Civil Engineering Reference
In-Depth Information
Elements around
x
Optimal point
Trial
points
x´
h
u
x
Level surface of γ
P
Figure 6.36
Shifting
x
along the gradient of
γ
P
.
iii. GETMe. GETMe smoothing will be applied according to the procedure detailed in
Section 6.3.3.3. As we have introduced γ-quality to hexahedral elements, patches and
meshes, meshes of inverted elements can also be handled by GETMe using a weight
given by w = 1 - γ, such that more weights are attached to open up negative elements.
In order to ensure that the quality of the mesh will be improved for each nodal move-
ment and to avoid the formation of inverted elements, the γ-quality of the patch before
and after the shifting of nodes are calculated, and the shift will only be materialised
should there be an increase in the γ-quality. As it is quite expensive to evaluate the
γ-quality of a patch of hexahedral elements, it is a trade-off between cost and quality,
and in the present version of GETMe, three strategic points are evaluated.
A hexahedral mesh of series (1) is generated by the sweeping method such that the cross sec-
tion increases with the angle of rotation. Elements of different size are created by subdividing
hexahedral elements at random locations, as shown in Figure 6.37a, and there are 4820 nodes
and 2400 hexahedral elements in the resulting mesh. Element irregularity is introduced by a
perturbation of all the interior nodes with random movement of nodes for an amount as large
as the diameter of the elements. Inverted elements are often found in the mesh with negative
γ values (Escobar et al. 2003). For each optimisation scheme, ten cycles of smoothing are car-
ried out to each of the ten test meshes, and the results are presented in Table 6.11 in which
(a)
(b)
Subdivided elements
marked in red
Figure 6.37
Hexahedral mesh with random subdivisions around interior nodes: (a) before optimisation;
(b) after optimisation.
