Civil Engineering Reference
In-Depth Information
Figure 8.92
Refinement with rotated axis.
Figure 8.93
Cylindrical anisotropy.
we would like to define a cylindrical size distribution inside a cube. A very small size of 0.01
is required normal to the cylindrical surface, which is placed at a distance of 7 units from
a vertical edge of the cube. Along the other two principal directions, relatively larger sizes
between 1 and 2 units are prescribed. The resulting mesh consisting of 7264 nodal points
and 35,871 elements is shown in Figure 8.93, in which elongated elements are generated
along the circumferential direction of the cylindrical surface. The cluster of elements and
their alignment are fairly obvious that a cylindrical surface in sandwich layers is clearly seen
inside the cube.
In the last test, the same metric of the previous test is applied again. This time, the prin-
cipal direction along the vertical axis of the cube has been rotated so that it is along one of
the diagonals of the cube. The resulting mesh consisting of 8683 nodal points and 45,437
elements is shown in Figure 8.94. It is interesting to note that a cylindrical surface can be
identified inside the cube with its axis along the diagonal of the cube. Anisotropic refine-
ment here presented based on edge refinements just suggests a possibility of one of the
basic components to produce anisotropy in an FE mesh. While promising results are readily
obtained for isotropic refinement, the result of anisotropic refinement is less satisfactory
probably due to the fact that there is a discrepancy in the geometry of the initial mesh and
the required anisotropy. Hence, unless coarsening or de-refinement is also used along with
