The modelling of unbounded domains is an important consideration in many engineeringudproblems, for example in fluid flow, electro-magnetics, acoustics and solidudmechanics. This thesis focuses on the problem of modelling elastic solids to infinity,udwith the specific purpose of modelling dynamic soil-structure interaction (DSSI).udHowever, the reader should be aware that the techniques presented may also beudadapted to address those other physical phenomena.udThe need for techniques to model the soil domain to infinity and a qualitativeudintroduction into the problems associated with dynamic soil-structure interactionudare outlined in chapter 1. This is done to illustrate why such an abstract mathematicaludconcept of modelling infinite domains has an important role to play withinudthe design process of large, safety critical, civil engineering structures.udA brief review of a number of alternative ways of addressing this problem is givenudin chapter 2. Their relative strengths and weaknesses along with the typical applicabilityudof the techniques is discussed. A consequence of this review is theudidentification of a very promising rigorous approach [59] which is singled-out forudfurther study. A detailed explanation of this (Consistent Infinitesimal Finite ElementudCell Method, CIFECM) method is then given in chapter 3. Attention isudrestricted to the use of the technique for solving the 3-D vector wave equation inudthe time domain.udThe features of the non-linear dynamic finite element code, into which the CIFECMudhas been incorporated, is highlighted in chapter 4. The non-linear (microplane) materialudmodel for quasi-brittle materials is described along with the solution strategyudemployed. It should be mentioned that the soil is treated within this thesisudas drained linear elastic medium. The method of coupling the CIFECM into theuddynamic equation of force equilibrium for both directly applied and transmittedudloading regimes is detailed.udApplication of the code follows in chapter 5; firstly by introducing the simplest testudproblem of one finite element coupled with one CIFECM element to model a surfaceudfoundation. Comparisons are made between the dynamic displacements resultingudfrom the method and standard FE solutions obtained from the use of extendedudmeshes and fixed boundary conditions, along with a study of the influence inputudvariables. Following these examples a larger (more realistic) engineering problemudis tacked involving the simulation of an aircraft impact on a reinforced concreteudnuclear containment vessel. This represents the first use of the method in a 3-D nonlinearudstructural analysis problem. The results illustrate the practical implicationsudof including DSSI in the analysis. udIIIudIn chapter 6, a series of general observations on the method are made with anudassessment of its value together with a discussion on its wider application to otherudengineering fields. Possible future developments to make the method more computationallyudefficient are finally suggested.
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