Abstract
This page shows a method for generating quadrilateral meshes
automatically, by converting triangular meshes.
By converting triangular meshes generated by bubble mesh method,
this method generates graded and well-shaped quadrilateral meshes.
Background
In some types of FEM analysis, such as automobile crash simulation and
sheet-metal forming simulation, quadrilateral meshes are preferred
to triangular meshes. because of the solution accuracy.
Many quadrilateral mesh generators employ mapping methods or recursive
subdivision as shown in the above figure, but the methods have the
following problems:
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Automation.
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Shape of elements.
-
Element size control.
Algorithm
This page propose an automated conversion method of triangular mesh
into quadrilateral mesh.
The above graded mesh is generated by bubble mesh method.
Red polygonal lines in the above figure show the adjacency of
triangular elements.
Topological distance from the boundary of the region is calculated
for each triangular elements, and they are grouped by the distance.
Blue lines in the above figure show layers of groups of elements.
This figure also show that the adjacency of elements in the different
groups has been cancelled.
Triangular elements in each group are then matched.
Red lines in the above figure show the matched elements.
Finally, triangular elements are converted into quadrilateral elements
by using the above templates.
Matched triangular elements are converted into four quadrilateral
elements. Unmatched triangular elements are converted into three
quadrilateral elements.
The above figure shows the generated quadrilateral elements.
This method has the following advantages:
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Element size control.
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Element alignment control.
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Practical computational time(O(n)).
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