An Introduction to Hex Meshing for Finite Element Analysis (FEA) with MSC Apex

The benefits of Hexahedral meshes in Finite Element Analysis have been extensively documented. On the other hand, the process to create a Hexahedral or Hex mesh has not been well documented.

This post seeks to offer an introduction to the thought process behind creating hexahedral meshes. Throughout this post, MSC Apex is used.

To successfully Hex mesh solid geometry, there are two guidelines:

1. The geometry must be loft-able.
2. The Hex mesh must consider subsequent features.

Let us start with the solid geometry shown below. When the MSC Apex Hex meshing tool is used, the solid geometry appears red in color indicating that the geometry cannot be meshed with Hexahedral elements.

To understand why the solid geometry cannot be Hex meshed, the solid geometry is separated into 2 parts. Then, the larger of the 2 parts is Hex meshed. In the diagram below, moving left to right, as the hex mesh is lofted, extruded, or swept, the same mesh cannot serve as a basis to mesh the second cylindrical solid object. The geometry satisfies the first guideline, i.e. must be loft-able, but does not follow the second guideline, i.e. the mesh must consider subsequent features.

To remedy the challenge, the larger of the 2 parts is partitioned. The partition acts as an imprint on the geometry and is indicated by the dotted line in the left most step in the image below. Now, as the Hex mesh is swept, the elements within the imprint serve as a basis to create the following cylindrical section.

MSC Apex features a Split Tool that speeds up partitioning geometry for Hex meshing. As shown in the image below, the Split Tool is used to partition the solid geometry. The face of the cylindrical section is used as the basis for the portioning. At no time is the solid geometry physically split, but there is an option in the Split Tool to achieve this.

The Hex mesher or 2.5D Meshing tool is used to mesh one of the partitions or cells. First the cylindrical partition is meshed. The smaller of the 2 parts is first meshed to visually show how much of the geometry the cylindrical partition spans and demonstrates the first guideline is satisfied, i.e. the geometry or partition must be loft-able.

As can be seen from the rear of the geometry, the mesh is swept along the full length of the partition. When the Hex mesh is completed, the cylindrical feature is considered and demonstrates the second guideline is followed, i.e. the mesh must consider subsequent features.

The larger partition is then meshed.

The rear of the geometry shows the Hex mesh is continuous. In this example, the Split Tool is used to create partitions that honor the 2 guidelines, i.e. the partitions are loft-able and consider subsequent features.

A more complex example is considered.

After the Split Tool is used, the partitions are indicated by dotted lines as shown below. Recall that the solid geometry is not physically split. The partitions or dotted lines act as imprints for the Hex mesh to follow.

In the diagram below, this is what the partitions look like if they geometry were separated into multiple solid geometries.

Below is the final Hex mesh.

To end this post, there are 2 guidelines for successful Hex meshing:

1. The geometry must be loft-able.
2. The Hex mesh must consider subsequent features.

The list of guidelines can be more extensive depending on who you ask, but given that this post is an introduction to Hex meshing, starting simple is always best.

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