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Please read the abstract in the section 00front of this document / Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2007. / Mechanical and Aeronautical Engineering / unrestricted

Friction stir welding is a relatively new joining process. The heat transfer involved is crucial in determining the quality of the weld. Experimenrtal data, though important, does not provide enough information about the heat transfer process and experiments can be costly and time consuming. A numerical model, using the finite element method, was developed to stimulate the heat transfer in the workpiece in which the heat generation due to friction and plastic deformation was modelled as a surface heat flux boundary condition. This model was applied to Aluminium AL6082-T6 and Titanium Ti6A1-4V for different welding condiitions. Results were validated with experimental results. The model was shown to give better predictions of the maximum temperatures at locations in the workpiece than the overall temperature trend. A parametric study was also performed on the Aluminium model in order o predict temperature fields of the workpiece for welding conditions that were additional to those undertaken experimentally. It was found that rotational speed had a larger effect on the change in temperature than the feed rate. From the parametric study it was also clear that lower rotational speeds (300 to 660 rpm) had a greater effect on the change in temperature than the higher rotational speeds (840 to 1200 rpm). It was concluded that the model was well suited for the estimation of temperatures involved in the FSw of Aluminium Al6082-T6 but was not as accurate when applied to the FSW of Titanium.

In this thesis, the finite element method (FEM) is applied to the calculation of frequency-dependent series impedances and shunt capacitances of underground power cables. The principal equations describing the quasi-magnetic fields and static electric fields are solved with FEM based on the Galerkin technique. The Js method and the loss-energy method are derived to calculate the impedances of a multiconductor system from its field solution, and the energy method and the surface charge method are derived to calculate the capacitances. With a single-core (SC) coaxial cable, the suitability of quadratic isoparametric elements and high-order simplex elements are studied, and a suitable division scheme is suggested for the auto-mesh program. The conventional FEM with a field truncation boundary is applied to the impedance calculation of buried SC cables. Suitable locations for the field truncation boundary and division schemes in the earth are studied. The results show that rb ≥ 12[symbol omitted] is required to obtain accurate impedances of shallowly buried cables with the conventional FEM. This requires a large solution region in the earth at low frequencies. A new technique based on the perturbation concept is proposed to reduce the solution region in the earth. Comparisons between the results from the conventional FEM and from the proposed technique with a significantly reduced solution region in the earth show good agreement. In the case studies, the FEM is applied to the parameter calculation of multiphase SC cables, PT cables, sector-shaped cables, and stranded conductors. The numerical results are compared with those from analytical formulas. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

The Experimental and Finite Element Investigation of Added Mass Effects on Ship Structures comprised three phases : 1) investigation of the fluid modelling capabilities of the Finite Element Program VAST, 2) experimental investigation to determine the effect of the fluid on the lowest natural frequencies and mode shapes of a ship model, and 3) comparison of these experimental results with numerical results obtained from VAST. The fluid modelling capabilities of VAST were compared with experimental results for submerged vibrating plates, and the effect of fluid element type and mesh discretization was considered. In general, VAST was able to accurately predict the frequency changes caused by the presence of the fluid. Experimental work both in air and water was performed on a ship model. The lowest four modes of vertical, horizontal, and torsional vibration were identified, and the effect of draught on the frequencies and mode shapes was recorded. When the experimentally obtained frequencies and mode shapes for the ship model were compared with the numerical predictions of VAST, good agreement was found in both air and water tests for the vertical vibration modes. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

The finite element method is applied in conjunction with Reissner's mixed variational principle to the investigation of two-dimensional elastic contact problems. The versatility of the mixed principle in incorporating boundary conditions pertinent to the contact problem is demonstrated. Contact conditions are modelled by appropriate manipulations of boundary variables. In cases where the contact region is independent of the applied loading, an iterative procedure is used to establish the sliding and adhering portions in the contact region. Numerical results for displacements and stresses are independently confirmed by the finite element analysis in conjunction with the minimum potential energy principle. In cases where the contact region is a function of the applied loading, or progressive contact, an incremental formulation is employed to describe the discretized contact stages. In the example of a frictionless contact between a long cylinder and a rigid base, good confirmation is obtained from Hertz's analytical solution. Criteria for taking one contact stage to another are also outlined for frictional progressive contact. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

South Africa is a water scarce country where a large number of people still are not provided with adequate water. This project will help to manage water resources in a sustainable manner that will benefit the country as a whole. This study concentrated on the behaviour of pipe materials with leak openings under different pressure conditions. The stress distribution throughout a pipe is known due to the pressures within the pipe i.e. the longitudinal and circumferential stresses as well as the working pressure of the pipe, however when a leak opening such as a hole or crack appears in the pipe the stress distribution around these openings change. It is the effect of this stress distribution that this study addressed. The effect of stresses around these leak openings may provide some knowledge as to how and when the pipes will fail completely as well as help in explaining the leakage exponents within pipes. Using the method of Finite Element Analysis (FEA) the project aimed to find the relationship between the pressure in the pipe and the behaviour of the leak openings for different leak types. The different leak openings investigated were: a circular hole, a longitudinal crack and a circumferential crack. This study used finite element analysis to understand what happens to a pipe when pressure is applied within the pipe and the pipe has a leak opening e.g. a small hole, a longitudinal crack or a circumferential crack in it. The materials studied were uPVC, steel, cast iron and fibre-cement. The main conclusions drawn from this study were that when a pipe has a circular hole in it the leakage exponent does not differ from the theoretical value of 0.5. With the longitudinal cracks it was found that regardless of whether there are longitudinal stresses in the pipe or not the leakage exponent is the same: and these exponents vary significantly from the theoretical value of 0.5 and can be in the order of 0.87, 0.82, 0.75, 0.55 for a 60 mm long crack in an uPVC, steel, cast iron and fibre-cement pipe respectively. With the circumferential cracks however, there were significant differences in exponents due to the longitudinal and lack of longitudinal stress. For the case when the pipe has the longitudinal stresses the exponents were significantly larger than 0.5. The exponents were in the order of 1.15, 1.02, 0.95, and 0.64 for a 150 mm long crack of uPVC, steel, cast iron and fibre-cement respectively. If there is no longitudinal stress then the exponents were smaller than 0.5 and tended to close the crack along the circumference. The exponents were 0.45, 0.47, 0.46, and 0.49 for a 150 mm crack of uPVC, steel, cast iron and fibre-cement respectively. / Prof. J.E. van Zyl

In the classical design method for gravity dams, the designs are conducted in the linear elastic isotropic material domain. For many decades the so-called ‘classical method’ (or conventional method) was used to design gravity dams. This method is based on the Bernoulli shallow beam theory. Despite much criticism expressed by academics regarding the basis of the theory, dam design engineers are still using the classical method to design gravity dams. Currently, in most dam building countries the various codes of practice are standardised and based on this method, and engineers have confidence in these codes. This state of affairs will probably continue until structural engineers come up with a viable alternative for designing gravity dams more precisely. The perception of increased risk is always a critical aspect to overcome when introducing an alternative design method, especially when the established, well-known methodology has proved to be safe. However, when so-called ‘back analyses’ are performed on existing dams, it is not so straightforward to assess the safety margin of these structures. Material properties and their yielding or failure characteristics are now becoming important in evaluating these structures accurately in the non-linear domain. With the growing popularity of roller compacted concrete as a dam building material, the attractiveness of gravity dams has also increased and the author is of the opinion that the finite element method could be utilised more efficiently to optimise gravity dams. But, as with any new or alternative design method, the parameters and means of evaluation should be developed to establish a workable and reliable technique. The objective of this dissertation is to develop a practical methodology for the non-linear analysis of gravity dams by means of the non-linear finite element method. A further aspect of this dissertation is the inclusion of a broad guideline on the application of the latest dam design standards used in South Africa for both the classical and finite element methods. In order to gain a better understanding of the basic design criteria, a literature survey was conducted on the evolution of dams and the various theories developed in the past to design and optimise gravity dams. The literature survey included the examination of gravity dam safety criteria and some available statistics on dam failures. The International Committee on Large Dams (ICOLD) has interesting statistics on dam failures and their causes. A few typical dam failures are presented to illustrate what can go wrong. During this literature research, a thorough study was done on the non-linear material theory, with special reference to the Mohr-Coulomb and Drucker Prager material models. The findings of the study are used to illustrate how the non-linear material models are incorporated into the finite element method and in what manner the different material parameters have an influence on the accuracy of the results. As already mentioned, currently the classical method is still a recognised design standard and for this reason a summary is presented of the South African Department of Water Affairs and Forestry’s practice for designing gravity dams. This includes the latest concepts on load combinations and factors of safety for these load conditions. This summary of current practice is used as a stepping stone for the proposed load combinations that could be used for the finite element method as these are not always compatible. However, this dissertation does not deal with the full spectrum of load combinations and the scope is limited to hydrostatic loads. Although the finite element method is a very powerful structural engineering tool, it has some serious potential deficiencies when used for dam design. The most serious problem concerns the singularities and mesh density, which develop high stress peaks at the heel of the dam wall. This problem is illustrated and some practical finite element examples are given. Some solutions for addressing this problem are also presented. It is concluded that an effective method for overcoming the singularity problem is to use the non-linear material yielding model. In order to calibrate the non-linear Drucker Prager model, several finite element benchmarks were conducted, based on work done by other researchers in the fracture mechanics field. Although the theory of the Drucker Prager model is not based on fracture mechanics principles, this model simulates the failure of the concrete material very well. To demonstrate this, various benchmarks were conducted, such as a pure tension specimen, a beam in pure bending, a beam combined with bending and shear, the flow models of Chen (1982), a model of a gravity dam and, finally, a full-size gravity dam. The next step in the study was to calibrate the Drucker Prager model with the concrete material properties used in existing dams of different construction methods and ages. The material strength of the concrete was statistically analysed and the average strength was calculated. The important ratio of tensile strength to compression strength (ƒt/ƒc) was also examined and the findings are presented. This ratio is important to get accurate results from the Drucker Prager model. The normal input parameters for the Drucker Prager model are the internal friction angle of the material (φ) and the cohesion (c). Scrutiny of the work done by Chen (1982) helped to find a useful solution to obtaining the parameters for the non-linear finite element method without determining the ö and c values, but by using the material tensile and compression strengths instead. The formulation is demonstrated in the chapter on theory. To illustrate the usefulness of the non-linear yielding model a few case studies were conducted. A hypothetical triangular gravity dam structure was analysed because it was widely used in other literature studies and a useful comparison could be made. Then, a case study of an 80-year-old concrete gravity dam was performed. The uniqueness of this dam lies in the fact that it was designed before the theory of underdrainage was used in South Africa and the dam has a characteristic shape due to its relatively steep downstream slopes compared with today’s standards. A study of material strength sensitivity was also done on this dam to evaluate its stability under severe load conditions. The last case study presented is on a recently designed 75-m-high roller compacted concrete gravity dam, optimised primarily by the classical method. The non-linear Drucker Prager yield model was used to evaluate this structure, with the actual material strengths taken from the laboratory design mix results. Although the finite element method was used during the design stage of this dam, it was used mainly to check the results of the classical method. The finite element method was also used to do studies on this dam where the classical method could not be used, such as studies of temperature and earthquake load conditions (not included in this research). The factor of safety against sliding was also determined using the results obtained from the finite element method and compared with the results obtained from the classical method. This case study gives an approximate comparison between the classical method and the finite element method. Finally, a methodology is proposed for analysing a gravity dam. Procedural steps are given to describe the methodology. With regard to the future, the advantage of the non-linear finite element method is that it can easily be extended to contemporary 3-D analysis, still using the same concept. Many dams can only be accurately evaluated by a full 3-D analysis. There is a modern tendency to design gravity dams in 3-D as well so as to evaluate their stability against sliding in the longitudinal direction. The non-linear 3-D finite element method is also used for arch dams, for which very few alternative numerical analysis methods are available. Moreover, the non-linear finite element method can be extended to earth and rock-fill embankments. / Dissertation (MEng)--University of Pretoria, 2009. / Civil Engineering / unrestricted

This diploma thesis is focused on combination of experimental study and computer modelling of diffusion processes in gel phases. The aim of experimental part of the diploma thesis was to test and optimize the setting of the diffusion coefficient in gel medium by using the method of horizontal diffusion cells, commonly used for study of diffusion processes through membranes. Specific description of experiments was to determinate the impact of presence of reactive component in inert hydro-gel carrier on final value of diffusion coefficient of low-molecular model diffusion probe. The defined dependencies were subsequently combined with computer simulation of diffusion process in a properly designed model in order to determinate the experimentally unavailable system parameters. The stated combination of both approaches was proved to be an appropriate instrument for studying of hydro-gels with a wide potential especially in the field of preparation of hydro-gel carriers with controlled release of active substances.

The user programmable features (UPF) of the finite element code ANSYS® are used to generate a customized ANSYS-executable including a more general creep behaviour of materials and a damage module. The numerical approach for the creep behaviour is not restricted to a single creep law (e.g. strain hardening model) with parameters evaluated from a limited stress and temperature range. Instead of this strain rate - strain relations can be read from external creep data files for different temperature and stress levels. The damage module accumulates a damage measure based on the creep strain increment and plastic strain increment of the load step and the current fracture strains for creep and plasticity (depending on temperature and stress level). If the damage measure of an element exceeds a critical value this element is deactivated. Examples are given for illustration and verification of the new program modules.