Please read the abstract in the section 00front of this document / Thesis (PhD (Applied Mathematics))--University of Pretoria, 2000. / Mathematics and Applied Mathematics / unrestricted

The long bones grow by the process of endochondral ossification, which occurs at the growth plate. This process is regulated by biological factors and mechanical factors. The biological factors which contribute to endochondral ossification process are genes, hormones, nutrients etc. The mechanical factor is the load acting on the bone. The major forces on the bone are due to joint contact load and muscle forces, which induce stresses in the bone. Carter and Wong proposed in a theory that cyclic or intermittent octahedral shear stress promotes the bone growth and cyclic or intermittent hydrostatic compressive stress inhibits the bone growth. Previously this theory has been used to predict the morphological development of long bones, but with studies using simplified femur and growth plate models. Furthermore, the Carter and Wong theory has a limitation that it does not intrinsically incorporate the resulting growth direction.In the first study, the importance of a subject-specific growth plate over a simplified growth plate has been studied, and growth has been simulated using two different growth direction models: Femoral neck shaft deformation direction and minimum shear stress direction. This study favors the minimum shear stress growth direction model, as it is less sensitive to applied boundary condition than the femoral neck shaft deformation direction model.The second study aims to understand how different muscle groups affect the bone growth tendency. Subject-specific femur and growth plate models of able-bodied children were used. The muscle forces and associated hip contact force from specific muscle groups were applied, and neck shaft angle and femoral anteversion growth tendencies were predicted. This study indicated a tendency for reduction of neck shaft angle and femoral anteversion. Hip abductor muscle forces contribute most, and hip adductor muscle forces least, to bone growth rate.Accurate prediction of bone growth tendency and knowledge of the influence of different muscle groups on bone growth tendency may help in better treatment planning for children at risk of developing bone deformity problems. / <p>QC 20151201</p>

These latest years, the green energy is highlighted and new technologies appeared. It is the case for wind turbines. The aim of latest developments has been to increase the power output. The use of new material enables the design of wind turbine with an impressive height, more and more flexible, inducing significant dynamic forces. However, several problems have been encountered on the connection between the foundation and the tower, which threaten the entire integrity of the structure. The initial lifetime could be impacted. The first aims of the master thesis are to understand the dynamic behavior of a wind turbine, determine the resultant forces at the foundation in order to explain the issues encountered at the foundation level on site, and compare these results with the resultant forces given by the wind turbine manufacturer. Indeed, the constructor transmits to the civil engineer one or more resultants forces without justifications in order to design the foundation. These loads are often issued from extreme load case. The analysis of the serviceability limit state is not well realized. It is this resultant force in operation which must be determined in this master thesis. After having presented the history of wind turbines, the different parts and the model use for the wind; the blade element model is used to calculate the forces of the wind on the rotor. These forces calculated from the theory used are eventually compared with the provider data. The turbulence component of the wind on the tower is evaluated by a spectral method and a fluid structure interaction with the software Abaqus. The inertial effects of the tower are calculated in order to give an order of magnitude of the resultant load on the foundations. This knowledge enables to analyze the connection in serviceability limit state which is another aim of the study. An analysis of the connection is done in order to get an idea of the risks. In particular, the punching resistance and the stability of the structure are verified.

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The objective of this research is to simulate crashworthiness for Out-of-Position (OOP) occupants incorporating a 50th percentile Hybrid III dummy and a side curtain airbag in a 1996 Dodge Neon under side impact scenarios. Two different methods of airbag techniques namely, the uniform pressure (UP) and the smooth particle hydrodynamics (SPH) were compared. This study revealed that there is minimal difference between UP and SPH methods when the dummy’s head impacts the airbag after it has fully inflated. However, when the dummy’s head impacts the airbag during the inflation process, the modeling of the airbag gas dynamics becomes critical in predicting the dummy response. The SPH method, which models the gas dynamics in the airbag, causes the airbag to unroll more uniformly. Depending on the timing of the dummy’s head impact with the airbag these differences in inflation can produce significant differences in dummy head accelerations.

Advanced high strength steels (AHSSs) are considered to have a promising future due to the outstanding properties compared with the conventional steel and have been widely adopted as the base materials for the automotive components. Some of the challenges preventing the extensive applications of AHSSs are due the solidification defects, i.e. hot tearing and segregation. In this thesis, a 3D mesoscale and multi-physics model is developed and validated to directly investigate solidification defects for semi-solid steel with dendritic morphology associated with the peritectic transformation. Similar to the prior models [1,2], the current model explicitly considers the solidification behavior of each grain prior to assembling, which allows for the mesoscale simulation within a semisolid containing thousands of grains. Six sub-models are incorporated: (i) microstructure generation model is used to create the fully solidified microstructure of equiaxed grains based on a Voronoi tessellation; (ii) a dendritic solidification module based on an average volume approach is developed for predicting the solidification behavior of a random set of grains, considering the diffusion in different phases along with peritectic transformation. The progressive coalescence to form a solid cluster is predicted by incorporating an interfacial energy determination model; (iii) a fluid flow module is developed for the prediction of both intra-dendritic flow and extra-dendritic flow within the dendritic network induced by solidification shrinkage and deformation; (iv) a semisolid deformation model is used and extended to simulate the semi-solid mechanical behavior of steel using a discrete element method. The solid grains are modeled using a constitutive law and implemented via Abaqus commercial software; (v) a coupled cracking model incorporated with a failure criterion is used and extended to predict the crack formation and propagation in semi-solid steel. This comprehensive model consists of models (i-iv) and considers the interaction between the deformation within the solid phase and pressure drop in the liquid phase; (vi) a one-way coupled solute transportation module is also developed and used to simulate the solute redistribution due to fluid flow and diffusion within the liquid channels assuming the solid grains are fixed. The movement of the solute-enriched liquid in the solute transport model is induced by solidification shrinkage and deformation. The new 3D mesoscale model is then applied to correlate the semisolid behavior during solidification to different physical and process parameters. The results from the dendritic solidification model show the evolution in semi-solid microstructure and consequently liquid film migration. The model is able to predict the solidification of equiaxed grains with either globular and dendritic structure having experiencing primary solidification and the peritectic transformation. The coalescence phenomenon between grains is considered at the end of solidification using Bulatov’s approach[24] for estimating interfacial energy. It is seen that only 0.9% of the grains are attractive based on their orientations within a specific domain, significantly depressing final-stage solidification. The dendritic fluid flow model quantitatively captures both semi-solid morphology and the fluid flow behavior, and provides an alternative to the convectional experiment for the prediction of permeability by using the given surface area concentration. Comparison of the numerical and experimental permeabilities shows a good agreement (within ± 5%) for either extra-dendrite or intra-dendritic flow, and deviation from the conventional Carman-Kozeny equations using simplified Dendritic Sv or Globular Sv are explained in detail. The results quantitatively demonstrate the effect of grain size and microstructure morphology during solidification on the permeability prediction. The localization of liquid feeding under the pressure gradient is also reproduced. Additionally, the fluid flow due to shrinkage and deformation for non-peritectic and peritectic steel grades with dendritic morphology during solidification was captured for the first time. The cracking model allows for the prediction of hot tearing initiation and the progressive propagation during a tensile test deformation and the results are compared with the experimental results conducted by Seol et al.[3]at different solid fractions. Parametric studies of coalescence criteria and surface tension on the constitutive behavior of the semisolid are discussed and the deformation behavior of alloys with different carbon contents under a feedable mushy zone is investigated. Finally, the solute transport model has been applied to the continuous casting process of steel for the investigation of centreline segregation, and results indicate that the grain size has a great impact on the solute distribution and solute partitioning combined with intra-dendritic fluid flow leads eventually to liquid channels enriched with solute. The predicted composition in these discrete liquid channels shows a great match with the experimental measured profile obtained via the microscopic X-Ray fluorescence (MXRF). / Thesis / Doctor of Philosophy (PhD)

Sheet trimming is an important forming operation in stamping industry. However, trimming of automotive magnesium sheet materials is not well understood. The objective of present study was to investigate the trimming behavior of AZ31 and ZEK100 automotive magnesium sheet materials using a laboratory-based experimental set-up and complementary finite element (FE) simulations of the lab-based experiments. The effects of the trimming process parameters that included tool setup configuration, punch speed, clearance, sheet thickness and sheet orientation (rolling and transverse directions) on the quality of trimmed edge were analyzed. Experimental results indicated that the trimmed edge quality depended strongly on the trimming conditions. The optimal trimming parameters for AZ31 and ZEK100 sheets were experimentally obtained. Interrupted trimming experiments were conducted to examine crack initiation and development, the mechanism of fracture, and the generation of the fracture profile of the trimmed edges. The R-value as a measure of material anisotropy and fracture strain of both materials were measured using uniaxial tension and plane strain tests and incorporated in the FE model. General purpose Finite Element software ABAQUS/Explicit was employed to simulate the trimming process where five different fracture criteria and element deletion method were used to predict profile of trimmed edge and the fracture initiation and development during the trimming process. Good general agreement was observed between experiments and FE simulations. However, some discrepancies were also observed. These are presented and discussed in the thesis. / Thesis / Master of Applied Science (MASc)

The research presented considers the effect of varying shear web spacing and mass for two blades; a61.5m 5MW blade (based on the NREL5MW reference turbine) and a 100m 13.2MW blade (based onthe SNL100 blade). The variations are analyzed using HAWC2 aeroelastic simulations and Abaqus/CAE finite element simulations;and the effect of the variations is measured by comparing natural frequencies, loads, tip deflection,equivalent fatigue loads, material strength and buckling. Additionally, a tool was developed to facilitatethe modeling of blade variations. Varying the web spacing showed that the web placement is able to reduce loads, tip deflection, and equivalentfatigue loads. Mass variations demonstrated that reducing the mass will decrease edge-wise loadingand equivalent fatigue loads. The increase in blade size has shown that edge-wise fatigue loads becomelarger than the flap-wise fatigue loads for the larger blade.

Thermoplastic welding utilizes a fiber laser to join samples that are clamped together. Laser energy is transferred through the natural sample to the interface with the opaque sample where heat energy creates a weld through conduction and radiation heat transfer modes. The overall goal of this research is to understand the effect of heat source loading on PA6 and PA66 thermoplastic materials from laser through transmission welding that is used to join natural and opaque materials. The welding process is studied through a combination of finite element simulation, experimentation, and design of experiment modeling. The results of temperature profile and melt properties of the material are compared with weld strength and quality to provide welds used in a range of applications from the automotive industry to hermetically sealed medical components. Research of heat source models is used to determine the best representation of the laser energy for laser through transmission welding of thermoplastic materials. The comprehensive objective is to find the best fit of laser parameters to PA6 and PA66 material samples to predict weld quality in the through transmission laser welding process. Results of the research include temperature profile behavior for surface exposure and single pass weld tests, and thermal conductivity verification of PA6 and PA66 through experimentation. Finite element simulations of the experiments provide analysis of temperature dependent properties and time dependent analysis of the laser heat source loading. The Gaussian surface model with penetration variable is determined to be the best representation of the laser through transmission welding of thermoplastic material after completing heat source literature review and analysis. Finally, surface response methods were used to find the most influential parameters in laser through transmission welding, which were the number of laser passes and laser power for PA6 and PA66 materials.

This thesis presents an engineering approach to the modeling and analysis of custom foot orthotics. Although orthotics are widely used and accepted as devices for the prevention of and recovery from injuries, the design process continues to be based on empirical means. There have been many clinical studies investigating the various effects that the orthotics can have on the kinematics and kinetics of human locomotion. The results from these studies are not always consistent, primarily due to subject variability and experimental nature of the design. Alternatively, a better understanding of the therapeutic effects of custom foot orthotics, as well as designing for optimal performance, can be achieved through simulation-based engineering modeling and analysis studies. Such an approach will pave the way to clarify some of the ambiguous findings found in the clinical studies-based literature. Towards this goal, this research presents a methodical process for the replication of the orthotics’ complex three-dimensional geometry and for the construction of finite element analysis models using estimated nonlinear material properties. As part of this research, laser scanning techniques are used to capture the objects’ details and geometry through generation of point cloud surface images by taking multiple scans from all angles. Material testing and Mooney-Rivlin equations were used to construct the hyperelastic nonlinear material properties. Using the mid-stance phase of gait for loading conditions, the ANSYS finite element package was utilized to run analyses on three different load classifications and the corresponding maximum stresses and deflection results were generated. The results indicate that the simulated models can augment and validate the use of empirical tables for designing custom foot orthotics. They can also provide the basis for the optimal design thicknesses of custom foot orthotics based on an end-users’ weight and activities. From a practical perspective, they can also be useful in further exploring different orthotics, loading conditions, material properties, as well as the effectiveness of orthotics for different foot and lower extremity deformities.