Thesis (MScEng)--University of Stellenbosch, 2004. / ENGLISH ABSTRACT: The aim of the thesis is to compare results obtained from a finite element analysis method (FEM) to experimental results of a 12.2m long semi-trailer driven off-road. Semi-trailers are of great importance in the transport industry. Furthermore, the need to obtain optimum and reliable semitrailers in this crucial stream of industry is indispensable. The work focuses on comparing the two results so that the finite element method may be used as design analysis and redesigning tool as a substitute to testing. The semi-trailer was driven on a relatively rough off-road at different speeds, at 70kmlh, 50kmlh and 40kmlh loaded with about 12 tonnes of brick pallets. The forces at the suspension of the semitrailer and strains at different parts were measured with the help of strain gauges and other data acquisition equipment. A finite element model of the semi-trailer was modelled in Nastran for Windows. The trailer parameters in the finite element were tuned to curve fit the test results. A comparison of the two /' results was made based on the average of absolute values and standard deviation, to verify the validity of the finite element model. / AFRIKAANSE OPSOMMING: Die doel van die tesis is om die resultate wat verkry is deur eindige element metodes (EEM) met eksperimentele resultate van 'n 12.2 m lang leunwa wat bestuur is op 'n grondpad te vergelyk. Leunwaens is baie belangrik vir die vervoer industrie. Verder is die behoefte om optimum en betroubare leunwaens in die industrie te vervaardig baie nodig. Die werk fokus daarop om die 2 resultate te vergelyk sodat die EEM gebruik kan word as ontwerp analiese en herontwerp gereedskapstuk en as 'n vervanging vir toetsing. Die leunwa was op 'n redelike rowwe pad teen verskillende snelhede nl. 70km/h, 50km/h en 40km/h met 'n 12 ton baksteen vrag gery. Die kragte by die suspensie van die leunwa en die vervorming by verskillende onderdele is gemeet met behulp van rekstrokies en ander data versamelings toerusting 'n Eindige element model van die leunwa is gemodelleer in "Nastran for Windows". Die sleepwa parameters in die eindige element model is verstel d.m.v krommepassing van die toets resultate. 'n Vergelyking van die 2 resultate is gebasseer op die gemiddelde van die absolute waardes en standaard afwykings, om die geldigheid van die eindige element model te kontroleer.

Thesis (MEng)--University of Stellenbosch, 2000. / ENGLISH ABSTRACT: The finite element technique was used to do an in-depth design evaluation and optimisation of a 15.45-metre refrigerated semi-trailer. Although the emphasis is placed on finite element modelling and its application on a heavy transport vehicle, the paper covers the whole design evaluation and redesign process. Special consideration is also given to the manufacturing process as to ensure that the data generated can be implemented in an effective manner. / AFRIKAANSE OPSOMMING: Eindige element spanrungs analises was gedoen op 'n 15.45-meter verkoelingsleunwa. Die doelwit was om die huidige ontwerp te evalueer en die ontwerp veral vanuit 'n koste en sterkte oogpunt te optimeer. Die fokus van hierdie tesis is die eindige element analises en ontwerpskommentaar hierop gebaseer. Die verhandeling hanteer egter die hele ontwerp en vervaardigingsproses sodat die data hierin versamel en verwerk, prakties uitgevoer kan word.

Radioactive waste repositories, designed in accordance with the current UK concept, would be required to provide containment for thousands of years beneath hundreds of metres of rock. The physical processes, both geological and other processes, that might lead to migration of radionuclides are slow in comparison to human timescales — it is impractical to make an experiment of the whole system and so these systems are typically investigated through the use of numerical models. Predictive models are based on combinations of: assumptions, mathematical formulations and parameter values derived from experimental observations. The Ventilation Experiment in the Opalinus Clay at Mont Terri, Switzerland, was designed to involve geological and other physical processes that would be active during the excavation and construction phases of a repository, and with consequences for the repository performance during the operational phase. The experiment consisted of a 10m long tunnel of 1:3m diameter through which air of known relative humidity was circulated in order to force drying and re-saturation through the tunnel wall. Two such cycles over four years have been observed via installed instrumentation. Several numerical models have been constructed of the ventilation experiment by different international teams under the decovalex project using different approaches for cross-validation. Through participation in this project, a 1D model using Richards’ Equation was developed that effectively reproduces the hydrodynamic, mechanical and conservative mass transport results. During the course of developing that model, many other domains, meshes, formulations and software versions were investigated. Now that the field scale Ventilation Experiment can be reproduced with numerical models, the findings (assumptions, formulations, parameter values, computational methods and software) would be transferable to other argillaceous formations to enable predictive modelling of similar scenarios and contribute to the safe disposal of nuclear waste and other problems involving similar geological processes. Work of this type fills the gap between laboratory scale experiments and regional scale modelling of geological systems. The gap is especially wide for low-permeability formations because the size and time-scale limitations effect the ability to make direct observations and measurements. Two particular problems were also addressed in this work: that of the use relative permeability functions and also the computational treatment of the physical interface between the tunnel domain and the rock domain. A sensitive component in many models of unsaturated flow through porous media and covering a wide variety of applications, including reservoir engineering, is the representation of permeability at an unsaturated point (kx) as a scaling of the saturated permeability (ksat) by introducing some function of the pressure head, or saturation as the relative permeability (krel) in the relation kx = ksatkrel. The choice of the particular function and its parameter values adds little to our understanding of the physical parameters. A solution is proposed to the second problem, of how to computationally represent, implement and manage the interface between two physical (i.e. spatial) domains. The scheme maps every part of the boundary of one domain onto the corresponding part of the boundary of the other domain, storing the state variables in shared memory and converting between physical components.

Thesis (MScEng)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: In this study, Ti6Al4V machining is modelled using finite element analysis of orthogonal machining. Orthogonal turning tests are conducted for the verification of FE models in terms of machining forces, temperatures, and chip geometry. Milling force predictions are made using the "unified" mechanics of cutting model which is applied to ball nose milling for this study. The model makes use of orthogonal cutting data, collected from the turning tests, to model milling forces. Model predictions are compared with test data from slot milling tests for verification. Finally a hybrid form of the "‘unified"’ model is presented in which orthogonal data, obtained from the FE simulations, is used to model ball nose milling operations. / AFRIKAANSE OPSOMMING: In hierdie studie word titaanmasjinering (Ti6Al4V) gemodelleer deur gebruik te maak van eindige element analise van ortogonale masjinering. Ortogonale draai toetse word uitgevoer om eindige element (FE) modelle te verifieer in terme van masjineringskragte, temperatuur en spaandergeometrie. Freeskragte word voorspel deur gebruik te maak van die "Unified Mechanics of Cutting" model wat toegepas word op ’n balneusfrees operasie in hierdie studie. Die model maak gebruik van ortogonale snydata, versamel gedurende snytoetse, om die freeskragte te modelleer. Die model word vervolgens vergelyk met die toetsdata afkomstig van die freestoetse vir verifikasie. Ten slotte word ’n hibriede weergawe van die model aangebied waarin ortogonale data verkry word van die FE simulasie om balneus freesoperasies te simuleer.

Dissertation (PhD)--University of Stellenbosch, 2002. / ENGLISH ABSTRACT: This document presents a Galerkin FE formulation for the full-wave, frequency domain, electromagnetic analysis of three dimensional structures relevant to microwave engineering, together with the investigation of two techniques to enhance the formulation's computational efficiency. The first technique considered is the fast multi pole method (FMM) and the second technique is adaptive refinement of the discretization, based on a posteriori error estimation. Thus, the motivation for the work presented in this document is to increase the computational efficiency of the FE formulation considered. The FE formulation considered is widely used within the microwave engineering, finite element community. Tetrahedral, rectilinear, curl-conforming, mixed- and full order, hierarchical vector elements are used. The formulation is extended to incorporate a cavity backed aperture employing the appropriate half-space Green function within a BI boundary condition, which represents a specific member of a large class of hybrid FE-BI formulations. The formulation is also extended to model coaxial ports via a Neumann boundary condition, using a priori knowledge of the dominant modal fields. Results are presented in support of the formulation and its extensions, including novel results on the coupling between microstrip patch antennas on a perforated substrate. The FMM is investigated first, with the purpose of optimizing the non-local BI component of the cavity FE-BI formulation, in light of its coupling with the differential equation based, sparse FEM. The FMM results in a partly sparse factorization of the BI contribution to the system matrix. Error control schemes for the FMM are thoroughly reviewed and an additional, novel scheme is empirically devised. The second technique investigated, which is more directly related to the FEM and larger in scope, is the use of a posteriori error estimation, in order to optimize the FE discretization through adaptive refinement. A overview of available a posteriori error estimation techniques in the general FE literature is given as well as a survey of available techniques that are specifically tailored to Maxwell's equations. Two known approaches within the applied mathematics literature are adapted to the FE formulation at hand, resulting in two novel, residual based error estimation procedures for this FE formulation - one explicit in nature and the other implicit. The two error estimators are then used to drive a single p adaptive analysis cycle of the FE formulation, experimentally demonstrating their effectiveness. A quasi-static condition is introduced and successfully used to enhance the adaptive algorithm's effectiveness, independently of the error estimation procedure employed. The novel error estimation schemes and adaptive results represent the main research contributions of this study. / AFRIKAANSE OPSOMMING: Hierdie dokument beskryf 'n Galerkin eindige element (EE) formulering vir die volgolf, frekwensiegebied, elektromagnetiese analise van driedimensionele strukture relevant vir mikrogolfingenieurwese, saam met die ondersoek van twee tegnieke om die numeriese effektiwiteit van die formulering te verbeter. Die eerste tegniek wat ondersoek word, is die vinnige multipooi metode (VMM) en die tweede is die aanpasbare verfyning van die EE diskretisering, gebaseer op a posteriori foutberaming. Dus, die motivering vir hierdie werk is om die numeriese effektiwiteit van die genoemde EE formulering te verbeter. Die bogenoemde EE formulering word algemeen gebruik deur die mikrogolfingenieurswese, eindige element-gemeenskap. Tetrahedriese, reglynige, curl-ondersteunende, hierargiese vektorelemente van gemengde- en volledige ordes word gebruik. Die formulering word uitgebrei om holtes in 'n oneindige grondvlak te kan hanteer, deur gebruik te maak van die toepaslike Green funksie binne 'n grensintegraal (GI) grensvoorwaarde, wat 'n spesifieke lid is van 'n groot klas, hibriede, EE-GI formulerings. Die formulering word ook uitgebrei om koaksiale poorte to modelleer via 'n Neumann grensvoorwaarde, deur die gebruik van a priori kennis van die koaksiale, dominante modus-velde. Resultate word gelewer om die formulering, saam met die uitbreidings daarvan, te ondersteun, insluitende oorspronklike resultate in verband met die koppeling tussen mikrostrook plakantennes op 'n geperforeerde substraat. Die VMM word eerste ondersoek, met die doelom die nie-lokale, GI komponent van die EEGI formulering vir holtes te optimeer, weens die koppeling daarvan met die yl, differensiaalvergelyking- gebaseerde, eindige element-metode. Die VMM lei tot 'n gedeeltelik-yl faktorisering van die GI bydrae tot die algehele matriksvergelyking. Skemas om die VMM fout te beheer word deeglik ondersoek en 'n addisionele, oorspronklike skema word empiries ontwikkel. Die tweede tegniek wat ondersoek word, wat meer direk verband hou met die eindige elementmetode, en van groter omvang is, is die gebruik van a posteriori foutberaming om die EE diskretisasie te optimeer deur middel van aanpasbare verfyning. 'n Oorsig van beskikbare, a posteriori foutberamingstegnieke in die algemene EE literatuur word gegee, asook 'n opname van beskikbare tegnieke wat spesifiek gerig is op Maxwell se vergelykings. Twee bekende benaderings binne die toegepaste wiskunde-literatuur word aangepas by die bogenoemde EE formulering, wat lei tot twee oorspronklike residu-gebaseerde foutberamingstegnieke vir hierdie formulering - een van 'n eksplisiete aard en die ander implisiet. Die twee foutberamingstegnieke word gebruik om 'n enkel, p-aanpasbare analisesiklus aan te dryf, wat die effektiwiteit van die foutberamingstegnieke eksperimenteel demonstreer. 'n Kwasi-statiese vereiste word beskryf en suksesvol gebruik om die aanpasbare algoritme se effektiwiteit te verhoog, onafhanklik van die foutberamingstegniek wat gebruik word. Die oorspronklike foutberamingstegnieke en aanpasbare algoritme-resultate verteenwoordig die hoof navorsingsbydraes van hierdie studie.

Thesis (MScEng (Civil Engineering))--University of Stellenbosch, 2005. / In the inverse finite element method (iFEM), given a finite element model of a structure and imperfect displacement measurements, the external loads acting on the structure can be assessed. The basic idea behind iFEM is the optimization of a quadratic cost function of the difference between the measured and estimated values, with a high cost corresponding to a high precision of the measurements. In the present research it is firstly shown how the iFEM theory was broadened to accommodate for strain measurements through the construction of cost matrices to express the cost associated with the estimation of the response. The main focus of the research falls however on the influence that the measurement set-up has on the quality of the iFEM estimates. Only a limited number of measurements may be available, therefore it is essential to plan the measurement set-up carefully to obtain the highest quality of estimates. The number of measurements and the precision required to obtain a realistic result from an iFEM analysis is also a factor which plays a role and varies for different types of measurements. A numerical method for systematic sensitivity study of the measurements set-up without involving the actual measurement data, is presented. Two examples consisting of structures with both displacement measurements and strain measurements being taken, are presented. It illustrates how the sensitivity study method can be used to plan a more effective measurement set-up.

Thesis (MScEng)--University of Stellenbosch, 2004. / ENGLISH ABSTRACT: Presented here is an Eulerian scheme for solving the unsteady pipe-flow equations. It is called the Characteristic Dissipative Petrov-Galerkin finite element algorithm. It is based on Hicks and Steffler's open-channel finite element algorithm [5]. The algorithm features a highly selective dissipative interface, which damps out spurious oscillations in the pressure field while leaving the rest of the field almost unaffected. The dissipative interface is obtained through upwinding of the test shape functions, which is controlled by the characteristic directions of the flow field at a node. The algorithm can be applied to variable grids, since the dissipative interface is locally controlled. The algorithm was applied to waterhammer problems, which included reservoir, deadend, valve and pump boundary conditions. Satisfactory results were obtained using a simple one-dimensional element with linear shape functions. / AFRIKAANSE OPSOMMING: 'n Euleriese skema word hier beskryf om die onbestendige pypvloei differensiaal vergelykings op te los. Dit word die Karakteristieke Dissiperende Petrov-Galerkin eindige element algoritme genoem. Die algoritme is gebaseer op Hicks en Steffler se oop-kanaal eindige element algoritme [5]. In hierdie algoritme word onrealistiese ossilasies in die drukveld selektief gedissipeer, sonder om die res van die veld te beinvloed. Die dissiperende koppelvlak word verkry deur stroomop weegfunksies, wat beheer word deur die karakteristieke rigtings in die vloeiveld, by 'n node. Die algoritme kan dus gebruik word op veranderbare roosters, omdat die dissiperende koppelvlak lokaal beheer word. Die algoritme was toegepas op waterslag probleme waarvan die grenskondisies reservoirs, entpunte, kleppe en pompe ingesluit het. Bevredigende resultate was verkry vir hierdie probleme, al was die geimplementeerde element een-dimensioneel met lineere vormfunksies.

Thesis (MScEng (Electrical and Electronic Engineering))--Stellenbosch University, 2007. / The finite element method is a very efficient numerical tool to solve geometrically complex problems in electromagnetics. Traditionally the method is applied to bounded domain problems, but it can also be forged to solve unbounded domain problems using one of various mesh termination schemes. A scalar finite element solution to a typical unbounded two-dimensional problem is presented and the need for a proper mesh termination scheme is motivated. Different such schemes, specifically absorbing boundary conditions, the finite element boundary integral method and infinite elements, are formulated and implemented. These schemes are directly compared using different criteria, especially solution accuracy and computational efficiency. A vector finite element solution in three dimensions is also discussed and a new type of infinite element compatible with tetrahedral vector finite elements is presented. The performance of this infinite element is compared to that of a first order absorbing boundary condition.

Thesis (MScEng (Electrical and Electronic Engineering))--Stellenbosch University, 2008. / The nite element method (FEM) is a powerful tool for the computational analysis of a wide range of electromagnetic problems. As the complexity of the problems is increased so are the demands in terms of the computational resources required to obtain a su ciently accurate solution. In an attempt to obtain a desired accuracy at a lower computational cost adaptive and higher order methods are often employed. These methods generally entail re ning the solution only in the areas where greater complexity is required, thus decreasing the total computational demand. The adaptive nite element method is implemented and used to analyse the transverse electric cuto eigenmodes of 2D waveguiding structures. The higher order hierarchical vector basis functions that form part of this implementation are automatically generated to very high orders, with the results presented in excellent agreement to analytical ones where applicable. Accuracy to the order of numeric precision is attained. Using these adaptive methods, it is also possible to achieve improved cost e ciency of the error metrics considered with respect to storage requirements and computational cost.

published_or_final_version / Orthopaedic Surgery / Master / Master of Philosophy