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We now consider an infinite space which contains an
array of pennyshaped cracks, each having the same radius a_{0},
subjected to the same asymptotic condition as in the previous
example. The centroids of these cracks are located at the same interval
of 4a_{0} in each coordinate direction, but the direction of each crack
is taken random. First, we consider an array of
pennyshaped cracks (total DOF=1,285,632) in the infinite
domain. Fig.4 plots the nondimensional crack opening displacement
(
)
on the nondimensional mesh
.
Notice
that the originally flat cracks appear curved since the crack opening
displacements have been superposed. The required CPU times with FMBIEM
and the new FMBIEM are 13,954(sec) and 8,290(sec), respectively. In
this example the error defined as
is
,
where
is the numerical
solution obtained with the new FMBIEM,
the one obtained with
the original FMBIEM and
denotes the L_{2}norm. Next we
consider an array of
pennyshaped cracks in
the infinite domain. Fig.5 plots the total CPU time (sec) required
by the original FMBIEM and the new FMBIEM with this array. In
Fig.5 the lines marked `Tfmm' and `Tfmmnew' indicate the CPU times
required with the original FMBIEM and the new FMBIEM,
respectively. These results show that the new FMBIEM is more efficient
than the original FMBIEM when the distribution of the boundary elements
is more threedimensional.
Figure 1:
crack mesh (DOF=5736)

Figure 2:
crack opening displacement of one pennyshaped crack

Figure 3:
CPU time (sec) for the numerical exmaples with one pennyshaped crack

Figure:
crack opening displacement(DOF=1,285,632) of an array of
pennyshaped cracks

Figure:
CPU time (sec) for the numerical exmaples with an array of
pennyshaped cracks

Next: Conclusions
Up: Numerical Examples
Previous: One crack
Kenichi Yoshida
20010326