Volume mesh generation by automatic tetrahedronization

Automatic tetrahedronization is one of the most advanced technique generating 3- dimensional volume meshes. This method is analogous to automatic triangulation for surface mesh generation. Automatic tetrahedronization fills a volume s u r rounded by boundary surface meshes, while automatic triangulation fills an area surrounded by boundary curves. The boundary surface meshes should form a closed surface enclosing a 3-dimensional space. A volume mesh is generated by an algorithm subdividing the volume space recursively along the surface element boundaries. A volume element is created at each end of the recursion. This method is very powerful and useful, because a volume mesh can be generated, with minimum user interaction, in a relatively arbitrarily shaped space. There is no requirement for convexity of the space. Only 4 node and 10 node tetrahedron elements can be generated by tetrahedronization in the current version of VisualFEA.

> Generating mesh by automatic tetrahedronization

A volume mesh can be generated by automatic tetrahedronization technique in a 3-dimensional space surrounded by closed surface meshes. The element shape generated by automatic tetrahedronization is limited to tetrahedron in the current version of VisualFEA. Either 4 or 10 node elements can be generated. If elements within the boundary meshes are 3-node triangles, 4-node tetrahedral elements will be generated. If elements within the boundary meshes are 6-node triangles, 10-node tetrahedral elements will be generated.

	1) Choose "Auto Mesh (Volume)" from menu.
	The surface selection tool is automatically activated, and "Auto Mesh Volume" dialog box appears.
	2) Set options for mesh generation process.
		"Check interference" : If this option is checked, interference between elements is detected during mesh generation.
		"Check aspect ratio" : The aspect ratios of generated elements are examined, and reported if they are not acceptable.
		"Visualize process" : The recursive process of mesh generation is graphically visualized.
	3) Set the level of smoothing.
	The shape of the individual element is polished through smoothing process. The level of smoothing is defined in four grades, 1, 2, 3 and 4. Grade 4 takes longest time, but produces the best shaped elements.
	4) Select surface meshes forming closed boundary.
	The selected meshes should form a closed surface boundaries. All the elements in the meshes should be triangular and have the same number of nodes. That is, they should consists of 3-node triangular elements only, or 6- node triangular elements only. button is enabled when acceptable boundary meshes are formed.
	5) Click button.
	A volume mesh is generated by automatic tetrahedronization, if the selected surface meshes are acceptable for automatic tetrahedronization as described in the next section. Otherwise, the action is ignored with a message notifying that automatic tetrahedronization cannot not be completed.

In the above procedure, the order of step 2), 3) and 4) can be interchanged. You may repeat the above procedure of generating a mesh by automatic tetrahedronization without issuing the command again, while "Auto Mesh Volume" dialog remains on the screen. This mesh generation command is terminated by closing the dialog box or issuing any other command. Automatic tetrahedronization usually takes a long time. While mesh generation is progressing, its status is indicated by a progress bar.

The pro g ress bar is not to the actual time scale. The display indicates only the progress in the recursion stages. If "Visualize process" box is checked, the recursive process of mesh generation is also graphically visualized.

> Forming boundary meshes for automatic tetrahedronization

For successful automatic tetrahedronization, surface meshes should be selected so that they form a boundary surfaces acceptable for mesh generation as described below.  

The automatic tetrahedronization will be aborted if the above conditions are not satisfied. The mesh generation may also fail if the 3-dimensional space is too complex. In this case, the space should be broken into two or more sub-regions which are simpler, and the automatic tetrahedronization should be applied for each of these sub-regions.

< Example of volume mesh generation by automatic tetrahedronization >