Surfacemeshgenerationbymapping

Mesh Generation > Surface Mesh Generation > Surface mesh generation by mapping

Surface mesh generation by mapping

If 2, 3 or 4 edges are given, a mesh region is formed between or within the edges. VisualFEA supports 3 types of edge formation as follows:

	2 edges
	3 edges
	4 edges

The nodal points of the generated mesh are computed by mapping techniques called "Lofting", "triangular mapping" or "transfinite mapping" respectively for each of the above 3 types. These techniques are not explained in detail here. The commands generating mesh by mapping are provided as menu items in menu.

> Generating mesh using 2 edges

A surface mesh can be generated using two opposite edges formed by a series of curves. This is the simplest and most frequently used method of mesh generation. The space between the two edges is filled with triangular or quadrilateral elements depending on your choice. The nodes on the mesh are created along the lines connecting two opposite nodes on the edges.

	1) Choose "2 Edges" from menu.
	The curve selection tool is automatically activated, and "2 Edge Surf" dialog box appears.
	2) Set the element type.
	ChoQose one of the 4 element types given as radio buttons in the dialog. "Tria 3", "Tria 6", "Quad 4" and "Quad 8" represent respectively 3 node triangle, 6 node triangle, 4 node quadrangle and 8 node quadrangle elements. 3) Select the type of arrangement for triangular elements.
	The radio buttons for triangle arrangement are enabled if the element type is set as "Tri 6" or "Tri 3" and disabled otherwise. These options are not effective for quadrilateral elements. The triangular elements can be generated in the 4 different types of arrangement as shown below.
	<Arrangement of triangular elements>
	4) Set the number of divisions between two edges.
	It is the same as designating how many rows of elements to be generated between two edges. The number of divisions is denoted by n in the following example.
	5) Set the weight of division density.
	The weight of division density is entered in the form of w1:wn , which is the ratio between the length of the first division l1 and that of the last ln a s indicated in the figure below.
	6) Select curves forming two edges.
	All the selected curves should be divided, and form two edges, each of which consists of one curve or serially connected curves. The total divisions on each edge should be equal. button is enabled when two edges are formed.
	The order of selecting curves does not make any difference in the resulting mesh generation. It is not necessary to designate the direction of the edges, although most other software asks to match the directions of the two edges. VisualFEA does it automatically. The division is directed from the first edge to the second. Which one is the first is determined by the input order of curves forming the edges.
	7) Click button.
	A surface mesh is generated between two edges, if the selected curves are compatible for mesh generation. Otherwise, the action is ignored after a message "Incompatible curve selection for 2 edge surface. In the above procedure, the order of step 2), 3), 4), 5) and 6) can be interchanged. You may repeat the above pro c e d u re of generating mesh using 2 edges without issuing the command again, while "2 Edge Surf" dialog remains on the screen. This mesh generation command is terminated by closing the dialog box or issuing any other command.

< Example of surface mesh generation between 2 edges >

> Setting 2 edges compatible for mesh generation

For successful 2 edge surface mesh generation, curves should be selected so that they may form 2 edges compatible for mesh generation as described below.

	The selected curves should be connected serially in two groups. This grouping for optimal mesh generation is automatically done by VisualFEA. Each of the two groups forms an edge. Each edge may consist of one or more curves.
	The two edges must be separated. They should not contact or cross with each other.
	Edges may be open or closed. If one edge is closed, the other edge must also be closed.
	Each edge should have an equal number of nodes on it.

Examples on the following page illustrate mesh regions compatible and incompatible for 2 edge mesh generation.

> Shifting alignment of node pairing on 2 edges

If the two edges form closed loops respectively, the one-to-one pairing of the nodes on the edges are optimally determined by the software. However, it is rare but possible that the automatic pairing results in generation of elements with distorted or improper shape. The mesh shape can be improved by manually adjusting the alignment of the node pairing. This is achieved by pressing button, in "2 Edge Surf" dialog, which is enabled when the mesh is generated. button is valid only in case both edges form closed loops respectively. There are 7 different alignments, each of which is obtained one after another as the button is pressed consecutively. The sequence of the alignment is as follows:

	1) The outer loop shifts clockwise.
	2) The inner loop shifts clockwise.
	3) Both the inner loop and the outer loop shift clockwise.
	4) The outer loop shifts counter-clockwise.
	5) The inner loop shifts counter-clockwise.
	6) Both the inner loop and the outer loop shift counter-clockwise.
	7) The initial alignment is obtained again.

< Example of alignment shifting in looped 2 edges >

> Generating mesh using 3 edges

A surface mesh can be generated using 3 edges formed by a series of curves. The region enclosed by the 3 edges is filled with triangular elements. The coordinates of the nodes on the mesh are determined by interpolating the nodal points on the 3 edges using triangular mapping technique. The region is mapped with an equilateral triangle. Therefore, the 3 edges should be formed in the configuration of a triangle.

	1) Choose "3 Edges" from menu.
	The curve selection tool is automatically activated, and "3 Edge Surf" dialog box appears.

	2) Set the element type.
	Only triangular elements can be generated using this method. Thus, the radio buttons for quadrilateral shape are not included in this dialog. "Tria 3" for 3 node triangle or "Tria 6" for 6 node triangle can be chosen as the element type.
	3) Select curves forming 3 edges.
	At least 3 curves are necessary to form 3 edges. They must be closed. If the selected curves meet these conditions, button is enabled. In addition, the number of nodes should be the same for all the 3 edges. This condition is checked in the next step.
	4) Click button.
	A surface mesh is generated in the region surrounded by the 3 edges, if the selected curves are compatible for mesh generation. When you click the button, the selected curves are automatically grouped into 3 edges compatible for mesh generation. Thus, all the 3 edges have equal number of nodes on them. If such formation of 3 edges is not possible, the action is ignored after a message "Incompatible curve selection for 3 edge surface."

< Example of surface mesh generation enclosed by 3 edges >

> Generating mesh using 4 edges

A surface mesh can be generated using 4 edges formed by a series of curves. The region enclosed by the 4 edges is filled with triangular or quadrilateral elements depending on your choice. The coordinates of the nodes on the mesh are determined by interpolating the nodal points on the 4 edges using transfinite mapping technique. The region is mapped with a square. There f o re, the 4 edges should be formed in the configuration of a quadrangle.

	1) Choose "4 Edges" from menu.
	The curve selection tool is automatically activated, and "4 Edge Surf dialog box appears.

	2) Set the element type.
	You may choose one of 3 node triangle, 6 node triangle, 4 node quadrangle, and 8 node quadrangle element as the element type.
	3) Select the type of arrangement for triangular elements.
	The triangular elements can be generated in the 4 diff e rent types of arrangement as explained in the previous section "Generating mesh using 2 edges"
	4) Select curves forming 4 edges.
	At least 4 curves are necessary to form 4 edges. They must be closed. If the selected curves meet these conditions, button is enabled. In addition, there must be the same number of nodes on each pair of opposite edges. This condition is checked in the next step.
	5) Click button.
	A surface mesh is generated in the region surrounded by the 4 edges, if the selected curves are compatible for mesh generation. When you click the button, the selected curves are automatically grouped into 4 edges compatible for mesh generation.

< Example of surface mesh generation enclosed by 4 edges >

> Setting 4 edges compatible for mesh generation

For successful 4 edge surface mesh generation, curves should be selected so that they may form 4 edges compatible for mesh generation as described below.

	The selected curves should be connected serially to form a closed loop with 4 edges.
	The 4 edges may be regarded as boundary lines of a quadrilateral region with two pairs of edges facing opposite to each other.
	Each pair of edges should have an equal number of nodes on them.
	Edges are constructed automatically by VisualFEA so that each pair of edges have equal number of nodes on them. If such construction is not possible, mesh generation is aborted after a message “Incompatible curve selection for 4 edge surface.”
	All the internal angles of vertexes made by two adjacent edges should be less than 180 .
	Even if this condition is not met, a mesh may be generated. But the generated mesh will have improper shape and will trespass outside of the mesh region

The following examples illustrate compatible and incompatible selection of curves