Boundary Element Methods For Wave Propagation In Elastic Media With Stochastic And Heterogeneous Properties

Some schemes of the boundary element methods that deal with the wave propagation in elastic media with stochastic and heterogeneous properties have been presented in this thesis.After a brief summary of the available references in the related fields, the numerical schemes developed in this thesis have been presented in the succeeded five chapters:1. The boundary integral equation for SH wave propagation was derived in advance. A multi-region scheme of boundary element method for SH wave propagation in an elastic half plane has been suggested to deal with the irregular geometry, e. g. , the underground structure and irregular topography. Some numerical results have been given to show the effectiveness of the suggested scheme.2. On the basis of the afore-mentioned scheme together with a perturbation technique, a scheme of stochastic boundary element method has been developed. This scheme can be applied to obtain the mean responses of the displacements of subsurface topography in random half plane, and to study the effects of randomness of the material properties. Some application of this stochastic boundary element method in the analysis of system reliability has been presented as well.3. A mathematical transforms technique has been adopted to reduce a heterogeneous Helmholtz equation into homogeneous one. On this basis a scheme of boundary element method that deal with the SH wave propagation in a kind of heterogeneous half plane has been developed. Some numerical examples of wave scattering by subsurface topography or structures in a special kind of heterogeneous half plane, of which the material properties are varied along the depth, have been presented to show the applicability of the suggested scheme.4. A stochastic model of the afore-mentioned special heterogeneous me-...