Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Electrical and Computer Engineering

First Advisor

William Lord


An increasing requirement for engineering system reliability provides the motivation for further development of nondestructive evaluation (NDE) techniques. An important objective of NDE system measurements is related to the inverse process which either images the defect (or material inhomogeneity) or sizes and locates the defect from the detected signals. Many inverse algorithms involve assumptions and approximations which are not realistic. Evaluation of these effects on the reconstructed images has always been difficult, as experimentally, these different factors cannot be easily distinguished. Thus, a powerful test bed is essential to study the sensitivity of an inverse algorithm. Numerical models are the most suitable technique for this purpose. In addition, an accurate forward model is also useful to implement iterative inverse schemes;This dissertation describes the development and use of finite element analysis to model ultrasonic wave propagation phenomena and to study diffraction tomography. The nature of the finite element model allows the accurate prediction of the displacement field for complicated situations including arbitrary anisotropy, inhomogeneity and attenuation. Basic formulations are presented for general three-dimensional (3-D) geometries and verified by comparing to analytical solutions. To optimize computer resources, the combination of central difference and forward difference schemes is chosen to approximate the time derivatives and a lumped mass schmeme is introduced to avoid the expensive matrix inversion. The two-dimensional (2-D) and axisymmetric formulations discussed at length in this thesis effectively model problems satisfying either plane strain or axisymmetric conditions. Absorbing boundary conditions are introduced for large geometries and applied to some typical test situations. Using this finite element model as a test bed, the diffraction tomographic algorithm is studied with regard to finite aperture effects and material anisotropy;Extensive comparison of the finite element results with analytic solutions proves the validity of the 2-D, axisymmetric and 3-D models. Applications of the 2-D and axisymmetric formulations correctly predict useful phenomena associated with wave/defect interactions and the anisotropic property of the material. Evaluation of the diffraction tomographic algorithm provides useful insights as to the effects of the assumptions and approximations. Among all the practical factors, the material anisotropy is the primary cause in degenerating the quality of the reconstructed image.



Digital Repository @ Iowa State University,

Copyright Owner

Zhongqing You



Proquest ID


File Format


File Size

216 pages