Converging the mesh

00:09

In the next unit, we will be converging the mesh and ensuring an Accurate FEA Solution.

00:18

So for this example, we'll be working with the model from the prior unit.

00:22

You'll notice that the Mesh Control of 10 millimeters has been added to the hole and the two fillet faces already.

00:28

So we've made that first mesh refinement.

00:31

The pins have been added at the two pivot points and then a 45,000 Newton force has been added at the end of the bar.

00:39

So we are ready to continue with our Mesh Refinement process.

00:45

Now, the final step of any FEA that you perform should always be Mesh Convergence.

00:50

The idea of mesh convergence is that we are attempting to minimize the error in our solution.

00:57

To do that, we want to identify how sensitive our result is to changes in the Mesh.

01:03

So as we reduce the mesh size, we want to control the amount of error in the stress and displacement results,

01:11

we want to find an acceptable amount of error in our results so that we can rely upon the solution and use it for decision making.

01:21

So there's two ways that you can run a mesh convergence study with Inventor Nastran.

01:26

There's the automatic method which is using the automatic convergence settings tool.

01:31

The other option is to use manual convergence,

01:34

which would mean making the refinements manually calculating the error from one result to the next, and finding an acceptable limit.

01:41

We'll start by using the automatic convergence settings from the mesh panel here.

01:47

In this tool, you have two options.

01:49

You can do a global refinement,

01:50

which is going to refine all the elements the same way as if you were making changes to the global average element size.

01:59

The other option is a local refinement which will only apply the mesh refinement to areas where you have a maximum amount of stress.

02:07

So where you see max number of refinements here, the default value is five.

02:13

Typically you only need about two or three refinements to reach convergence.

02:17

This is how many times the solver can rerun the study and produce a new result set for comparison.

02:24

The stop criteria percentage is the amount of error at which the solver will stop.

02:30

So if it sees less than 5% error from one mesh result to the next mesh result,

02:36

it will stop the study and give you your converged result.

02:40

The refinement threshold here can be a value from 0 to 1,

02:44

a value of zero means that all of the elements in your model can be refined during the study.

02:51

A value of one means that none of the elements in the model can be refined during the study.

02:57

That means that a value of 0.9 assumes only the top 10% of the elements seeing stress.

03:05

So the elements that are showing the top 10% of Von Mises Stress can be refined.

03:10

Everything else will be ignored and not touched the refinement factory here it has to be greater than one.

03:18

This is the same as your max element growth rate set in the advanced mesh settings.

03:23

This controls how quickly an element can grow or how rapidly it can grow from a refined region to the global mesh.

03:30

So it controls that transition from your fine mesh to your coarse mesh.

03:35

So once you've confirmed these settings and you're ready to go, you can check this include an analysis box.

03:42

If it's not checked, it will not be used for the study.

03:45

So I will activate it here and select "Ok".

03:48

And now I can run my study but it will activate the convergence tool for me.

03:53

So I'll select "Run".

03:56

It will always run the first mesh as is.

03:60

It will then make a refinement to those key regions,

04:04

and then rerun the study as many times as it needs to until it sees less than 5% error from one result to the next.

04:12

So it's solving a second time here and it's going to plot my results as we go.

04:21

And it looks like it achieved convergence after just one additional study.

04:24

This is partly due to the fact that we already had a refinement in place.

04:28

Sometimes it'll take three or four studies in order to achieve convergence.

04:33

So I'll select, "Ok",

04:35

I can see what the result looks like and you can see it added some additional elements around this corner here around the holes,

04:43

and maybe along that top edge there as well.

04:45

So it made a few subtle refinements that saved me the time of going in there and doing it manually.

04:51

I can then go to the convergence plot along the top here.

04:55

And this allows me to review what those values were and what the actual convergence rate,

05:00

and error was from one result to the next.

05:04

So now I know that this has an acceptable amount of error and I can use it for design and decision making.

05:12

Now, the other way you can perform a mesh convergence study with Nastran is by completing this process manually.

05:19

So what we can do is look at areas that we've added a mesh control,

05:22

and we can reduce that mesh control each time comparing the result from one mesh to the next and calculating the error.

05:29

The advantage of a manual method is that I can confirm error on results such as displacement and strain in addition to Von Mises Stress.

05:38

So to do that, I will edit my mesh control.

05:41

But first, I'm going to run my baseline study.

05:45

This will give me a starting point.

05:47

And I can start to record my results and compare as I go.

05:51

So I want to write this result down on a piece of paper or put it into a spreadsheet to keep track.

05:56

So I'm seeing around 65.3 megapascals and for displacement,

06:02

we'll check that it's about 1.394.

06:07

So now I will edit my mesh control and I recommend reducing the element size by about 25 to 30%.

06:15

With each reduction, you shouldn't see a significant amount of error with that level of refinement.

06:22

But you'll want to run several studies to confirm that.

06:25

So I will go down to 7.5 millimeters, a reduction of 25% regenerate my mesh and then run the study again.

06:39

Once I have this next result, I can calculate the error from the original and determine what my rate of convergence is going to be.

06:47

So displacement comes out 1.394 which is exactly the same as the first study. So basically a 0% error there.

06:56

And for Von Mises stress, I can check that as well.

06:59

I'm seeing about 71.

07:01

So even though I only made a 25% reduction in the mesh, I saw a jump of about six mega pascals.

07:10

So if I take six and divide it by the original seeing about 9% error,

07:16

generally, you want to see less than 10% error in your results less than 5% error is even better.

07:26

So to achieve less than 5% I'm going to need to run an additional study to compare my von mises results.

07:31

So I will edit my mesh control once again and reduce this by 25%.

07:36

So 7.5 reduce it by 25%. So 5.625 will be my new mesh.

07:45

I will then regenerate and then solve a third time.

07:55

Once the solution is complete, I can then compare these results. And I'm seeing about 75.

08:02

So roughly four divided by 71 here, about a 5.6% error.

08:07

That's really good. If you can be around 5% error, that is a great place to be. And you can rely on this solution.

08:15

I'm also going to check my displacement results. So I'll switch to "Displacement" and I should be seeing around 1.394 once again.

08:25

So my results have not changed much for displacement.

08:28

And I'm still seeing a small amount of error for Von Mises stress.

08:32

But again, we are searching for an acceptable amount of error around 5% which we have achieved.

08:38

You will notice that the stress was slightly higher than the automatic method.

08:42

That is fairly typical just because the reductions are more focused on one area,

08:47

and likely to be a little bit greater than what the convergence tool will do by default.

08:52

Either method is acceptable, but you will want to go through this process to ensure that your result is reliable,

08:58

moving forward and something you can use for decision making.