# Mesh Convergence Study in ABAQUS

• dfitz1000

#### dfitz1000

Hi,
I just have a quick question about mesh convergence, hopefully someone can help.

I have a model of a pipe bend that I've meshed using ABAQUS and then found the location and value of the maximum von Mises stress. I then refined the mesh a few times and plotted the max stress against the number of elements in each mesh. The resulting graph has the following shape with no. of elements on the X axis and stress on the Y axis
.
http://people.sinclair.edu/nickreeder/eet150/PageArt/exponentialI.gif

Any mesh convergence graphs I've seen however have the following shape.

http://www.chalice-engineering.com/News/images/knowledge1_fig1.GIF [Broken]

Does it matter that my graph is a mirror image of what it "should" be? ie the stress in my model converges from a higher stress to a lower stress rather than vice versa.

Any help would be appreciated.

Thanks.

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As you refine your mesh, the maximum stress goes to zero?

Are you sure that you are plotting the maximum stress and not perhaps stress at a certain element (which as the stress location could change, could change)?

You are correct that when your mesh is fine enough, the maximum stress should not change appreciably.

Apologies for not being clear but what I meant was that as I refine the mesh, it approaches some value (not zero, actually it's around 6.6 MPa). I understand the first graph is misleading, just ignore the axes and look at the shape of the graph (it's the only graph I could find quickly on google with the correct shape).

As the mesh gets finer, the max stress drops from a higher value (say around 7 MPa) and eventually converges at around 6.6 MPa. Any mesh convergence graph I've ever seen starts at a lower stress (say 6 MPa) and then increases and eventually converges at 6.6 MPa. This gives my graph a shape similar to that in the first picture (just the shape, forget the values plotted on those axes) as opposed to what is shown in the second picture. Does this matter? Is my mesh convergence graph still valid or have I done something wrong?

No, you may be valid.

With coarse meshes typically I see erroneously high values of stress. This is mostly due to the elements in that region become very faceted. The high stress location is almost always in a curved region, so lack of meshing can introduce nonphysical stress concentrations.

Now it's very likely that you may be coarsely meshing over a feature which can add to stress, and you can see something like you have in Figure 2.

Computational physics is really a gray-box. It's important to know that, and know that things don't always happen the same way (in fact they rarely do).

Thanks minger. I'm going to try mesh finer and finer and then see what the graph looks like, if it continues to converge, then so be it and if it doesn't I may be back with more questions! I'm also going to try using different element types.

If your analysis and geometry are pretty straightforward then you shouldn't see too much of a difference between element types, so long as they are similar. Years ago, there were rather large differences in high-order vs low-order, and you may see that today if you use legacy elements. However, if you use updated elements, they should be similar.

Good luck,