Civil Engineering Reference
In-Depth Information
8.4.3.3 Examples
The refinement algorithm is tested with meshed objects of various shapes and subject to dif-
ferent node spacing distribution requirements. The data for the initial mesh are the vertices
of the tetrahedral elements and the co-ordinates of the nodal points. A node spacing func-
tion has to be specified, which allows the element size of the mesh to be evaluated at any
point within the meshed domains. The algorithm is coded in Visual Fortran on PC i7 CPU
870 at 2.93 GHz running on XP mode with QuickWin graphic supports. The algorithm is
to refine the initial mesh by repeatedly bisecting the edges of the mesh following the priority
sequence of the edge length until the specified node spacing is achieved.
The first example is the refinement of a cube along a vertical edge. The cube shown in
Figure 8.80 is divided into five tetrahedral elements, which are refined into 34,616 node
points and 179,553 elements, as shown in Figure 8.81. The size of the elements at the refine-
ment edge is 0.05 unit, whereas those at the far end are of size 10 units, which is also the
length of the cube. Owing to the rapid change in the element size, this is the only example
where the γ-quality has decreased slightly from a relatively high value of 0.7791 to 0.7374.
The same cube is used in the second example in which refinement is carried out following
one octant of a spherical surface. The initial mesh consists of six tetrahedral elements with a
γ-value of 0.6606, which is improved to 0.7244 in the refined mesh of 186,524 node points
and 1,024,650 elements, as shown in Figure 8.82.
In the third example, a more complicated density distribution function was employed. It is
intended to generate elements of relatively smaller size on a spherical surface inside a cube.
Figure 8.80
A cube of five tetrahedra.
Figure 8.81
Refined along an edge.
