Volume mesh generation by sweeping operations

VisualFEA supports the following 4 types of sweeping operations for volume

mesh generation: 

Sweeping operations for volume mesh generation are analogous to those for surface mesh generation explained in the previous section. Refer to "Surface mesh generation by sweeping operations." For volume mesh generation, sweeping operations are based on selected surfaces, i.e. seed surfaces while surface mesh generation is based on seed curves. The commands for volume mesh generation by sweeping are provided as menu items in menu.

In case of volume mesh generation by sweeping, the type of element is determined by the type of element on the seed surfaces as shown below. Therefore, it is not necessary to set the type of the element.

< Element types in the seed mesh and in the generated volume mesh >

> Generating mesh by extrusion

A volume mesh can be generated by extruding the seed surfaces up to the specified height and in the specified direction. The height of the extrusion is entered using the "Extrude" dialog. This is the simplest but most frequently used method of generating volume meshes. There are three methods generating a volume mesh by extruding seed surfaces. The other 2 methods are explained in the following sections.

	1) Choose "Extrude(Volume)" from menu.
	The curve selection tool is automatically activated, and "ExtrVol" dialog box appears.
	2) Set the element type.
	If the element shape of the seed mesh is triangle, either tetrahedron or prism elements can be generated. Otherwise, only hexahedron elements can be generated, and thus this step is not necessary.
	3) Set the direction of extrusion.
	The mesh may be extruded either in the direction of a coordinate axis, or in the direction normal to the seed surface. The normal direction is determined independently at each of the extruding nodes on the seed surface. If more than one surfaces are joined at a node and their slopes are not continuous, there exists more than one normals at the node. In this case, the normal direction is evaluated by averaging the multiple normal directions.
	4) Enter the height of extrusion.
	Extrusion height is the distance from the seed surface to the extent of the generated volume mesh. If extrusion direction is set as "Normal" the extrusion height designates the uniform thickness of the generated volume mesh.
	5) Enter the number of divisions for extrusion.
	Specify how many layers of elements to be generated by extrusion. If the element type is 15 node prism or 20 node hexahedron, the number of element layers is half the number of divisions , because 2 divisions are required to make one layer of the elements.
	6) Enter the weight of division density.
	Enter the weight of division density in the form of w1:wn , which is the ratio between thickness of elements at the starting part, l1 and at the ending part of extrusion, ln.
	7) Select the seed surfaces for extrusion.
	Select surface meshes forming seed surfaces for mesh generation. button is enabled when more than one or more surfaces are selected. More than one surface may be used as the seed surfaces. In this case, the seed surfaces should be connected so that their extrusion may generate a continuous volume.
	8) Click button.
	A volume mesh is generated by extruding the seed surfaces. If mesh generation is successful, button is enabled. In case the mesh is generated opposite to the desired direction, click button to reverse the direction of extrusion. Then, mesh will be regenerated with the reverse direction. You may repeat the above procedure of generating mesh by extrusion without issuing the command again, while "Extr Surf" dialog remains on the screen. This mesh generation command is terminated by closing the dialog box or issuing any other command.

< A volume mesh generated by extrusion in normal direction >

> Generating mesh by extrusion up to bounding surface primitives

The bound of the extrusion may be specified by selected surface primitives instead of specifying the height of extrusion. These surface primitives are termed here as "Bounding primitives." This method of mesh generation is the same as the above described extrusion method except that the extent of extrusion is determined not by its height but by the bounding primitives. In generating a volume mesh by this method, you can control the direction of extrusion as well as the boundary of the mesh. Thus, a volume mesh of desired shape can be constructed with relative ease.

	1) Choose "Extrude to Surface Prim." from menu.
	The surface selection tool is automatically activated, and "Extr to Primitive" dialog box appears.
	2) Set the element type.
	If the element shape of the seed mesh is triangle, either tetrahedron or prism elements can be generated. Otherwise, only hexahedron elements can be generated, and thus this step is not necessary.
	3) Set the direction of extrusion.
	The mesh may be extruded either in the direction of a coordinate axis, or in the direction normal to the seed surface. The direction is always signed toward the bounding surface primitive.
	4) Set the side of the bound.
	There are usually more than two sides of the bounding surfaces applicable as the boundary of the generated mesh. Therefore, it is necessary to specify which side of the bounding primitives should be applied.
	5) Set the number of divisions for extrusion.
	Specify how many layers of elements to be generated by extrusion.
	6) Set the weight of division density.
	Enter the weight of division density in the form of w1:wn , which is the ratio between thickness of elements at the starting part, l1 and at the ending part of extrusion, ln.
	7) Select surface meshes forming seed surfaces for extrusion.
	button is enabled when one or more surface meshes are selected.
	8) Click button.
	The selected surface meshes are reserved as the seed surfaces for mesh generation, and the button changes into indicating that selection of bounding surface primitives is expected in the next step. At the same time, the primitive selection tool is automatically activated.
	9) Select the bounding surface primitives.
	The selected bounding primitives are highlighted in bright red color. The dimmed button is enabled when bounding primitives are selected.
	10) Click button.
	A mesh is generated by extruding the seed meshes up to the bounding primitives. button is restored to button, and the surface selection tool is activated. The program is now ready for generating another volume mesh. The bounding primitives must be wide enough to cover the whole front of the extrusion. Otherwise, the mesh generation process will be aborted with a message "The bounding primitives cannot cover the range of the extrusion."

< Example of mesh generation by extrusion to a surface primitive >

> Generating mesh by extrusion up to surface meshes

The bound of the extrusion may be specified by surface meshes. This method of mesh generation is useful when the bound of extrusion is a f ree-form surface which cannot be expressed by surface primitives supported in VisualFEA. These surface meshes are termed here as "Bounding mesh." This method of mesh generation is the same as the above described method of "Extrusion up to surface primitives" except that surface meshes instead of bounding primitives are used as the bounding limit. In order to apply this method, the bounding surface mesh should be generated before starting the process of mesh generation.

	1) Choose "Extrude to Mesh" from menu.
	The surface selection tool is automatically activated, and "Extr to Mesh" dialog box appears.
	2) Set the element type.
	If the element shape of the seed mesh is triangle, either tetrahedron or prism elements can be generated. Otherwise, only hexahedron elements can be generated, and thus this step is not necessary.
	3) Set the direction of extrusion.
	The mesh may be extruded either in the direction of a coordinate axis, or in the direction normal to the seed surface. The direction is always signed toward the bounding surface meshes.
	4) Specify whether to delete the bounding mesh automatically after mesh generation.
	In most cases, the only usage of the bounding mesh is to generate the volume mesh by this method. Then it is desirable to delete the bounding meshes after the mesh generation. If "Selete bounding mesh" box is checked, the bounding mesh will be deleted automatically when the mesh is generated. Otherwise, the bounding meshes remain undeleted after mesh generation.
	5) Set the number of divisions for extrusion.
	Specify how many layers of elements to be generated by extrusion.
	6) Set the weight of division density.
	Enter the weight of division density in the form of w1:wn , which is the ratio between thickness of elements at the starting part, l1 and at the ending part of extrusion, ln.
	7) Select surface meshes forming seed surfaces for extrusion.
	button is enabled when one or more surface meshes are selected.
	8) Click button.
	The selected surface meshes are reserved as the seed surfaces for mesh generation, and the button changes into indicating that selection of bounding surface meshes is expected in the next step. At the same time, the mesh selection tool is automatically activated.
	9) Select the bounding surface meshes.
	The selected bounding meshes are highlighted in bright red color. The dimmed button is enabled when bounding meshes are selected.
	If the bounding surface is flat, its density does not affect the result of the mesh generation. But, in case the bounding surface is curved, the smoothness of generated mesh may be affected by its density. Higher density is required in order to represent curved surfaces more accurately.
	10) Click button.
	A volume mesh is generated by extruding the seed meshes up to the bounding meshes. button is restored to button , and the surface selection tool is activated.

< Example of mesh generation by extrusion to a surface mesh>

> Generating volume mesh by translation

A volume mesh can be generated by translating the selected seed meshes along the specified sweeping path. Every node on the seed meshes makes a trace parallel to the sweeping path. New nodes are created along these traces, and all of them are contained in the newly generated mesh. This method is useful in modeling curved structural members with uniform section. In applying this method, some care should be taken not to make a self-interfering mesh.

	1) Choose "Translate (Volume)" from menu.
	The surface selection tool is automatically activated, and "Translate Vol" dialog box appears.
	2) Set the element type.
	If the element shape of the seed mesh is triangle, either tetrahedron or prism elements can be generated. Otherwise, only hexahedron elements can be generated, and thus this step is not necessary.
	3) Select the option for path setting.
	Choose one of the 3 options setting the sweeping path, "Input", "Select" and "Last" by clicking the corresponding radio button. The "Last" button is enabled only when this method of mesh generation was applied at least once since the dialog box appeared.
	4) Set the number of divisions for translation.
	Specify how many rows of elements to be generated by translation. This setting is applied only when the sweeping path is not divided. If divided curves are selected as the sweeping path, their divisions will be applied regardless of this setting.
	5) Set the weight of division density.
	Enter the weight of division density in the form of w1:wn , which is the ratio between width of elements at the starting and at the ending part of the curve.
	6) Check or uncheck "Keep angle to path" check box.
	If this check box is checked, the meshed layers are created so that they have a constant angle with the sweeping path. Otherwise, all the layers are made parallel.
	7) Select surface meshes for seed meshes.
	button is enabled when one or more surface meshes are selected.
	8) Click button.
	The selected surfaces are reserved as the seed meshes for mesh generation, and the button changes into indicating that setting the sweeping path is expected in the next step.
	9) Set the sweeping path.
	Set the sweeping path by the method selected at step 3). Tools corresponding to the method are automatically activated, and the cursor changes accordingly. The sweeping path should be open, and its one end point should meet with a node on the seed curve. The sweeping path may be one curve or serially connected curves. If the sweeping path consists of more than one curve, they must be either all divided or all undivided. Mixed use of divided and undivided curves for sweeping path is not allowed.
	10) Click button.
	A mesh is generated by translating the seed meshes along the sweeping path. button is reverted to button. The program is now ready for generating another volume mesh. The surface selection tool is automatically activated, if it is not in action.

< Example of volume mesh generation by translation >

> Generating volume mesh by revolution

A solid of revolution is generated by revolving seed surfaces about the specified axis. Volume elements are created within a ring formed by revolving each of the surface element on the seed mesh. The axis of revolution may be set interactively in any desired direction. The revolution may be full or partial depending on the specified angle. The direction of revolution can be reversed if necessary.

	1) Choose "Revolve (Volume)" from menu.
	The surface selection tool is automatically activated, and "Revolve Vol " dialog box appears.
	2) Set the element type.
	If the element shape of the seed mesh is triangle, either tetrahedron or prism elements can be generated. Otherwise, only hexahedron elements can be generated, and thus this step is not necessary.
	3) Select the option for setting the axis of revolution.
	Choose one of the 3 options setting the axis of revolution, "Input, "Select" and "Last" by clicking the corresponding radio button. The "Last" button is enabled only when this method of mesh generation was applied at least once since the program started.
	4) Set the angle of revolution.
	Insert the angle of revolution in the dialog box. The angle should be greater than or equal to -360  and less than equal to 360 . Both -360  and 360  make a full surface of revolution. The negative sign reverses the direction of revolution.
	5) Set the number of divisions for revolution.
	Specify how many rows of elements to be generated by revolution in circumferential direction.
	6) Set the weight of division density.
	Enter the weight of division density in the form of w1:wn , which is the ratio between width of elements at the starting part and at the ending part of revolution.
	7) Select surface meshes forming seed meshes for revolution.
	button is enabled when one or more surface meshes are selected.
	8) Click button.
	The selected surfaces are reserved as the seed surfaces for mesh generation, and the button changes into indicating that setting the axis of revolution is expected in the next step.
	9) Set the axis of revolution.
	Set the axis of revolution by the method selected at step 3). Tolls corresponding to the method is automatically activated, and the cursor changes accordingly
	10) Click button.
	A mesh is generated by revolving the seed meshes about the axis of revolution. button is reverted to button. It is now ready for generating another volume mesh. The surface selection tool is automatically activated, if it is not in action. button is enabled, only when mesh generation is successful. Clicking button reverses the sign of the revolution angle and regenerates the mesh.

< Example of volume mesh generation by revolution >

> Generating volume mesh by twisting

Twisting is a method of mesh generation by extrusion combined with revolution. So, it may be termed as "Twisted extrusion" Elements are generated on the surface which is formed by extruding the selected seed curves along the specified axis while twisting the direction of extrusion about the axis by the specified angle. Along this twisted extrusion, the trace of a node on the seed curve makes a helix on which new nodes are created.

	1) Choose "Twist (Volume)" from menu.
	The surface selection tool is automatically activated, and "Twist Vol" dialog box appears.
	2) Set the element type.
	If the element shape of the seed mesh is triangle, either tetrahedron or prism elements can be generated. Otherwise, only hexahedron elements can be generated, and thus this step is not necessary.
	3) Select the option for setting the twist axis.
	Choose one of the 3 options setting the twist axis, "Input". "Select" and "Last" by clicking the corresponding radio button. The "Last" button is enabled only when this method of mesh generation was applied at least once since the program started.
	4) Set the extrusion height.
	Insert the extrusion height in the dialog box. The direction of extrusion is given by that of the twist axis which is directed from the first input point to the second.
	5) Set the twist angle.
	Insert the twist angle in the dialog box. There is no limit in the acceptable range of twist angle. A negative sign reverses the direction of twist.
	6) Set the number of divisions.
	Specify how many rows of elements are to be generated in the direction of the twisted extrusion.
	7) Set the weight of division density.
	Enter the weight of division density in the form of w1:wn , which is the ratio between width of elements at the starting part and at the ending part of twisting.
	8) Select surface meshes forming seed surfaces for twisting.
	button is enabled when one or more surface meshes are selected.
	9) Click button.
	The selected surfaces are reserved as the seed surfaces for mesh generation, and the button changes into indicating that setting the twist axis is expected in the next step.
	10) Set the twist axis.
	Set the twist axis by the method selected at step 3).
	11) Click button.
	A mesh is generated by twisted extrusion of the seed surfaces. button is reverted to button. The program is now ready for generating another volume mesh. button is enabled only when mesh generation is successful. Clicking button reverses the sign of the twist angle and regenerates the mesh.

< Example of modeling 3-D solid by twisting>