Automatic triangulation

Automatic triangulation is the most convenient and powerful method of generating surface meshes. There are two types of automatic triangulation for surface mesh generation, i.e., unconstrained and constrained. Unconstrained automatic triangulation is to generate a mesh using the selected curves only. In this case, there are no other constraints for mesh generation than the curves inside and at the boundary of the region. This type of automatic triangulation is chiefly used for generating a plane mesh. Constrained automatic triangulation is to generate a mesh on a predefined surface primitive. This type of automatic triangulation is useful for generating a mesh on a trimmed surface.

> Generating mesh on a plane by automatic triangulation

The easiest way of generating mesh on a plane is "Unconstrained" automatic triangulation. An arbitrarily shaped surface mesh is generated simply by designating the curves of the mesh boundary and issuing a mesh generation command. A curved surface as well as a plane may be meshed by this method. However, it is advisable to limit the usage of this method to a plane mesh, and for a curved surface mesh to apply "Constrained" automatic triangulation as explained in the later section. You can easily fill an arbitrarily shaped surface region with triangular or quadrilateral elements using automatic triangulation as described below.

	1) Choose "Auto Mesh" from menu.
	The curve selection tool is automatically activated, and "Auto Tri" dialog box appears.
	2) Set the element shape using "Auto Tri" dialog.
	Click one of the buttons for element shape. There are following 3 options.
		"Triangle only" : Only triangular elements are generated.
		"Triangle and quad" : The generated mesh is filled with mixture of triangular elements and quadrilateral elements.
		"Quad only" : Only quadrilateral elements are generated. In order to use this option, the total number of divisions in the selected curves should be even.
		< Mesh generated using different options of element type>
	3) Set the element order.
	Click one of the buttons for the order of elements. Either linear or quadratic order can be selected.
		"3 or 4 nodes" : Linear elements (3 node triangle or 4 node quadrangle) are generated.
		"6 or 8 nodes" : Quadratic elements (6 node triangle or 8 node quadrangle) are generated.
	4) Set the level of smoothing using "Auto Tri" dialog.
	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.
	5) Select curves.
	All the selected curves should be divided. Some of the selected curves are used in defining the boundary of the mesh region. Others may be needed to control the mesh density and element boundaries inside the region.
	6) Click button.
	A surface mesh is generated by automatic triangulation, if the selected curves a re compatible for automatic triangulation as described in the next section. Otherwise, the action is ignored with a message notifying that automatic triangulation cannot not be executed with the selected curves.

In the above procedure, the order of step 2), 3), 4) and 5) can be interchanged. You may repeat the above Quadratic procedure of generating mesh by automatic triangulation without issuing the command again, while "Auto Tri" dialog remains on the screen. This mesh generation command is terminated by closing the dialog box or issuing any other command.

< Example of automatic triangulation >

> Setting a compatible region for automatic triangulation

For successful automatic triangulation, curves should be selected so that they may form a region compatible for mesh generation as described below. 

If you issue the automatic triangulation command with improper curve selection, you may receive one of the responses shown from VisualFEA depending on the state of the curve selection.  

< An example of compatible region for automatic triangulation >

< Examples of incompatible region for automatic triangulation >

> Handling the incompatibility due to mismatching curve ends

Although you selected curves compatible for automatic triangulation, you may not get a successful mesh generation. It is the case in which there exists visually unidentifiable incompatibility in the formation of boundary curves. The major source of such incompatibility is the numerical errors in various operations related to curves including curve-curve intersection. You may get a notice dialog box as shown below.

The dialog box informs that the boundary curves are not closed probably because some curve ends are mismatching. You may choose one of the 3 buttons provided by this dialog box.

	: cancel the mesh generation command.
	: display the suspected mismatching curve ends.
	: Close the gap between the mismatching curve ends so that the

boundary curves are close. You may set the tolerance range of the gap to be closed.

< A example of showing mismatching curve ends >

> Generating mesh on a surface primitive by automatic triangulation

You may create surface primitives such as spheres, cylinders, toru s , Bezier surface and so on (refer to "Creating surface primitives". A mesh can be generated using selected curves and a surface primitive. The mesh is bounded and controlled by the selected curves, and at the same time, is confined on the surface primitive.

	1) Choose "Auto Mesh on Primitive" from menu.
	The curve selection tool is automatically activated, and "Auto Primitive" dialog box appears.
	2) Set the element shape.
	Click one of the buttons for element shape. There are 3 options.
		"Triangle only" : Only triangular elements are generated.
		" Triangle and quad" : The generated mesh is filled with mixture of triangular and/or quadrilateral elements.
		"Quad only" : Only quadrilateral elements are generated. In order to use this option, the total number of divisions in the selected curves should be even.
	3) Set the element order.
	Click one of the buttons for the order of elements. Either linear or quadratic order can be selected.
		"3 or 4 nodes" : Linear elements (3 node triangle or 4 node quadrangle) are generated.
		"6 or 8 nodes" : Quadratic elements (6 node triangle or 8 node quadrangle) are generated.
	4) Choose the part of the primitive on which mesh is to be generated.
	A mesh may be generated inside, outside or both sides of the region boundary of the surface primitive. Choose the part by turning on one of the radio buttons "Inside" "Outside" and "All"
	5) Set the level of smoothing using "Auto Primitive" dialog.
	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.
	6) Select curves.
	All the selected curves should be divided. Some of the selected curves are used in defining the boundary of the mesh region. Others may be needed to control the mesh density and element boundaries inside the region. The initially dimmed button is enabled, when one or more curves are selected.
	7) Click button.
	The selected curves are reserved for mesh generation, and the button changes into indicating that selecting surface primitive is expected in the next step. The primitive selection tool is automatically activated.
	8) Select a surface primitive.
	The selected surface primitive is highlighted in bright red color. Only one surface primitive should be selected. The dimmed button is enabled when a surface primitive is selected.
	9) Click button.
	A mesh is generated on the selected surface primitive. button is restored to button. It is now ready for inputting another surface mesh.

You may repeat the above procedure of generating mesh on a surface primitive, without issuing the command again, while "Auto Primitive" dialog remains on the screen. This mesh generation command is terminated by closing the dialog box or issuing any other command.

< Comparison of meshes generated using different options of part to mesh >

< Example of mesh generation using surface primitives and their intersection curves >