published_or_final_version / Civil Engineering / Master / Master of Philosophy

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This thesis presents the development of a reliable and efficient technique for the numerical simulation of dynamic soil-structure interaction problems in anisotropic and nonhomogeneous unbounded soils of arbitrary geometry. Such a technique is indispensable in the seismic analysis of large-scale engineering constructions and, to my best knowledge, does not exist at present. The theoretical framework of the research is based on the scaled boundary finite-element method. The following advances are achieved: The scaled boundary finite-element method is extended to simulate the dynamic response of non-homogeneous unbounded domains. The scaled boundary finite element equations in the frequency and time domains are derived for power-type non-homogeneity frequently employed in geotechnical engineering. A high-frequency asymptotic expansion of the dynamic-stiffness matrix is developed. The frequency domain analysis is performed by integrating the scaled boundary finite-element equation in dynamic stiffness. In the time domain, the scaled boundary finite-element equation including convolution integrals is solved for the unit-impulse response at discrete time stations. A Pad?? series solution for the scaled boundary finite-element equation in dynamic stiffness is developed. It converges over the whole frequency range as the order of the approximation increases. The computationally expensive task of numerically integrating the scaled boundary finite-element equation is circumvented. Exploiting the sparsity of the coefficientmatrices in the scaled boundary finite-element equation leads to a significant reduction in computer time and memory requirements for solving large-scale problems. Furthermore, lumped coefficient matrices are obtained by adopting the auss-Lobatto-Legendre shape functions with nodal quadrature, which avoids the eigenvalue problem in determining the asymptotic expansion. A high-order local transmitting boundary constructed from a continued-fraction solution of the dynamic-stiffness matrix is developed. An equation of motion as occurring in standard structural dynamics with symmetric and frequency-independent coefficient matrices is obtained. This transmitting boundary condition can be coupled seamlessly with standard finite elements. Transient responses are evaluated by using a standard timeintegration scheme. The expensive task of evaluating convolution integrals is circumvented. The advances developed in this thesis are applicable in other disciplines of engineering and science to the analysis of scalar and vector waves in unbounded media.

[Truncated abstract] The scaled boundary method is a powerful, though undervalued, computational analysis method. The complex mathematics of the original derivation of the method has rendered it unattractive to researchers. However, the method has proven more efficient than conventional computational analysis methods for problems involving unbounded domains and for problems involving stress singularities. The advantages of the scaled boundary method in dealing with stress singularities make it uniquely suited to the analysis of fracture mechanics problems. This study will extend the capabilities of the scaled boundary method, exploring fracture mechanics applications in particular. Only benchmark elastostatic fracture mechanics problems are analysed as the focus of this work is the development of the scaled boundary method. It will be demonstrated that the intimidating mathematics of the method can be distilled into an elegant method which offers considerable advantages when used in the analysis of crack problems. This thesis will argue that the advantages of the scaled boundary method make it more valuable than is generally perceived and that coming to grips with the sometimes intimidating method is worthwhile. In this study, a significant contribution is made to the development of the scaled boundary method with a number of advances. The scaled boundary method is used to determine the higher order terms in asymptotic crack tip fields. The higher order terms play an important role in characterising the behaviour of cracked structures, but can only be evaluated analytically for a few simple cases. The higher order terms for a number of crack configurations are calculated using the scaled boundary method. Excellent agreement with results obtained from the literature is demonstrated. A penalty formulation is developed for use with a recently developed solution procedure for the scaled boundary method. The new solution procedure is based on the theory of matrix functions and the real Schur decomposition. ... A study is presented of error estimation and adaptivity procedures for use with the scaled boundary method when a reduced set of base functions is used. The error estimation procedure based on the superconvergent patch recovery technique and the error estimation procedure based on reference solutions are modified for use with the scaled boundary method when a reduced set of base functions is used. The use of a reduced set of base functions in an adaptivity procedure for the scaled boundary method is trialled. Adaptivity based solely on the set of base functions is shown to be inefficient. In contrast, the judicious use of a reduced set of base functions is shown to improve the overall efficiency of other adaptivity procedures.

Thesis (Ph.D.)--McMaster University (Canada), 1995. / Source: Dissertation Abstracts International, Volume: 57-03, Section: B, page: 1839. Adviser: A. Peirce.

Thesis (M. App. Sc.)--Carleton University, 2002. / Includes bibliographical references (p. 109-111). Also available in electronic format on the Internet.

Techn. Univ., Habil.-Schr.--Braunschweig, 2001. / Literaturverz.S. [159] - 168.

Mémoire (M.Sc.A.)--Université du Québec à Chicoutimi, 1987. / Document électronique également accessible en format PDF. CaQCU

Thesis (Ph.D.). / Written for the Dept. of Electrical & Computer Engineering. Title from title page of PDF (viewed 2009/06/10). Includes bibliographical references.

Thesis (M. Phil.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 81-82).