Global Refinement

This tutorial will cover how to globally refine the mesh for a beam bending model.  It starts with a beam model with a coarse mesh (10X2X2) and covers how to incrementally refine that mesh until the beam tip displacement has reached an asymptote. The concepts of solution error and solution error versus computational time are also presented.

The beam model has the left face constrained in all degrees of freedom with a unit pressure load applied to the top face of the beam.  These boundary and loading conditions will not change throughout this tutorial.

Open the Beam Model

1. Open FEBio Studio and click the Repository tab in the lower left of the screen.
2. Click Connect and then Login to the Repository using your FEBio account information.
3. Navigate to the Tutorials>Mesh Convergence Tutorial folder and select: MeshConvergenceBeam.fsprj file.

Run the Model

1. Select FEBio -> Run FEBio … from the menu, or alternatively press F5, and click the Run button.
2. A dialog box should appear informing you that the simulation terminated normally.
3. Click OK.

View the Results

1. Select the new job entitled “BeamTest_job” that was added to the bottom of the Model Tree located on the left side of your screen.
2. Under the Properties section, click the button labeled Open in FEBio Studio.
3. Enable the Color Map in one of two ways: On the top toolbar locate the dropdown menu that is next to a grayed-out icon showing concentric circles . From this menu, select displacement -> Total displacement. Alternatively in the Model tab on the left side of the window click on the arrow next to BeamTest_job.xplt to see more options and then select Color Map. Then in the Properties box that appears below click on the dropdown menu for the Data field property and select displacement -> Total displacement.
4. Change the model view in one of two ways: In the menu select View -> Standard views -> Front. Alternatively, right click in the model view window and select Standard views -> Front.
5. Locate the animation toolbar near the top of the window . If you cannot locate it, ensure that it is enabled by right clicking anywhere on the toolbar and ensuring that the Animation bar is checked. If only part of the toolbar is visible either enlarge your PostView window, or click on the double arrow icon on the left side to expand the toolbar and see all of the options.
6. Press the Play button to watch the animation. By default the animation will loop and will continue to play until the play button is pushed again. You should see the beam deflect in the -Z direction with a gradient of colors indicating the left side has no displacement (blue) and the right side has maximum displacement (red).

Record the Beam Tip Displacement

1. Rotate the beam so you can see the right end (the end that moved) and select the Select nodes button at the bottom of the view window.
2. Select the center node on the end of the beam.
3. Create a new graph in one of two ways: In the menu select Post -> New Graph … or by pressing F3.
4. Select Total displacement in the blank grey drop down menu at the top of the Graph1 – FEBio Studio window.
5. Select the final data point on the graph by left clicking on it. You may need to left click hold and drag first to be able to select the last data point.
6. Record the end of the beam displacement (Y: 1.66498) from the graph and the Time in linear solver: 0:00:00 from the Output window in a spreadsheet along with the mesh density for this model: 10X2X2.
7. Create a spreadsheet with the following columns:

Refining the Mesh

1. Select the Model tab in the upper left corner of the view window.
2. Verify that the Select Objects button is selected on the top toolbar.
3. Select the beam by left clicking on it.
4. In the Build window on the right select the Mesh tab.
5. Change Nx: 20, Ny: 4, Ny: 4 and select Apply. Your View and Build Windows should look like this:

Incremental Mesh Refinement

1. Repeat the Run the Model through Refining the Mesh steps above so you have Beam Displacement and Time in Solver data for the following mesh refinements: 10X2X2, 20X4X4, 40X8X8, 60X12X12 and 80X16X16.
2. Add a Percent Error column to your spreadsheet with the following calculation: Percent Error = ((LastMeshBeamDeflection – CurrentMeshBeamDeflection)/LastMeshBeamDeflection)*100
3. When you are done your spreadsheet should look similar to this:
4. Create an XY scatter plot of Beam Deflection versus Number of Elements. It should look similar to this:
5. 
6. As you can see from the graph, the beam deflection asymptotes with the third mesh refinement (40X8X8).
7. Often times an analyst is looking to reduce the error due to discretization below a particular threshold. This threshold should be less than 1% to 2% for most analyses. To evaluate this plot Percent Error versus Number of Elements. That graph should look similar to this:
8. As you can see from this graph, the error is <1% with the third mesh refinement (40X8X8).
9. Finally, sometimes for larger models the mesh that is used comes down to a judgement call that balances discreitation error with the time to run the model. To evaluate this plot Percent Error versus Time in Solver. That graph should look similar to this:
10. Although this is a small model and these times are short, you can still see it takes four times longer to run the 60X12X12 mesh compared to the 40X8X8 mesh.

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