### Browsing by Author "Martin, JB"

Now showing 1 - 20 of 21

###### Results Per Page

###### Sort Options

- ItemOpen AccessAnalysis of the dynamic behaviour of the hangingwall beam during a seismic event(1992) Daehnke, A; Martin, JBIn a deep-level gold mine planes of weakness oriented parallel to the reef allow the hangingwall to separate from adjacent rock strata. The hangingwall then acts as a separate beam supporting only its selfweight. Mining-induced near vertical shear fractures divide the hangingwall beam into distinct blocks of relatively intact material. The objective of this study is to investigate the response of the isolated hangingwall beam during a seismic event. The study is particularly concerned with the global, resonant behaviour of the hangingwall and local shear or crushing failure of the rock at the shear fractures is not considered. A finite element program is developed to compute the hangingwall response during seismicity. The response is normalised, thus permitting the response spectrum method to describe maximum hangingwall motions during a seismic event at various beam lengths. By comparing the response spectrum describing a single-degree-of-freedom (SDOF) system with the spectrum of the hangingwall, it is evident that, although the hangingwall response spectrum is shifted to a higher frequency and velocity domain, the shapes of the two spectra are essentially the same. The frequency and velocity shift is calculated for 15 seismic events and empirical rules are developed to quantify the spectral shift for a wide range of event magnitudes. Unlike the spectrum describing hangingwall motions, the construction of a SDOF response spectrum is computationally cheap and is standard practice in earthquake engineering. By applying the empirical rules the seismologist can extrapolate the SDOF spectrum to estimate maximum hangingwall motions due to a seismic event and critical beam lengths which are prone to resonance. The effect on the response of the hangingwall supported by backfill consisting of dewatered and cemented tailings is evaluated. It is shown that a fill-to-face lag of less than 5m reduces hangingwall motions considerably. Further, at small strains the stiffer cemented tailings provide superior support than that offered by comparatively soft dewatered tailings. A chart is presented which correlates event magnitudes to critical beam lengths prone to resonance.
- ItemOpen AccessAn analytical model for the seismic analysis of reinforced concrete frame structures(1988) Mercer, Colin Douglas; Martin, JBThe thesis is concerned with developing an analytical model to describe the cyclic behaviour of reinforced concrete members. The mechanisms which are important in the behaviour of members dominated by flexural deformations are identified. They include bar-slippage due to deterioration of the bond between the steel and concrete, the crack opening and closing criterion, and the cyclic response of steel and concrete. All these mechanisms are incorporated in an analytical model based on a layered beam approach. The model is developed for a member in double curvature bending and consists of two inelastic zones on either side of a central elastic zone. The bar-slippage which occurs in the beam-column joint is included at the ends of the beam model. A linear bending moment distribution is assumed along the beam. The moment-curvature relationship is calculated in the inelastic zones; the curvature is then integrated along the inelastic zone to determine the displacements. Damage measures with an objective of predicting the onset of failure are also proposed. The implementation of the model into a frame analysis computer program is discussed. Special attention is devoted to the solution strategies and numerical algorithms employed in the computer program. The model is shown to perform satisfactorily when compared to experimental results. A simplified analytical model which approximates the concrete with only two layers is also presented. The simplified model is shown to predict the response as competently as a model with far more concrete layers; however, the computational time for the simplified model is significantly less.
- ItemOpen AccessAn expert system utility prototype for the evaluation of environmental impacts of civil engineering projects(1994) Mercer, K G; Martin, JB; MacGregor, KenThe idea of this thesis is to create a prototype primary environmental impact assessment computer program for use by engineers in the planning of civil engineering projects. The idea is that this system will be used early in the planning phase of projects, to identify potential negative environmental impacts and there by iteratively modify proposals before further work on them is undertaken. The result would be a saving in time and money to clients by minimising abortive work. The problem is highly complex in that there are almost limitless combinations of environmental characteristics available for selection for the evaluation of a project proposal. Each characteristic in turn, is able to assume a varying level of importance. The structure of the system developed to solve this problem uses a combination of an expert system shell and conventional computer programs. The trend of modern environmental impact assessment methods is towards qualitative methods of assessment. As a result, the expert system shell SYNAPSE was chosen to provide a decision making facility for each environmental characteristic using heuristic techniques. Due to certain limitations of SYNAPSE a number of computer programs were developed to enable other supporting capabilities to be available to users. These programs were written in the Turbo Pascal language together with Turbo Vision, an object-orientated application framework for providing features such as windowing and event-driven regimens.
- ItemOpen AccessFinite element algorithms for the static and dynamic analysis of time-dependent and time-independent plastic bodies(1994) Kaunda, Modify Andrew Elton; Martin, JBContinuum and finite element formulations of the static and dynamic initial-boundary value evolution (elastoplastic) problems are considered in terms of both the classical and internal variable frameworks. The latter framework is employed to develop algorithms in the form of convex mathematical programming and Newton-Raphson schemes. This latter scheme is shown to be linked to the former in the sense that it expresses the conditions under which the convex non-linear function can be minimised. A Taylor series expansion in time and space is extensively employed to derive integration schemes which include the generalised trapezoidal rule and a generalised Newton-Raphson scheme. This approach provides theoretical foundations for the generalised trapezoidal rule and the generalised Newton-Raphson scheme that have some geometrical insights as well as an interpretation in terms of finite differences and calculus. Conventionally, one way of interpreting the generalised trapezoidal rule is that it uses a weighted average of values (such as velocity or acceleration) at the two ends of the time interval. In this dissertation, the generalised trapezoidal scheme is shown to be a special case of the forward-backward difference scheme for solving first order differential equations.
- ItemOpen AccessFormulations for incremental elastic-plastic analysis and the consolidation of porous media(1987) Bird, Wyndham Wadham; Martin, JBThe formulation and solution of the problem of an elastic-plastic body subject to successive increments of loading is a fundamental problem in plasticity. A variety of powerful iterative techniques are available for the solution of the problem, mostly based on Newton-Raphson methods using an explicit scheme for the integration of the constitutive relations. The procedures in current use can be criticised in that they are essentially heuristic, and they are not fully linked to the governing mechanical principles of the incremental plasticity problem. Recent work aimed at the improvement of the accuracy and stability of the numerical algorithms in plasticity explores the fundamental relationship between the nature of the forward integration algorithm and the mechanical principles of the problem. In this thesis we attempt to advance this understanding. Through the use of an internal variable formulation of the problem, we are able to explore links between a consistent mathematical programming formulation of the incremental problem in plasticity and the conventional Newton-Raphson iterative solution procedures.
- ItemOpen AccessAn incremental, non-linear displacement method for the elastic analysis of space trusses and plane frames(1975) Dittmer, Colin Thomas; Martin, JBAn incremental displacement method which takes account of finite deflections is developed for the elastic non-linear analysis of space trusses. In the incremental loading procedure the elastic critical load of a structure is determined by establishing the load at which the determinant of the stiffness matrix passes through zero. Chord shortening due to bowing of truss compression members which have an initial imperfection in straightness is included in the analysis by modifying the member axial stiffness term. Numerical examples of truss analyses are presented and comparisons made with published results. An incremental non-linear displacement method is then developed for plane frame analysis taking account of finite deflections and the effect of axial force on flexural stiffness, but ignoring member chord shortening due to flexure. Numerical examples of plane frame analyses are presented and comparisons made with published results.
- ItemOpen AccessAn investigation into the material behaviour of reinforced concrete beams(1988) Samaai, Mogamat Faldi; Martin, JBAn investigation into the material behaviour of reinforced concrete beams is presented. This investigation is divided into two parts. First, the experimental load-deflection tests on eleven under-reinforced two-span- and four slightly over-reinforced simply-supported beams are presented. The finite element simulation of these beams using the program, NLFRAM is then presented. This is followed by a material parameter study. In this study, the sensitivity and numerical efficiency of the material models in NLFRAM is assessed. This is done by systematically varying the parameters in the material models and comparing the load-deflection results. The load-deflection results from these examples are compared with the experimental results. In this way, the accuracy of NLFRAM in simulating practical structures is examined. The results of these comparisons indicate that with the simple material models used in NLFRAM, numerical results which are cost effective and in good agreement with the experimental observations may be obtained
- ItemOpen AccessAn investigation into the performance and problems of first-year engineering students at the University of Cape Town(1992) Jawitz, Jeff; Martin, JB; Cowan, BillThe first- and second-year results of the 1989 engineering student intake were analysed and revealed that matriculants from Black Education Departments performed significantly worse in the first year than those from White Education Departments. Matric point scores were found to be good predictors for White Education Department matriculants, but less so for Black Education Department matriculants, with matric Physical Science a better predictor than matric Maths, for both first- and second- year courses. Using interviews and a survey of students, a set of academic and non-academic problems experienced by first-year engineering students were identified with black students found to have experienced a particular set of problems to a greater degree than white students. The data produced a portrait of the interaction between first-year engineering students and the academic and social systems of the university. The dominant feature that emerged was one of distance between the individual students and elements of the university environment, including staff, fellow students and the academic material. Factors from the student's personal and educational background that appeared to accentuate this experience of distance were identified. Recommendations to the Engineering Faculty were compiled on the basis of this analysis together with student suggestions for improving the first-year engineering programme.
- ItemOpen AccessLimit Analysis and Shakedown in Plane Frames and Plane Stress Problems(1977) Douglas, Andrew Sholto; Martin, JBA method is developed for the determination of the shakedown load factor for elastic, perfectly plastic plane frames subjected to cyclic loading or random loads varying between fixed limits. The essential feature of the method is the employment of an automatic force method of elastic analysis which provides self-stress systems for the frame. This in turn permits the ready formulation of the compatibility requirements which are imposed on plastic hinge rotations. As a result, the analysis proceeds with data input which is comparable to straightforward kinematic analysis. A preliminary study of the generalisation of this approach to the limit analysis of plane stress problems is also given.
- ItemOpen AccessModelling of the binary alloy solidification process(1992) McAdie, R L; Martin, JBA thermodynamically consistent model capable of modelling a binary alloy undergoing solidification or melting is developed. The theory is continuum based, and the solid-liquid phase change system is described macroscopically by a single set of conservation equations. The model is an extension of that presented in the literature. The thermodynamic theories of this type in the current literature are based on the assumption of local equilibrium. This assumption is not representative of most alloy solidification processes where the solid-liquid phase region, termed the mushy region, is of dendritic nature with the rates of diffusion in the liquid being orders of magnitude faster than that in the solid. The propose model includes the assumption of local non-equilibrium where solute diffusion in the solid phase is assumed to be zero. The thermodynamic formulation is expressed in terms of three thermodynamic variables: pressure, temperature and average solute concentration for both the equilibrium and non-equilibrium case. A generalized set of conservation equations of mass, energy, momentum and solute with the necessary constitutive equations is presented. A Finite Element (FE) formulation of a simplified form of the governing equations is developed. The reduced set of equations implemented in the FE formulation consists of a fully coupled heat conduction and solute diffusion formulation, with solid-liquid phase change, where the effects of pressure and convection are neglected. The FE formulation is based on the fixed grid technique where the elements are two dimensional, four noded quadrilaterals with the primary variables being enthalpy and average solute concentration. Temperature and solid mass fraction are calculated on a local level at each integration point of an element. A fully consistent Newton-Raphson method is used to solve the global coupled equations and an Euler backward difference scheme is used for the temporal discretization. The solution of the enthalpy-temperature relationship is carried out at the integration points using a Newton-Raphson method. A secant method employing the regula falsi technique takes into account sudden jumps or sharp changes in the enthalpy-temperature behaviour which occur at the phase zone interfaces. The Euler backward difference integration rule is used to calculate the solid mass fraction and its derivatives for the non-equilibrium case. Two solidification examples, using both the local equilibrium and the local non-equilibrium cases, are analyzed. The finite element results obtained for the two cases are compared, and the accuracy of the finite element model is checked. Both dendritic and eutectic phase change are tackled. Even though the discrete eutectic phase change is approximated using the fixed grid approach, the results are considered to be reasonable approximations to what occurs in reality. Favorable comparisons of the results are obtained with that in the literature and convergence of the finite element results for different mesh sizes are shown. For dilute alloy solutions, the solidification results for the local equilibrium and the local non-equilibrium cases are shown to differ markedly, whereas for near eutectic solutions little difference is observed. The use of the local non-equilibrium assumption in the finite element solidification model is shown to effect the macro-segregation of solute.
- ItemOpen AccessNonlinear heat transfer and thermo mechanical stress analysis using finite elements.(1985) Pennington, Derek Steven; Martin, JBThis thesis deals with the development, implementation and testing of numerical procedures for the heat transfer and thermo-mechanical analysis of sol id continua. Steady state conduction heat transfer is developed as a particular case of the general field equation. Internal heat generation and the boundary conditions of specified temperatures, flux, convection. and radiation are included. The stress - strain - temperature relationships for a corresponding body are not coupled to the heat transfer relationships for steady state conditions. The heat transfer problem is thus solved prior to, and independently of, the mechanical problem. The resulting temperature field is adopted for the solution of the thermal deformation problem. Finite element formulations using a common discretization are developed for these problems using Galerkin' s method. The formulations are implemented in an existing temperature independent nonlinear finite element stress analysis code. Four, eight and nine noded isoparametric continuum finite elements with the option of the plane stress, plane strain and axisymetric cases are utilized. Nonlinear heat transfer due to temperature dependent thermal conductivity and/or internal heat generation is solved using an iterative method based on the Newton-Raphson algorithm. Thermal deformations and stresses are determined by calculating equivalent nodal loads corresponding to the thermal strains which result from the temperature field. These are then applied to the mechanical model. The implementation is illustrated by three examples whose solutions compare favourably with analytical solutions taken from the literature.
- ItemOpen AccessNumerical simulation of recrystallization behaviour of A1-1Mg during multi-pass rolling(1994) Jansen, Dieter Jorg; Martin, JB; Mitchell GMicrostructural changes which occur in aluminium alloys during rolling operations often play a large role in the performance of subsequent forming processes, such as deep-drawing and sheet-metal forming. It is becoming increasingly important to control these microstructural changes in order to optimise the subsequent processing route and thereby produce a cost-effective product. The ability to model the microstructural evolution of the alloy during rolling would greatly reduce the development cost and development time of a particular rolling schedule. This thesis investigates the recrystallization behaviour of A1Mg for a three pass rolling process. Equations describing the recrystallization process are implemented into a Finite Element code, and the effect of changing the roll speed is investigated. The results indicate that further work is required to empirically characterise the recrystallization behaviour of the particular alloy in question.
- ItemOpen AccessThe permanent deformation of steel portal frames subjected to impulsive loading(1977) Hanan, Davide; Martin, JBThe inelastic response of steel portal frames with a mass attached to the centre of the beam member and subjected to large dynamic loads is studied. The analysis is carried out using the mode approximation technique extended to include strain-rate sensitivity, finite deflections and pulse duration. Experimental results are presented which show good agreement with theoretical predictions. The use of the extended Hamilton's principle for mode form solutions is discussed.
- ItemOpen AccessA program for the automatic plastic design and analysis of plane steel frames(1977) Griffin, Paul Dominic; Martin, JBThe desire for more efficient and realistic structural design of plane steel frames has brought plastic methods of analysis to the fore. Though not commonly used in South Africa, plastic methods have been adopted elsewhere, particularly in the United States. An incremental approach is presented, leading to the determination of the collapse load of a structure and its consequent design. The structure is then analysed using deformation theory analysis, and the results are checked using the A.I.S.C. recommendations, a summary of which is presented. A computer program which automatically executes the design and analysis of any plane steel frame is included, and some of the results obtained from the program are presented.
- ItemOpen AccessQuick methods of analysing earthquake forces on viaduct bridges having continuous decks and tall piers(1980) Strickland, Ian Graham; Martin, JBThe available methods of calculating the effects of earthquakes on viaduct-type bridges with continuous decks and tall piers are examined. Particular emphasis is laid on the use of a relatively quick method of analysis using response spectra and taking account of the effects of damping. The use of this method is illustrated by applying it to a mathematical model representing a real. bridge. Manual calculations are performed and refined by the application of Rayleigh's Principle. A number of variations to the configuration of the model are analysed by the computer programme "SAP IV" under earthquake excitation in each of three mutually perpendicular directions. The computed results are compared with those obtained by manual calculation. The earthquake loading effects are compared with the effects of deadload, traffic loading and windload and there is a discussion on the design of suitable structural configurations to contend with seismic loading. The work ends with some generalisations about other types of bridges.
- ItemOpen AccessSeismic analysis of pipelines with yielding supports(1984) Ibell, Christopher Anthony; Martin, JBPipelines in structures such as a nuclear reactor can be analysed separately when the structure is subjected to seismic type loading. The pipeline is modelled with various types of supports, such as a rigid support or an elastic support. The pipeline is analysed and designed so that stresses in the pipeline and at the supports are acceptable. When the pipeline is subjected to a larger intensity earthquake than that designed for, the stresses at some supports may exceed the yield stresses, causing the support to yield. The yielding of a support can influence the response at the other supports in the pipeline, and in some cases cause failure of the supports to occur. This thesis investigates the effect yielding of an internal pipe hangar support in a two-span pipeline has on the adjacent end supports. Essentially the findings are that the yielding of the pipe hangar support is not detrimental to the overall stability of the pipeline, as long as the support does not yield excessively.
- ItemOpen AccessSome structural theorems for inelastic solids : an internal variable approach.(1976) Carter, Peter; Martin, JBThe theory of inelastic solids involving thermodynamic potential functions with internal variables is reviewed. Use is made of the condition for stable thermodynamic equilibrium in order to obtain dual minimum principles for the equilibrium state of a solid inelastic body. This leads to dual forms of the incremental (or rate) theorems and their respective extended forms. The extended static incremental theorem is applied to a pin-jointed truss and an algorithm suggested for solution of the ensuing programming problem. Numerical examples are given. A class of bounding theorems is also studied from the point of view of the potential functions. Bounds on the work and complementary work are obtained and properties of the bounding functions examined. Finally, the bound on a functional, which has been used to obtain general work and displacement bounds for dynamically loaded structures, is discussed.
- ItemOpen AccessTime integration algorithms for finite element analysis of creep problems(1989) Marais, Nicholas John; Martin, JBThe fundamental principles involved in the selection and implementation of time integration schemes for finite element analysis of nonlinear creep problems are investigated. The relationship between the nature of the integration algorithms and the mechanical principles of the time-dependent problem is explored. The emphasis is on uniaxial creep and simple constitutive laws are adopted. The essential nature of the problem is presented in different formulations. The creep problem is contained in a system of nonlinear first order ordinary differential equations in the creep strains only. This suggests that the integration scheme should be applied to the creep strains whereas traditional methods approximate the stresses. An internal variable framework is used to demonstrate the links between a consistent mathematical programming formulation and the conventional Newton-Raphson procedures. The incremental creep problem is cast as a nonlinear programming problem and is written as a minimum principle in the incremental displacements and creep strains.
- ItemOpen AccessTime integration schemes for piecewise linear plasticity(1991) Rencontre, LJ; Martin, JBThe formulation of a generalized trapezoidal rule for the integration of the constitutive equations for a convex elastic-plastic solid is presented. This rule, which is based on an internal variable description, is consistent with a generalized trapezoidal rule for creep. It is shown that by suitable linear extrapolation, the standard backward difference algorithm can lead to this generalized trapezoidal rule or to a generalized midpoint rule. In either case, the generalized rules retain the symmetry of the consistent tangent modulus. It is also shown that the generalized trapezoidal and midpoint rules are fully equivalent in the sense that they lead to the establishment of the same minimum principle for the increment. The generalized trapezoidal rule thus inherits the notion of B-stability and both rules offer the opportunity to exploit the second order rate of convergence for a = Â½. However, in the generalized trapezoidal rule, the equilibrium. and constitutive equations are fully satisfied at the end of the time increment. This may be more convenient than the generalized midpoint rule, in which equilibrium and plastic consistency are satisfied at the generalized midpoint. A backward difference return algorithm for piecewise linear yield surfaces is then formulated, with attention restricted to an associated flow rule and isotropic material behavior. Both the Tresca and Mohr-Coulomb yield surfaces with perfectly plastic and linear hardening rules are considered in detail. The algorithm has the advantage of being fully linked to the governing principles and avoids the inherent problems associated with corners on the yield surface. It is fully consistent in that no heuristic assumptions are made. The algorithm is extended to include the generalized trapezoidal rule in such a way that the general structure of the backward difference algorithm is maintained. This allows both for the computational advantages of the generalized trapezoidal rule to be utilized, and for a basis for comparison between this algorithm and existing backward difference algorithms to be established. Using this fully consistent algorithm, the return paths in stress space for the Tresca and Mohr-Coulomb yield surfaces with perfectly plastic and linear hardening rules are identified. These return paths thus provide a basis against which heuristically developed algorithms can be compared.
- ItemOpen AccessTransient nonlinear heat transfer analysis using the finite element method in the context of the requirements of thermal analysis in a mine(1990) French, L de F; Martin, JB; Mercer, Colin; Marais, NicholasThe aim of this thesis is to develop a computer program, together with a users' guide, to analyse two-dimensional; nonlinear, transient heat conduction in non-isotropic solids using the finite element method. This program is an extension of an existing program that analyses thermomechanical stress in solids which may have prescribed temperature and flux boundary conditions. The program has been extended using the requirements for modelling heat transfer in mines as a guide. The theory of conduction, thermal radiation, convection and heat transfer due to evaporation and condensation is presented.