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Many penny-shaped cracks

We now consider an infinite space which contains an array of $4\times
4\times 4$(=64) (total DOF=32,256) penny-shaped cracks, each having the same radius a0 subjected to the same incident wave field (ka0=1) 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. In GMRES we use the block diagonal matrix corresponding to the cracks as the preconditioner. In Fig.3.50 and Fig.3.51 we have superimposed the real part and the imaginary part of the non-dimensional crack opening displacement $\vert\phi\vert/u_0$ plotted in the normal direction on the non-dimensional mesh $\mbox{\boldmath$\space x $ }/a_0$, respectively. The required CPU time with FM-BIEM is 8706(sec).


  
Figure 3.41: Total CPU time (sec) ( ka0=1,2,3,4,5)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/Helm3D/aho.eps,scale=1.0}\end{center}\end{figure}


  
Figure 3.42: CPU time per iteration (sec) ( ka0=1,2,3,4,5)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/Helm3D/Tfmm-itr.eps,scale=1.0}\end{center}\end{figure}


  
Figure 3.43: Crack opening displacement $\vert\phi\vert/u_0$ (ka0=1)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/Helm3D/disp_ka=1.eps,scale=1.0}\end{center}\end{figure}


  
Figure 3.44: Displacement |u|/u0 at both sides (ka0=1)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/Helm3D/hikaku_ka=1.eps,scale=1.0}\end{center}\end{figure}


  
Figure 3.45: Crack opening displacement $\vert\phi\vert/u_0$ (ka0=2)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/Helm3D/disp_ka=2.eps,scale=1.0}\end{center}\end{figure}


  
Figure 3.46: Displacement |u|/u0 at both sides (ka0=2)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/Helm3D/hikaku_ka=2.eps,scale=1.0}\end{center}\end{figure}


  
Figure 3.47: Crack opening displacement $\vert\phi\vert/u_0$ (ka0=3)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/Helm3D/disp_ka=3.eps,scale=1.0}\end{center}\end{figure}


  
Figure 3.48: Displacement |u|/u0 at both sides (ka0=3)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/Helm3D/hikaku_ka=3.eps,scale=1.0}\end{center}\end{figure}


  
Figure 3.49: Comparison of computational times for Laplace's equation and Helmholtz's equation (ka0=1)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/TEST/lap-helm.eps,scale=1}\end{center}\end{figure}


  
Figure 3.50: Real part of crack opening displacement (DOF=32,256, ka0=1)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/Helm3D/real.ps,scale=0.5}\end{center}\end{figure}


  
Figure 3.51: Imaginary part of crack opening displacement (DOF=32,256, ka0=1)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/Helm3D/imag.ps,scale=0.5}\end{center}\end{figure}


next up previous contents
Next: Relation between formulations in Up: Numerical examples Previous: One penny-shaped crack
Ken-ichi Yoshida
2001-07-28