Civil Engineering Reference
In-Depth Information
(b)
(a)
(c)
(d)
Figure 8.125
Merging of two strings into a single object: (a) first string partitioned into 12 zones; (b) second
string divided into 12 zones; (c) eleven regions identified; (d) mesh of merging of strings.
followed by a subdivision of the hexahedra into tetrahedra. The resulting tetrahedral mesh
consists of 1953 nodes, 7200 tetrahedra and 2800 triangles on the boundary surface. The
intersection as a result of hand penetration produces 744 intersection segments (points), which
could be grouped into five loops. The boundaries of the hand and that of the board are each
partitioned into six zones, as shown in Figure 8.126a and b. Two regions of intersection could
be recovered from the intersection loops and surface patches, as shown in Figure 8.126c. Two
holes will be perforated in the board by subtracting the regions of intersection from the slave
object, as shown in Figure 8.126d. When the hand is inserted into the perforated board, the
two objects merge with a tight fit at the contact surfaces, as shown in Figure 8.126e.
Example 5 is about the intersection of a cuboid with a machine part. The machine part,
which consists of 21,241 nodes, 71,222 tetrahedra and 39,200 triangles on the boundary
surface, is a realistic engineering object provided by Prof. Z.Q. Guan of Dalian University of
Technology, China. The cuboid is created by first generating hexahedral elements, followed
by a subdivision of the hexahedra into tetrahedra. The large difference in the element size
between the objects is adopted to test the performance of the merging algorithm. As shown
in Figure 8.127a, elongated triangles of large aspect ratios are created on the surface of the
cuboid. The 104 triangles on the surface of the cuboid are divided into 1312 triangular
facets, and the number of tetrahedral elements increases from 144 to 1395. There are 624
