Transient wave scattering by inhomogeneities and cracks in elastic media

The transient scattering of elastic waves by inhomogeneities and cracks in elastic media is investigated in time as well as in frequency domains by using a hybrid numerical method combining the finite element discretization of the near field with the boundary integral representation of the far field. This hybrid method makes use of numerical techniques to reduce both the computational time and memory, such that the transient responses can be easily obtained.; An adaptive integration scheme is used for the evaluation of the Green's functions and higher order elements for the finite element mesh have been used to get good accuracy at high frequency. The response in frequency domain is obtained from solving a set of large sparse unsymmetric complex equations, which are stored in a column list scheme data structure, by the biconjugate gradient method, then it is transformed into the time domain by FFT. This hybrid method is then applied to study scattering problems in the fields of earthquake engineering and quantitative nondestructive evaluation.; The ground motion amplifications of two semi-elliptical alluvial valleys and one semi-elliptical canyon have been investigated due to incident SH, P, and SV wave pulses in homogeneous and layered half-spaces. It is found that the surface waves, Love and Rayleigh waves, could propagate back and forth on the surfaces of valleys and create very large amplification of the surface displacement and very long duration of shaking. This may cause severe damage when earthquake occurs.; The transient scattering of Rayleigh-Lamb waves by two surface-breaking cracks with different depths and one subsurface crack in a glass plate has been studied. The source function generated by a steel ball impact is extracted by a direct integration technique. It was then used to simulate the experimental results. Good agreement has been obtained. The cracks are detectable and their depths are distinguishable from the scattering responses. This implies that the hybrid numerical method described in this dissertation is a potential tool in the field of quantitative nondestructive evaluation.