FEA Mesh Generation Commands

The best way to generate an FEA mesh is to use Keypoint, Path, and Area commands and possible combine them with image files or shape commands .

Scripted Input Files

In scripted input files, you build the mesh by using multiple Mesh Generation Commands. These commands are usually grouped together, but may be at various locations in the input file. The commands are:

Keypoint: Define a keypoint used in defining paths
Keypoints: Add multiple defined keypoints to a path.
Path: Define a path used in defining areas.
Paths: Add multiple defined paths to an area.
Area: Define an area for mesh generation.

<a href="Origin.html">Origin</a>: Define coordinate system origin for entry of <a href="keypoint.html">Keypoints</a> using polar coordinates.
<a href="element.html">Element</a>: Define type of element to use in the mesh.
<a href="fliptriangles.html">FlipTriangles</a>: Select the direction of triangular elements in meshes that use those elements.
<a href="resequence.html">Resequence</a>: To turn on the option to resequence the nodes, which will minimize the bandwidth of the problem and speed the calculations.

<a href="bmpregion.html">BMPRegion</a> ... <a href="endregion.html">EndRegion</a>: Generate elements from an image in a BMP file.
<a href="hole.html">Hole</a> ... <a href="endhole.html">EndHole</a>: Remove elements using a series of shape commands.
<a href="oval.html">Oval</a>: Define oval to set element material type.
<a href="polypt.html">PolyPt</a>: Define polygon to set element material type
<a href="rect.html">Rect</a>: Define rectangle to set element material type.
<a href="region.html">Region</a> ... <a href="endregion.html">EndRegion</a>: Generate elements for a series of shape commands.

XML Input Files

In XML input files, all Mesh Generation Commands must be within a single Mesh block:

<Mesh>
  <<a href="#Keypoints"><code>Keypoints</code></a>>
    <pt x='0' y='0' id='lowerleft'/>
    <pt x='0' y='10' id='upperleft'/>
    <pt x='50' y='0' id='lowerright'/>
    <pt x='50' y='10' id='upperright'/>
  </Keypoints>

  <<a href="#Paths"><code>Path</code></a> id="bottom" intervals='6' ratio='1'>
    <keypt id='lowerleft'/>
    <keypt id='lowerright'/>
  </Path>
  <Path id="right" intervals='3'>
    <keypt id='lowerright'/>
    <keypt id='upperright'/>
  </Path>
  <Path id="top" intervals='6'>
    <keypt id='upperright'/>
    <keypt id='upperleft'/>
  </Path>
  <Path id="left" intervals='3'>
    <keypt id='upperleft'/>
    <keypt id='lowerleft'/>
  </Path>

  <<a href="#Areas"><code>Area</code></a> mat="1" thick="10" type="4" flip="0" angle="0">
    <path id="bottom"/>
    <path id="right"/>
    <path id="top"/>
    <path id="left"/>
  </Area>
</Mesh>

<!-- image and shape methods to set element properties -->

<BMP name="MatImage.bmp" width="50" angles="MatAngles.bmp">
  <Origin x="0" y="0"/>
  <Intensity mat="2" imin="76" imax="255">
    <Thickness units="mm">1</Thickness>
  </Intensity>
  <Intensity mat="3" imin="1" imax="75">
    <Thickness units="mm">1</Thickness>
  </Intensity>
  <Intensity imin="0" imax="255" minAngle="0.000000" maxAngle="90.000000"/>
</BMP>

<Body mat='1' angle='0' thick='1'>
   <Oval units='mm' xmin='10' xmax='40' ymin='10' ymax='40'/>
   <Rect units='mm' xmin='10' xmax='40' ymin='10' ymax='40'/>     
</Body>

<Hole>
   <Rect xmin='20' xmax='30' ymin='20' ymax='30'/>     
</Hole>

Keypoints

The <Keypoints> section must come first. It can define any number of key points. Each subordinate <pt> command defines a key point, provides its x and y coordinates and gives it an id. The id's can be text or numbers and must all be unique among key points.

Paths

Following the <Keypoints>, there are a series of <Path> commands that link the key points into lines or arcs and define mesh information along those paths. Subordinate to each <Path> command are a series of <keypt> commands that list the key points that define the path. Use two key points to define a line or three key points to define an arc. Currently the path can only have two or three key points. The key points are selected by their id. The attributes for a <Path> command are:

id: An id for the path. The id's can be text or numbers and must be unique among all paths.
intervals: Number of elements along this path when it is meshed into an area.
ratio: Ratio of the size of the first element along the path to the last one. If ratio<0, then the absolute size of the first element on the path with be |ratio|. The default is 1.0 which gives equally sized elements.

Areas

Finally, the FEA mesh is created by a series of <Area> commands. An <Area> command links a series of paths into a region to be meshed. Subordinate to each <Area> command are a series of <path> commands that list the paths that define the area. Currently NairnFEA only supports areas with four paths, to mesh quadrilateral areas, or areas with two paths, to mesh interfaces.

For quadrilateral areas, the end of the last path must connect to the start of the first path. The direction of each path does not matter as they will be rearranged if needed to define the area; but the paths must circumnavigate the area in the counter-clockwise direction. If n₁, n₂, n₃, and n₄ are the number of nodes along each of the four paths, the meshing algorithm requires that n₁+n₂=n₃+n₄.

For interface meshing, the two paths must be different, but indentical paths. In other words, they must connect different keypoints, but the coordinates of the keypoints, the number of intervals along the path, and the path ratios must be identical. The order and orientation of the two paths in the area command does not matter. Finally, interfaces only function when they connect two areas. To insure this connection, the paths for an interface must have each been previously used in exactly one quadrilateral area.

The attributes for a <Area> command are:

mat: Material number in the list of defined materials when referring to material "By Number". If you are using the optional [[BMP, Region, and Hole Commands|BMP, Body, and Hole commands method to set element properties, the mat should be 0 for elements that will be set later by other commands.
matname: Alternatively, materials can be specified "By Name".
angle: Optional material angle relevant to anisotropic materials. It can be entered as a number or as a user-defined function. A function is evaluated at the midpoint of an element. Triangular elements are created in pairs and the function is evaluated at the midpoint of each pair.
thick: Thickness in mm for plane stress or plain strain analysis; not needed for axisymmetric analysis.
type: The type of [[FEA Elements|element to create by number]. The first <Area> command must define an element type. Subsequent <Area> commands can omit the element type unless the element type is changed to have an analysis with mixed elements. When mixed elements are used, they must be compatible elements (i.e., you can mix linear elements (types 1, 2, and 5) with each other or quadratic elements (types 3, 4, 6, and 8) with each other, but cannot mix linear elements with quadratic elements). Whenever a type attribute is used, it will apply to that area and all subsequent areas until it is changed. Finally, quadrilateral areas can only use solid elements (types 1, 2, 3, 4, and 8) and interface areas can use only interface elements (type 5 and 6).
flip: For triangular elements, the initially created quadrilaterials are split into two elements by drawing a diagonal across the quadrilaterial. The flip option can change which diagonal is used. It should be 0 or 1. Once it is set, it will apply to that area and all subsequent areas until it is changed.

BMP, Region, and Hole Commands

A powerful way to mesh complicated structures or composite materials with complicated morphologies is to do most of the work in <BMP> commands or using shapes in <Body> or <Hole> commands. The process is:

Create a standard mesh as described above. For sections of the mesh that will be set from a BMP file or from shapes, set the material attribute to 0.
One the <Mesh></t> section is done, use one or more interspersed <BMP>, <Body>, or <Hole> commands. They will map elements they cover currently with material 0 to the the material defined by the image or the region settings. The grid can be regular or irregular. The material will be selected from the image information at the centroid of the element; for shapes it will be set if the centroid of the element is in the shape. To resolve complicated structures, the grid has to be fine enough to resolve object details.

When the mesh is done, any elements initialized to material 0 but not assigned to a material by <BMP>, <Body>, or <Hole> commands will automatically be removed from the mesh. This feature allows calculations on materials with voids or irregular edges without needing to use <Area></a> commands to construct all details of the shape. If these removals cause the mesh to be partitioned into disconnected sections, however, the FEA analysis will fail. A good way to verify connectivity is to attempt to resequence the nodes

The image and shape commands are:<a name="body"></a><BMP> The details on the <BMP> command and the meaning of its attributes and subordinate commands are given <a href="definempm.html#BMPShape">here</a> (in the MPM documentation). <a name="body"></a><Body> Defines a block of material. All material points in the block will be assigned the same material number (mat, see <a href="definematl.html">Defining Materials</a>; numbers can be replaced by names using a matname attribute as explained <a href="definematl.html#usemats">here</a>), material angle (angle in degrees which is used for some <a href="definematl.html">anisotropic materials</a>; t can be entered as a number or as a <a href="function.html">user-defined function</a>), and thickness (thick in mm) A single <Body> for 2D FEA can contain any number of the <a href="definempm.html#2DShapes">2D shape commands</a>. The shapes can overlap; if they do the element material will be for the first shape command that intersects that elements centroid. If not specified angle will be zero and the thickness will be 1 mm. <Hole> Defines empty space within a body. A single <Hole> group for 2D FEA can contain any number of the <a href="definempm.html#2DShapes">2D shape commands</a>. Any subsequent <BMP> or <Body> structures that overlap the hole will not assign those elements.