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Numerical Examples

We now present a numerical example obtained by the method described above.

The true crack is a penny shaped one having a radius of and located at the position in Fig.2.

Figure 2: Mode of Convergence---3D Elastodynamics (Galerkin)

The following incident waves are used:


where f and are given by

Simulated far fields with no error for the 8 observation directions shown in Fig.2 are used as the input data. The mesh for the crack has 21 nodes and the time increment is chosen as . The number of time steps used for computing J is 15, and Poisson's ratio is 1/4. Also, the following constraints are introduced to avoid divergence of solutions.

Fig.2 shows the mode of convergence. The initial guess is as shown in the same figure. The plots for the intermediate configurations are made at each evaluation of in the process of NLP. As the figure shows the final result was almost the same as the true one. The CPU time was about 1 hour with a lap-top computer.

N. Nishimura
Thu Feb 19 01:36:51 JST 1998