Civil Engineering Reference
In-Depth Information
Figure 4.39
Completed mesh of 8934 triangles.
Figure 4.40
Parametric curved surface of 8934 triangles.
4.2.13 Optimisation of anisotropic meshes
Unlike the optimisation of isotropic meshes of which the shape of the element is the only
concern, for anisotropic meshes, both the shape of the elements and how close the edges are
in compliance with the unit metric have to be considered. Hence, the quality of a triangle
consists of two parts: the α-value of the triangle and the δ-coefficient of all its edges, i.e.
quality of metric triangle ABC, ψ = αδ
1
δ
2
δ
3
where the α-value of metric triangle ABC on a parametric domain is defined in Section
4.2.10, and δ
1
, δ
2
and δ
3
are the conformity coefficients of the edges discussed in Section
4.2.12. In general, the optimisation of an FE mesh can be achieved by geometrical and
topological means. For the optimisation of unit metric meshes, one geometrical operation
and one topological operation are proposed, which are performed in an alternative manner
to achieve the best results.
4.2.13.1 Node smoothing
The quality of the mesh is to be improved by shifting each node to a more strategic position
by means of the smart Laplacian method and its variation. For each interior node I (nodes
generated by insertion in the triangulation process), determine the polygon of all the n sur-
rounding triangles, as shown in Figure 4.41. Compute the average and minimum qualities
of the triangles in this polygon:
