of elements under hourglassing mode is zero. But the hourglass energy is not equal to zero.
• 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.

To solve this problem,

1. Mesh Refining is a solution. Hourglassing is more prone in 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 hourglass deforms. This is only a FEA point of view and in actual physical system, there is no such stiffness. This is what is called as Built in hourglass controls.
4. Viscous damping.