Area Command

The Area command defines a 2D area or a 1D interface which will automatically be divided into elements to generate all or part of an FEA mesh.

Area Command Blocks

Scripted Area Block

In scripted files, the Area command is a block that begins with an Area command and ends with an EndArea command. Between the Area and its matching EndArea, the area is defined by a collection of paths that enclose the area. To define a solid 2D area, the area block must include four paths:

Area (id),(thick),<(angle)>
  Paths "Bottom"
    Keypoint "BotLeft",0,0
    Keypoints "BotRight"
  EndPath
  Paths "Right", "Top" "Left"
EndArea

To define a 1D interface, the area block must includes two separate, but identical paths:

Area (id),(thick),<(angle)>
  Path "Left",6
    Keypoint "LeftBot",0,0
    Keypoints "LeftTop"
  EndPath
  Paths "Right"
EndArea

The Area command starts with three arguments

• (id) is the material ID for a previously defined material. All elements in the area will be set to this material. When the mesh will be defined using images and shapes, set the material ID for any region that will use the images and shapes to be _NONE_; the images and shapes will fill in the materials later.
• (thick) is the thickness of all the elements in length units for 2D plane stress or plain strain analyses. It is ignored for axisymmetric analyses, but is still required.
• The optional (angle) is a material angle for all the elements. It may be needed for certain 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.

Each path can be explicitly defined (e.g., the paths with subordinate Keypoint commands) or can refer to a previously defined path (e.g., the Paths commands with one or more path names). See the Path and Keypoint commands for details on defining paths and keypoints.

The element type to use when meshing the area is determined by the Element and FlipTriangles commands.

See more details below.

XML Area Block

In XML input files, all Area blocks must be within the single <Mesh> block and they must come after the <Keypoints> block and all path definitions. Each area block has the form

  <Area mat="1" thick="10" type="4" flip="0" angle="0">
    <path id="bottom"/>
    <path id="right"/>
    <path id="top"/>
    <path id="left"/>
  </Area>

An <Area> block links a series of previously defined paths into a region to be meshed. Subordinate to each <Area> block are a series of <path> commands that list the paths that define the area and specifies them by their id. Currently NairnFEA only supports areas with four paths, to mesh quadrilateral areas, or areas with two paths, to mesh interfaces. The attributes for an <Area> block are:

• mat: Material number in the list of defined materials when referring to material "By Number". When the mesh will be defined using images and shapes, the mat should be 0 for elements that will be set later by images and shapes.
• 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 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 length units (for plane stress or plane strain 2D calculations); not needed for axisymmetric analysis.
• type: The type of element to create in the meshed area.
• 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.

Area Details

Quadrilateral areas must use solid elements and interface areas must use interface elements.

For quadrilateral areas, the end of the fourth 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. Furthermore, if n₁, n₂, n₃, and n₄ are the number of intervals along the four paths, they must satisfy

      [math]\displaystyle{ n_1+n_2 = n_3+n_4 \qquad{\rm or}\qquad n_1+n_4 = n_2+n_3 }[/math]

For interface meshing, the two paths must be different, but indentical paths. More more details see help on imperfect interfaces in FEA.

Notes

1. An FEA analysis can have any number of areas. To connect areas into a solid object, the areas must share common paths.
2. The Area command is only allowed for FEA analyses.