Civil Engineering Reference
In-Depth Information
which cannot be lower than that of the element to be refined. The possible nodal configura-
tions in 3D transition hexahedral elements are much more complex in 3D than those of 2D
transition elements. Besides mid-edge nodes, there can also be mid-face nodes in 3D transi-
tion elements. All possible node patterns of eight types of transition hexahedral elements for
refinements on one, two, three, four or five faces are shown in Figure 5.109.
In an adaptive refinement analysis of a 3D cantilever beam discretised into regular hexa-
hedral elements, after three cycles of adaptive refinements to achieve an error in energy
norm of less than 10%, the end section of the final refined transition hexahedral mesh con-
sisting of 15,812 elements is shown in Figure 5.110. Figure 5.111 shows a joint connecting
structural beams and columns of a building, which is refined to a mesh of 25,060 transition
hexahedral elements to achieve an error of less than 8% in energy norm in four cycles of
adaptive refinement. Readers are also referred to the classical papers on FE MG by Octree
decompositions by Yerry and Shephard (1984) and Shephard and Georges (1991, 1992) for
possible comparison and enhancement.
Figure 5.110
Transition hexahedral mesh of a beam.
F i g u r e 5 .111
Transition hexahedral mesh of a structural joint of a building.
