Tutorial: Strain Energy Density Analysis

Tutorial Level: Beginner 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
Figure 1. Strain Energy Density Analysis Results

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. On the Structure ribbon, click the Run OptiStruct Analysis button in the Analyze tool group.


    Note: To find and open a tool, press Ctrl+F. For more information, see Find and Search for Tools.
  5. Run a Normal Modes analysis using the following settings:
    1. Change the Element Size to 5 mm.
    2. Set the number of Normal Modes to 3 and use the supports from Load Case 2.
    3. Set Speed/Accuracy to Faster.
    4. Click Run to perform the analysis.

Review the Strain Energy Density Results

  1. When the analysis is complete, select it in the Run Status window and click View Now to view the results.
  2. Click the button on the animation toolbar to visualize the displacement. Click the button to pause the animation. Note that although the mode shape is clear, it is difficult to know which parts of the structure are most critical.
  3. Adjust the Analysis Explorer using the following settings:
    1. Select Strain Energy Density under Result.
    2. Change the legend maximum to 1.0e8 kg/(mm*s2).

    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.
    Note: To find and open a tool, press Ctrl+F. For more information, see Find and Search for Tools.
  2. Click each face of the large side cutouts with the Move Faces tool to select them.
  3. Click the Z Translation arrow and type 20 mm in the box to move the cutouts in the Z direction.
  4. Click the Y Translation arrow and type 10 mm to move the cutouts in the Y direction. This adds material to the area of high strain energy density without changing the mass of the design.
  5. On the Structure ribbon, click the Run OptiStruct Analysis button in the Analyze tool group to run the analysis again.


    In the Analysis Explorer, note that the first frequency has increased from 457.982 Hz to 488.684 Hz.

  6. 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.
    1. On the Geometry ribbon, select the Move Faces tool.
    2. Select each face of the right slot on the top of the bracket.
    3. Click the X Translation arrow and type 10 mm to move the slot 10 mm toward the outside of the bracket.
    4. Select each face of the left slot on the top of the bracket.
    5. Click the X Translation arrow and type -10 mm to move the slot 10 mm toward the outside of the bracket
  7. On the Structure ribbon, click the Run OptiStruct Analysis button in the Analyze tool group to run the analysis again.


    In the Analysis Explorer, note that the first frequency has increased again, from 488.684 Hz to 499.108 Hz.

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.