# Tutorial: Strain Energy Density Analysis

Run a normal modes analysis and examine the strain energy density results.

Run a modal analysis and use the strain energy density results to improve the design of a simple bracket that supports a mass.

In this lesson, you will:

• Run a normal modes analysis on a simple bracket supporting a mass
• Examine the strain energy density results
• Change the design of the bracket (without adding any mass) based on these results
• Compare the designs

The purpose of the tutorial is to demonstrate the following principles:

• When a structure deforms, different regions strain by different amounts. The sum of the energy in the structure due to the deformation is called the strain energy.
• Eigenvalues are normalized when a modal analysis is performed. The strain energy density results are used to determine which areas of the structure are under the greatest strain and contribute most to the stiffness.
• Targeting areas of high strain energy density for design changes is a common method to increase the natural frequencies in a modal analysis.

## Examine the Model and Run a Modal Analysis

1. Press F7 to open the Demo Browser.
2. Double-click the 0.0_SED_tutorial.stmod file to load it in the modeling window. Note that the model has a concentrated mass and four grounded bolts in a load case.
3. Make sure the display units in the Unit System Selector are set to MMKS (mm kg N s).
4. Click Run Analysis on the Analyze icon to open Run Analysis window.
5. Run a normal modes analysis using the following settings:
6. Change the Element size to 5 mm.
7. Set the number of Normal Modes to 3 and use the supports from Load Case 2.
8. Make sure Speed/Accuracy is set to Faster.
9. Click Run to perform the analysis.

## Review the Strain Energy Density Results

1. When the analysis is complete, double-click on the name of the run to view the results. (Alternatively, open the 0.1_SED_tutorial.stmod file in the Demo Browser to load and view the results.)
2. Animate the displacement result for the first normal mode. Note that although the mode shape is clear, it is difficult to know which parts of the structure are most critical.
3. Change the result type to Strain Energy Density and change the legend maximum to 1.0e8 kg/(mm*s2).
4. This highlights the areas of the structure with the highest relative strain. Adding material to these high strain regions is normally a good way to increase the natural frequency.

## Add Material to the High Strain Regions

1. On the Geometry ribbon, select the Move Faces tool.
2. Translate the large side cutouts 20 mm in the Z direction.
3. Translate the large side cutouts 10 mm in the Y direction. This adds material to the area of high strain energy density without changing the mass of the design.
4. Re-run the modal analysis (or open the 1.0_SED_tutorial.stmod file in the Demo Browser and load the analysis results.) Note the first frequency has increased.
5. Now translate the two slots on the top of the bracket outwards by 10 mm. The purpose of this change is to increase the bending section near the areas of high strain energy density on the top of the bracket.
6. Re-run the modal analysis (or open the 1.1_SED_tutorial.stmod file in the Demo Browser and load the analysis results.) Note the first frequency has again increased significantly.

In summary, targeting areas of high strain energy density is a powerful approach for increasing the stiffness of structures. In this tutorial the first mode was increased significantly with no material added.