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Mapped Meshing

There are situations when it is necessary or desirable, to create a geometrically regular finite element mesh. This is referred to as "mapped" meshing. In Slide2, a mapped mesh may be created within triangular or rectangular regions, using the Mapped Triangular Region or Mapped Rectangular Region options in the Mesh Refinement sub-menu of the Mesh menu.

Mapped Triangular Region

The Mapped Triangular Region option allows the user to create a regular (mapped) mesh, within any region bounded by THREE line segments. NOTE:

  • The three line segments must form a closed region
  • Each of the three line segments MUST have the same number of nodes (discretizations). In most cases, you will have to use the Custom Discretize option, in order to ensure that each line segment has the same number of nodes.

If the above two conditions are met, then you may use the Mapped Triangular Region option as follows:

  1. Select Mapped Triangular Region from the Mesh Refinement sub-menu of the Mesh menu.
  2. Use the mouse to select three boundary line segments which form a closed triangular region.
  3. Right-click the mouse and select Done Selection (or press Enter), and a regular mapped mesh will automatically be generated, within the triangular region. The mapped mesh will be generated according to the discretization of the three line segments, and the Element Type in Mesh Setup (Triangles or Quadrilaterals).

Mapped Rectangular Region

The Mapped Rectangular Region option allows the user to create a regular (mapped) mesh, within any region bounded by FOUR line segments. NOTE:

  • The four line segments must form a closed region, and the region must be concave (convex regions not allowed).
  • Opposite line segments of the rectangular region, MUST have the same number of nodes (discretizations). In most cases, you will have to use the Custom Discretize option, in order to achieve this. (Unlike the Mapped Triangular Region option, it is not necessary for ALL line segments to have the same discretization).

If the above conditions are met, then you may use the Mapped Rectangular Region option as follows:

  1. Select Mapped Rectangular Region from the Mesh Refinement sub-menu of the Mesh menu.
  2. Use the mouse to select FOUR boundary line segments which form a closed rectangular region.
  3. When you are finished selecting line segments, right-click the mouse and select Done Selection (or press Enter), and a regular mapped mesh will automatically be generated, within the rectangular region. The mapped mesh will be generated according to the discretization of the four line segments, and the Element Type in Mesh Setup (Triangles or Quadrilaterals).

NOTE:

  • Either Triangular or Quadrilateral finite elements may be used with either mapped meshing option. However, if Quadrilateral elements are used with a Mapped Triangular Region, then some of the elements will necessarily be triangles.
  • If the mesh is reset with the Reset Mesh option, all mapped meshing will be lost. However, remember that you can always use the Undo option to Undo any actions in Slide2.
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