Development of a solver system for an inverse problem of defect shape determination with elastic wave

1. 基于BIEM的时域弹性动力裂纹判定工作站代码的开发我们可以利用BIEM开发二维和三维时域弹性动力裂纹判定问题的计算机代码。这些代码在便携式工作站上运行得很快。这个问题的调查取得了比计划更大的进展；实际上，我们进行了裂纹确定问题，其中裂纹具有许多几何自由度。此时，我们可以用配点法求解波动方程的二维和三维裂纹确定问题，而不是用变分法求解。特别是在二维问题中，我们可以借助Tikhonov正则化来确定相当复杂的裂纹形状。我们现在计划将这些研究扩展到弹性动力学，包括各向异性的情况，这在复合材料的无损评价中很重要。用PZT换能器对圆形硬铝试样进行超声测量。测量是投球式的。我们首先用一个完整的标本做了这个实验，然后用同样的标本做了同样的实验，但是用锯切了。我们尝试用傅里叶变换将换能器的输出电压转换成位移，但分辨率不理想。用半导体应变计进行的类似试验也不太成功。因此，我们决定使用统计方法从传感器输出重建裂纹。我们计划继续研究使用激光测量的可能性。2.实验数据的反演经过统计处理以确定裂纹的位置，取得了中等程度的成功。然而，利用BIEM进行反演还需要更多的研究。

1. Development of a workstation code for the time domain elastodynamic crack determination with BIEMWe could develop computer codes for 2 and 3 dimensional time domain elastodynamic crack determination problems with BIEM.These codes are found to run fast on a portable workstation. The investigation of this subject made more progress than planned ; actually, we proceeded to the crack determination problems where the crack has many geometrical degrees of freedom. At this moment we can solve 2 and 3 dimensional crack determination problems for the wave equation with the collocation BIEM, rather than the variational one. In 2D problems, in particular, we can determine quite complicated crack shapes with the help of the Tikhonov regularisation. We now plan to extend these studies to elastodynamics including anisotropic cases, which are important in the non-destructive evaluation of composite materials.2. Measurement of scattered waves from a crackAn ultrasonic measurement is carried out with a circular duralumin test piece using PZT transducers. The measurement is of the pitch-catch type. We first made the experiment first with an intact specimen, and then repeated the same experiment with the same specimen but with a saw cut. We tried to convert the output voltage from the transducer into displacements by using Fourier transform, but the resolution was not satisfactory. A similar trial with a semi-conductor strain gauge was not very successful, either. We therefore decided to use a statistical method to reconstruct the crack from the transducer output. We plan to continue this investigation looking into the possibility of using laser measurements.3. Inversion of the experimental dataThe data obtained in 2. was processed statistically to determine the location of the crack, with a moderate success. The use of the BIEM for the inversion, however, needs more investigation.