This work concerns the use of resonance, in a proposed test designed to rapidly determine the fatigue life of coil-springs. A method is described whereby any number of the lower natural frequencies and corresponsing mode-shapes, of a coil-spring, constrained by a variety of simple boundary-conditions, may be determined. A method which uses the predicted natural mode-shapes is described, whereby an index of stress, corresponding to the rate of fatigue damage to the coil-spring, resulting from: resonance, the application of opposing static longitudinal forces to the ends of the spring, and residual stresses, may be determined. The predicted stress is used, to determine the most useful of the classes of natural modes, for use in the proposed test of fatigue life, and a method whereby the fatigue life of a spring, resonating in this mode, may be determined. A jig has been designed to hold a spring of largely arbitrary geometry, in this mode of resonance, such that sufficient stress is induced in the wire, to exceed the endurance limit of the material of the spring's wire, for sufficient time to cause failure by fatigue. This includes a method for the application of opposing static longitudinal forces to the ends of the spring, should this be required to supplement the alternating stress caused by resonance.

The analysis presented in this thesis is an application of the finite element method to the determination of stresses in plane, linear viscoelastic bodies. In Chapter 1, the basic concepts of viscoelastic behaviour are introduced and some simple mathematical models are considered. Two classical forms for mathematical representation of viscoelastic behaviour are presented. These are the differential operator form and the hereditary integral form. An example problem is solved using the differential operator form by applying the elastic-L viscoelastic analogy. The concept of time-temperature equivalence is introduced to take into account the affect of temperature on the viscoelastic material responses. The hereditary integral representation is adopted in this thesis owing to the ease with which the measured creep or relaxations can be incorporated and also to the superiority of integrals over the differential operator representation, in taking into account the affect of temperature on the responses. In Chapter 2, a stress analysis for plane problems in linear thermoviscoelasticity using the finite element formulation is presented. The method employed is based on the assumptions that: (1) the material is isotropic, homogeneous and linear, (2) the stress-strain laws are expressed in the hereditary integral form, (3) the material is thermorheologically simple, which implies the validity L of time-temperature equivalence hypothesis, and finally, (4) the viscoelastic stress response is independent of thermal response. The associated computer program includes both linear and quadratic isoparametric elements and the frontal method of Gaussian elimination is employed. The element matrices that result in the equilibrium equations involve hereditary integrals which are approximated by a stable and converging trapezoidal finite difference scheme for time marching. The solutions for two problems are compared with analytical results evaluated by the integral transform method. Since it is assumed that the thermal response is independent of the stress response, a nonlinear heat conduction analysis may be performed concurrently with the stress analysis. The basic equations and the finite element method of analysis for heat conduction are presented briefly. For approximate solutions which require less computer time alternative forms of the equilibrium equations utilizing an iterative technique is presented and an example problem is included. Finally, the affect of incompressibility is considered for an axisymmetric problem. The equlibrium equations based on the theorem of minimum potential energy are inaccurate for Poisson's ratios in the vicinity of 0.5, and degenerate completely for the case of incompressibility. Based on the assumptions made in Chapter 2, an alternative formulation of the viscoelastic stress analysis is presented in Chapter 3. The problem now has two displacement variables and a mean pressure variable. A variational principle is presented whose simultaneous minimisation with respect to the displacement variables and pressure variable leads to the equilibrium equations which are valid for all admissible values of Poisson's ratio. The hereditary integrals that result are approximated by a finite difference scheme for time marching and the finite element method is used for spatial discretisation and solution. An example problem is solved to examine the accuracy of the present formulation. Similar to the iterative technique developed in Chapter 4, an alternative form of the equilibrium equation is also presented here for approximate solutions that require less computer time. In Chapter 4 an orthotropic viscoelastic stress analysis is presented with particular reference to the modelling of drying stresses in timber. The heat and mass transfer taking place during drying are assumed to be independent of viscoelastic stress relaxation. Luikov's partial differential equations are used to model the heat and mass transfer and the finite element method is used for the solution. The shrinkage strains that develop during drying of timber are taken as input to the stress analysis problem. The effects of temperature and moisture content on the viscoelastic material responses are taken into account by postulating the validity of the time-temperature and moisture content equivalence hypothesis. The materials which can be characterised thus are called thermo-hygrorheologically simple models. Since all the material responses for wood which are required for stress analysis are yet to be evaluated experimentally, only a parametric study based on limited experimental results is presented in this thesis. A review of the literature relevant to each of the chapters is presented at the beginning of the chapters themselves and not as an independent entity.

The analysis presented in this thesis is an application of the finite element method to the determination of stresses induced by drying processes in porous capillary bodies. The formulation is quite general but the application in this instance is restricted to the problem of timber drying. The problem involves two distinct stages where first the distribution of the thermal and the moisture content fields are determined and then a stress analysis is carried out to find the stress distributions set up by these drying processes. The first stage involves the solution of the non-linear heat and mass transfer problem, using Luikov's partial differential equations to describe the phenomenon. Subsequently the results are then used to determine the stresses by assuming that an elasto-viscoplastic constitutive model describes the rheological behaviour of timber. The heat and mass transfer results presented are an attempt to find an efficient solution algorithm for the timber drying problem. Firstly results from the numerical model are compared with previously quoted experimental work. Secondly the influence of choice of time stepping algorithm is investigated and finally the effect of non-linearity of the thermophysical parameters is examined. The stress analysis results are illustrated by means of a typical section of timber which is subjected to various combinations of drying conditions and assumed material properties. The phenomenon of stress reversal known to occur in practice is successfully modelled and the effect of varying the relevant parameters such as drying conditions, elastic properties and plastic yield criteria is then investigated.

Experimental research has been carried out with the purpose of evaluating the tensile properties, stress and strain control fatigue properties and, crack propagation behaviour of a particulate reinforced metal matrix composite. Fractographic examination has also been undertaken of the powder metallurgy processed 2124 Al-alloy with two volume fractions (17 and 25vol%) and different particle sizes (2.5μm and 15μm) silicon carbide particles (SiC<SUB>p</SUB>). The present study shows that tensile properties of composites significantly improve with the incorporation of hard, brittle ceramic particles. The composite materials were cyclically deformed over a range of constant stress amplitudes at R=0.1 and R=0.5 using a variety of notch geometries in air and elevated temperatures. Results indicated that for a given aged condition (T4), load controlled fatigue lives of the composites are significantly improved compared with the unreinforced base alloy. However the severity of a notch, i.e. increased stress concentration factor and elevated temperatures shift down the S-N curves of the 2124 25vol% SiC<SUB>p</SUB> (AMC225) composite material. The effects of particle size and volume fraction on strain controlled fatigue behaviour were evaluated for a variety of composite materials at different strain range levels. An increased volume fraction of particles reduces fatigue lives due to the lower monotonic ductility of the AMC225 composite which showed some degree of softening at R=-1, but stable behaviour at the R=0 conditions under strain loading. At R=0.5 the composite cyclically hardened. On the basis of these results, fatigue life predictions for the notch geometries have been made by using a critical strain approach.

This study presents the application of the Boundary Element Method (BEM) to spherical and radome geometries. The boundary of the solution domain was discretized by using both linear and quadratic elements and the validity of the results were compared against other analytical and numerical methods. Several improvements to the BEM have been presented. These include the efficient evaluation of the singular integrals where new methods have been implemented and compared with other schemes. Improvement is also shown by the implementation of the semi-continuous elements to solve the well known limitation of the Corner Problems present in the BEM. Exhaustive numerical experimentation is carried out to establish the optimum collocation point for the semi-continuous elements and to link this to the quadrature rule used for the integration of that element. The present study also includes the limitations of the BEM in applications involving geometries of long and thin sections. The study shows in detail the circumstances under which accurate results can be expected in the BEM. In this case, the emphasis is placed on the element size and the section thickness. A relationship linking these two parameters in the control of the accuracy of the BEM results is also established. For the surface stresses and strains of the domain, a detailed implementation of a natural cubic spline is illustrated which greatly improved these surface results.

No description available.

No description available.

A fuzzy relational sliding mode observer (FRSMO) and proportional integral observer (FRPIO) are proposed to estimate the magnitude of slowly evolving faults in information-poor, i.e., difficult to model and non-linear systems. Where there is no fault in the system, the mismatch between the actual output and the model output can be shown to be zero. When the fault occurs in the system, the error is not zero, which is called a residual and can be used to diagnose the fault. In the fuzzy PI observer, the size of the fault can be obtained from the error passing the PI feedback compensation. In the fuzzy sliding mode observer, the equivalent injection signal is used to compensate for the fault thus obtaining the magnitude of the fault. To reduce modelling errors, an on-line learning fault identification scheme (OLFIS) is used to update the model and identify the fault in a periodical mode with different time intervals during the whole procedure. The selection of the intervals between model update and fault identification, convergence and speed of the scheme are investigated. The performance of the proposed methods is evaluated using a cooling-coil subsystem of an air-conditioning plant in a simulation environment. An actuator fault in the valve and a flow reduction fault are two typical incipient faults in the cooling coil system. The results of the actuator fault estimation and flow reduction fault estimation confirm the effectiveness of the methods.

No description available.

No description available.