Date of Award

Spring 1-1-2018

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

Ronald Y. S. Pak

Second Advisor

Richard A. Regueiro

Third Advisor

Jeong H. Song

Fourth Advisor

Yida Zhang

Abstract

Time-domain boundary element method (TD-BEM) is a powerful tool for transient elastodynamic modeling of soil and structures especially for unbounded domain problems. Aimed to add to the advancement of this class of methods and facilitate its coupling with other numerical approaches, a number of new analytical and computational formulations are developed and explored in this study. The work includes the development of a regularized convolution-type boundary integral equation in the time domain for 3-D elastodynamics, the formulation of a rigorous stability analysis via a hybrid amplification matrix of direct TD-BEMs, an extension of a displacement potential-integral transform method from the frequency- to the time-domain, a generalization of the classical Cagniard-de Hoop method in wave propagation theory for Laplace transform's inversion, and the derivation of exact as well as asymptotic forms of the time-domain point-load Green's functions for a homogeneous and a multi-layered half-space. The theoretical developments are employed to develop new computational algorithms such as the new variable-weight multi-step collocation TD-BEM scheme with higher-order time projections and a new numerical contour integration method to compute the fundamental integrals in exact half-space time-domain Green's functions. The efficacy and performance of these developments are evaluated with respect to benchmark elastodynamic problems for both bounded and unbounded domains. The formulation and effectiveness of coupling the proposed TD-BEM approach with a local finite element zone for dynamic soil-structure interaction problems as a rigorous form of wave-absorbing boundary are also investigated.

Share

COinS