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Next: Crack problems for three-dimensional Up: Numerical examples Previous: One penny-shaped crack

Many penny-shaped cracks

We now consider an infinite space which contains an array of $4\times
4\times 4(=64)$ penny-shaped cracks, each having the same radius a0 subjected to the same asymptotic condition as in the previous example. The centroids of these cracks are located regularly with an interval of 4a0 in each coordinate direction, but the orientation of each crack is taken random. Fig.3.14 shows the mesh for 64 cracks (total DOF=30,208), with each crack having 472 DOF. Fig.3.15 shows the crack opening displacements; we superimposed the non-dimensional crack opening displacement $\phi / u_0$plotted in the normal direction on the non-dimensional mesh $\mbox{\boldmath$\space x $ }/a_0$. The required CPU time with FM-BIEM is 2426 (sec).
  
Figure 3.5: Crack mesh (DOF=9592)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/Laplace3D/mesh9592.ps,scale=0.7} \end{center}\end{figure}


  
Figure 3.6: Total CPU time (sec)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/Laplace3D/Lap3D:time_p10.eps,scale=1.0} \end{center}\end{figure}


  
Figure 3.7: CPU time per iteration (sec)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/Laplace3D/Lap3D:timeiter.eps,scale=1.0} \end{center}\end{figure}


  
Figure 3.8: Ratio of the time required with FM-BIEM (TimeFM-BIEM) to the time required with the conventional BIEM (TimeBIEM)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/Laplace3D/ratios.eps,scale=1.0} \end{center}\end{figure}


  
Figure 3.9: L2-norm Error
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/Laplace3D/L2Error.eps,scale=1.0} \end{center}\end{figure}


  
Figure 3.10: Crack opening displacement $\phi / u_0$ obtained with NE1 and NE2
\begin{figure}\begin{center}
\leavevmode
\epsfile{file=FIG/Laplace3D/disp12.eps,scale=1.0} \end{center}\end{figure}


  
Figure 3.11: Crack opening displacement $\phi / u_0$ obtained with NE1 and NE3
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/Laplace3D/disp13.eps,scale=1.0} \end{center}\end{figure}


  
Figure 3.12: Crack opening displacement $\phi / u_0$ obtained with NE1 and NE4
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/Laplace3D/disp14.eps,scale=1.0} \end{center}\end{figure}


  
Figure 3.13: Crack opening displacement
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/Laplace3D/disphikaku.eps,scale=1.0} \end{center}\end{figure}


  
Figure 3.14: Crack mesh (DOF=30,208)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/Laplace3D/mesh64.ps,scale=0.5} \end{center} \end{figure}


  
Figure 3.15: Crack opening displacement (DOF=30,208)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/Laplace3D/open64.ps,scale=0.5} \end{center} \end{figure}


next up previous contents
Next: Crack problems for three-dimensional Up: Numerical examples Previous: One penny-shaped crack
Ken-ichi Yoshida
2001-07-28