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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 $8\times
8\times 8(=512)$ 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.4.6 shows the mesh for 512 cracks (total DOF=241,664), with each crack having 472 DOF. Fig.4.7 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 times with the original FM-BIEM and the new FM-BIEM are 4930(sec) and 3633(sec), respectively, while the numerical results obtained with these methods coincided. This result shows that the new FM-BIEM is more efficient than the original FM-BIEM when the boundary elements are distributed densely in the domain.


  
Figure 4.3: Crack mesh (DOF=1912)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/NEWFMM:Lap3D/mesh.eps,scale=1.0}\end{center}\end{figure}


  
Figure 4.4: Crack opening displacement
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/NEWFMM:Lap3D/dispall.eps,scale=1.0}\end{center}\end{figure}


  
Figure 4.5: CPU time (sec)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/NEWFMM:Lap3D/Time.eps,scale=1.0}\end{center}\end{figure}


  
Figure 4.6: Crack mesh (DOF=241,664)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/NEWFMM:Lap3D/mesh512.ps,scale=0.8}\end{center}\end{figure}


  
Figure 4.7: Crack opening displacement (DOF=241,664)
\begin{figure}
\begin{center}
\leavevmode
\epsfile{file=FIG/NEWFMM:Lap3D/open512.ps,scale=0.8}\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