## Investigating FEA Results

The best starting point when investigating FEA results is to check the total displacement. It is usually the case that displacements are too small for the naked eye and it is necessary to exaggerate the displacements to get a feel for what is going on. Examples of exaggerated displacement plots are shown below. If the displacements look right you are halfway there.

Hand calculations are a good sanity check for most FEA. Even for a complicated structure you can usually do a simple hand calculation to check part of it. You can also check reaction forces of FEA models at the constraints and compare these with your hand calculation.

When performing non-linear analysis it is advisable to do a linear run first to make sure there are no obvious errors such missing constraints. When doing contact analysis it is advisable to check the level of penetration to make sure this is realistic.

One of the most important and often overlooked checks is mesh quality and density. Uneven stress contours are an indication of a mesh that is too course. The following pictures show the results from a coarse mesh using the bracket model.

Hand calculations are a good sanity check for most FEA. Even for a complicated structure you can usually do a simple hand calculation to check part of it. You can also check reaction forces of FEA models at the constraints and compare these with your hand calculation.

When performing non-linear analysis it is advisable to do a linear run first to make sure there are no obvious errors such missing constraints. When doing contact analysis it is advisable to check the level of penetration to make sure this is realistic.

One of the most important and often overlooked checks is mesh quality and density. Uneven stress contours are an indication of a mesh that is too course. The following pictures show the results from a coarse mesh using the bracket model.

Notice that the stress contours appear patchy and uneven; this is a sign of inadequate mesh density. Let’s try the same analysis with a medium mesh density.

Another good technique for checking if the mesh is fine enough is to compare averaged and unaveraged results in the area of interest which is the radius in this case.

There is an 85 MPa difference between the averaged and unaveraged nodal results and the mesh is clearly not refined enough. You can’t see any red because the peak stress is hidden away underneath the surface.

Let’s try it again but with a much finer mesh.

Notice that the stress contours are much smoother and there is no difference in averaged and unaveraged stress. This is an accurate result!

The fine mesh produced a total translation or displacement of 19.41mm and the coarse mesh was 19.09mm. The mesh density has a big effect on stress but hardly any impact on displacement. Also the Von Mises Stress of 1635 MPa is well above yield for steel therefore this linear stress and displacement is not real. Non-linear material analysis would be required to check permanent deformation and real stress.

A more reliable method of ensuring that your mesh is fine enough is to carry out a mesh convergence study. The hole in plate example has been used to demonstrate a mesh convergence study.

**Tip**The fine mesh produced a total translation or displacement of 19.41mm and the coarse mesh was 19.09mm. The mesh density has a big effect on stress but hardly any impact on displacement. Also the Von Mises Stress of 1635 MPa is well above yield for steel therefore this linear stress and displacement is not real. Non-linear material analysis would be required to check permanent deformation and real stress.

A more reliable method of ensuring that your mesh is fine enough is to carry out a mesh convergence study. The hole in plate example has been used to demonstrate a mesh convergence study.

The analysis is run with ever increasing mesh density until there is no significant difference from one run to another. You can then be absolutely sure that your mesh is fine enough and the stress results are accurate.

In some cases you may find that no matter how many times you increase the mesh density you never reach convergence and the stress just keeps going up and up. This is called a singularity and is caused by fixed constraints and sharp corners. There is no such thing as a true fixed constraint or sharp corner in the real world. Even a component that looks like it has a sharp corner really just has a very small fillet radius. In this case you need to take the stress some distance away from the sharp corner or fixed constraint.

In some cases you may find that no matter how many times you increase the mesh density you never reach convergence and the stress just keeps going up and up. This is called a singularity and is caused by fixed constraints and sharp corners. There is no such thing as a true fixed constraint or sharp corner in the real world. Even a component that looks like it has a sharp corner really just has a very small fillet radius. In this case you need to take the stress some distance away from the sharp corner or fixed constraint.