FEA for beginners (Part II)

Some of you may have found some difficulties when trying to create a structured mesh for circular/spherical parts. For that reason, this week I’m going to write about a simple procedure that you can follow in order to solve this problem: the “Butterfly Method”.

For achieving more accurate results, it is always recommended to use quad-structured meshes. Most of the FE packages include options for meshing parts in an automatic way, where you only have to define the number (or size) of elements and the type (i.e. quad, tri or even a combination of quad+tri elements). However, when geometries include circular parts or when you are creating an sphere or a cylinder, the automatic option for creating a structured mesh is not available any more. How can we solve that? Let’s find out.

Some people tend to use triangular elements for meshing this kind of shapes, but my advice is to use quad, as the quality of the results are much better and they describe a better behaviour. The reason why people use triangular elements is that a relatively structured mesh can be obtained automatically in contrast to quads, as illustrated in Figure 1.


Figure 1 Automatic meshes

In order to solve this problem so that we can improve our results, the commonly known as the “Butterfly Method” is introduced in the following lines.

Create just one quarter of your geometry. Then, create partitions as shown in Figure 2. The key aspect that has to be taken into account is that in order to have a good mesh, we have to create regions which are limited by four edges.


Figure 2 Partitions

Create the mesh. Specify an appropriate element size and select quad as the element type
and structured as the preferred method. Then, selecting the three regions, you should obtain a mesh like the one presented in Figure 3.


Figure 3 Partial mesh

Create the corresponding symmetry in order to have a complete circle. Otherwise, depending on the case you are studying, you may prefer to use symmetry boundary conditions to save computational time.

This may be the most important thing to do when using this technique: EQUIVALENCE THE NODES. If you don’t do that, you will have created double nodes and that can give rise to an unreal and unexpected behaviour. In this case (and depending on the software which has been used), the nodes which are double are identified in Figure 4.


Figure 4 Equivalence and final mesh

By using the appropriate option (depending on the package) you will easily find the nodes which need to be equivalenced and then the programme will correct it. 

As you can see, now the final mesh is perfectly structured with quad elements. You can try to run a few simulations testing some random meshes and then compare the results with a mesh created with the Butterfly Method.

This apparently simple tip is useful for beginners who can get stuck when trying to mesh complex geometries. Not too much information can be found regarding this issue and that is the reason why I wanted to share this easy technique with you. I hope you enjoyed it!




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