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Next: Comparison of formulations for Up: Numerical examples Previous: One penny-shaped crack

Many penny-shaped cracks

We now consider an infinite space which contains an array of $8\times
8\times 8(=512)$(total DOF=380,928) 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.3.25 shows the mesh for 512 cracks (total DOF=380,928), with each crack having 744 DOF. Fig.3.26 shows the crack opening displacements obtained with FM-BIEM. In this figure we superimposed the non-dimensional crack opening displacement $\mu \mbox{\boldmath$\space \phi $ }/a_0 p_0$ on the non-dimensional mesh $\mbox{\boldmath$\space x $ }/a_0$. The required CPU time with FM-BIEM is 6739 (sec).
  
Figure 3.17: Total CPU time (sec)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/ES3D/es3d:time.eps,scale=0.9} \end{center} \end{figure}


  
Figure 3.18: CPU time per iteration (sec)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/ES3D/es3d:timeiter.eps,scale=0.9} \end{center} \end{figure}


  
Figure 3.19: 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/ES3D/ratios.eps,scale=1.0} \end{center} \end{figure}


  
Figure 3.20: L2-norm Error
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/ES3D/L2Error.eps,scale=1.0} \end{center} \end{figure}


  
Figure 3.21: Crack opening displacement NE1 and NE2
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/ES3D/disp12.eps,scale=1.0} \end{center} \end{figure}


  
Figure 3.22: Crack opening displacement NE1 and NE3
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/ES3D/disp13.eps,scale=1.0} \end{center} \end{figure}


  
Figure 3.23: Crack opening displacement NE1 and NE4
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/ES3D/disp14.eps,scale=1.0} \end{center} \end{figure}


  
Figure 3.24: Crack opening displacement
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/ES3D/disphikaku.eps,scale=1.0} \end{center} \end{figure}


  
Figure 3.25: Crack mesh (DOF=380,928)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/ES3D/mesh512.ps,scale=0.75} \end{center} \end{figure}


  
Figure 3.26: Crack opening displacement (DOF=380,928)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/ES3D/open512.ps,scale=0.75} \end{center} \end{figure}


next up previous contents
Next: Comparison of formulations for Up: Numerical examples Previous: One penny-shaped crack
Ken-ichi Yoshida
2001-07-28