Free Quad

) to generate an unstructured quadrilateral mesh on boundaries in 3D and domains in 2D, as shown in Figure 8-66. The operation can also be used to remesh faces of imported surface meshes in 3D.

Figure 8-66: An unstructured quad mesh in a 2D geometry with four domains (left). The Free Quad mesher inserts triangles (yellow) at acute angles to avoid too skewed quad elements. This image also shows how the size of the elements grows from small in narrow regions to larger some distance away. The quad mesh on the face in the 3D geometry (colored in blue to the right) is swept together with the triangular face mesh (gray) on adjacent faces, resulting in a mixed prism and hexahedral mesh. The default face meshing method for Swept is to create an unstructured quad mesh.


	The quadrilateral mesh generator does not strictly create only quadrilateral elements. In places of the geometry where it judges it as necessary, it can also create triangular elements, as shown in Figure 8-66.

You can control the number, size, distribution, and refinement of elements by using Distribution, Size Expression, Size, and Corner Refinement subnodes (only and subnodes are available for Finalizing the Mesh).

For meshes that define their own geometric model, use to remesh one or several faces. The operation separates the selected boundaries from the mesh, creates geometry from the separated mesh, meshes the geometry, and then copies the new generated mesh onto the original mesh. This operation has the following practical implications:

•

External edges of the selection are kept unchanged, while internal edges are remeshed.

•

Before generating geometry, the mesh is simplified according to the settings in the Mesh Preprocessing section below.

•

If remeshing fails, the error message might be referring to a problem in generating geometry from the mesh.


	Only surface meshes with first-order elements can be remeshed. Clear the Import domain elements check box in the mesh Import node to import only boundary elements. Select check box Import as linear elements to ignore second-order mesh data. See Importing Meshes for more information.


	See The Mesh Node to learn more about meshes that define their own geometric model.

To add a (

) node, select boundaries (3D) or domains (2D) in the , then choose one of the following:

•

Right-click in the Graphics window and select (

) from The Graphics Context Menu.

•

In The Mesh Toolbar, choose (

) from the (

) menu (3D components and parts) or click the (

) button (2D).

•

Right-click a node and choose (

). For 3D components and parts, this is selected from the menu.

Then enter the properties for the quadrilateral meshing operation using the following sections:

Entity Selection

Define the boundaries (3D) or domains (2D) where you want to create an unstructured quad mesh. Choose the level of the geometry from the list:

•

Choose to specify unstructured quad mesh for remaining, unmeshed faces (3D) or domains (2D).

•

Choose to create an unstructured quad mesh in the entire geometry.

•

Choose (3D) or (2D) to specify the geometric entities for which you want to create an unstructured quad mesh. Choose in the list to select the boundaries or domains in the window, choose a named selection to refer to a previously defined selection, or choose (3D) or (2D) to select all entities.

For imported meshes in 3D, the available options in the list are and .

Scale Geometry

To scale the geometry during the meshing operation, change the x-scale, y-scale, and z-scale in 3D to positive real numbers. If any of the scale factors are not equal to one, the software scales the geometry in those directions before meshing; after meshing, it restores the geometry and mesh to fit the original size, as shown in Figure 8-67.

The scale factors make it possible to generate meshes that are anisotropic. They are also useful if the mesh generator creates many elements due to a thin geometry or due to large aspect ratios in the geometry (compare the first and last meshes in Figure 8-68). Compare this to changing the parameter in a mesh Size attribute to only affect the mesh size in narrow regions.

Figure 8-67: Three copies of the same geometry, where the quad mesh is more or less resolved in the y direction by scaling the geometry in the background before it is meshed. The top geometry is not scaled. The one in the middle is scaled with a factor 2 in the y direction. The geometry at the bottom is scaled with a factor 0.5 in the y direction.

Control Entities


	This section is not available for meshes that define their own geometric model.

Select the check box to smooth the transition in element size across removed Controlling the Mesh Size Using Mesh Control Entities. You can specify the number of smoothing iterations in the field. In the field you can specify the maximum element depth for the mesh points to be smoothed.

Figure 8-68: Comparing meshes where Smooth across removed control entities has been used vs. not used. The two edges (highlighted in blue in left image) adjacent to the domain in the middle are designated as Mesh Control Edges. A finer distribution is set between the edges and when all domains are meshed, the edges are removed, leaving only one rectangular domain. With the Smooth across removed control entities check box selected (upper right image), the mesher adjusts the sizes of the quad elements to get a smoother transition from large to small elements. Clear the check box to not adjust the mesh (lower right image).

Tessellation

From the list, choose the tessellation method to use for generating an unstructured quadrilateral mesh:

•

Select (the default) to make the mesh generator determine the best algorithm to use for each domain.

•

Select any of the legacy versions to use a specific version of the algorithm.

Mesh Preprocessing


	This section is only available for meshes that define their own geometric models. Refer to the section Remeshing Imported Meshes for more information and related tutorials.

You can optionally simplify the mesh when remeshing faces in an imported mesh. The simplification can remove small defects typically present in mesh data from measurements, such as tomography, and it can speed up the process by removing unnecessary elements. The check box is selected by default to enable simplification.

The (default value: 0.01) is relative to the dimensions of the entire geometry and specifies a global limit for how much the mesh can be modified. The (default value: 1) is relative to the local feature size, as estimated by the algorithm, and is combined with the global limit to produce a limit for how much the mesh can be modified at a certain location. If the mesh contains many defects that you want to remove, you could try to increase the value of the . If the mesh describes the desired geometry with high accuracy, you might want to decrease this factor instead.