[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.
|Qualification||Doctor of Philosophy|
|Publication status||Unpublished - 2007|