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Submitted by Marcele Costal de Castro (costalcastro@gmail.com) on 2017-09-06T13:30:34Z No. of bitstreams: 0 / Made available in DSpace on 2017-09-06T13:30:34Z (GMT). No. of bitstreams: 0 Previous issue date: 1984-05 / This work is concerned with the application of the finite element method to the study of creep brittle rupture of structural components. In the formulation material behavior is described by an elastocreep model in which the total strain rates are assumed to be the sum of elastic and creep components. The elastic strain rates are given by Hooke’s law while the creep strain rates and the damage rates are espressed by the multiaxial form of the Kachanov-Rabotnov equations proposed by Leckie and Hayhurst. The incremental equations of motion are derived from the principle of virtual work using an updated Lagrangian formulation which accounts for geometric effects due to large displacements, large rotations and deformation dependent loadings. The finite element incremental equations are developed according to a displacement-based formulation. Isoparametric elements with quadratic shape functions are employed for the domain discretization and simple numerical procedures are developed to deal with the presence of partially and/or fully ruptured elements in the mesh. For integration of the creep strain rate equations a family of implicit time marching schemes is developed which can be regarded as Runge-Kutta methods of second order. The integration of the coupled damage rate equations is performed using a first order predictor-corrector scheme with automatic time step length control. For material nonlinear problems only, a substructuring technique is employed in conjunction with the time integration algorithms. Selected numerical applications are presented and discussed in detail. Comparison with alternative numerical, analytical and/or experimental results is made whenever possible.

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To manufacture a high precision component, the aircraft industry in particular, employs computer numerical control machining to produce the aircraft components. However, it has often been found that problems of distortion occur when thin and slender components are manufactured this way. It is believed that the distortion arises due to the re-distribution of the residual stress field that was present in the original component in addition to the effects of cutting forces and temperatures that were induced during the machining process. At present, the process to produce a component with acceptable tolerance limits is one of trial and error. This often consumes a lot of time and produces considerable material wastage. The finite element method has been used to develop a methodology to model the actual machining process that produced the aircraft component. The finite element model that has been developed so far was able to demonstrate the effects of redistribution of the residual stresses on the distortion of the final machined component. It was found that the final component distorted differently when the materials were simply removed from a solid billet with different material removal sequences. A preliminary investigation on the effects of cutting temperature and forces has also been made. The investigation showed that such effects could not be totally ignored as they significantly affect the distortion of the final component. In addition to modelling the machining process, a methodology has also been developed to introduce and simulate the clamps and machine worktable that are part of the machining process. Although there is a considerable amount of work relating to modelling machining processes, there has not been any previous attempt to address the problem as a whole as described in this thesis. It is hope that the work undertaken here would be able to provide a stepping-stone to such attempts in future. However, further experimental data would be required to complement a more refined model in the attempt to accurately predict the distortion in machined components. It is believed that it would be possible to then extend the developed methodology to minimise the distortion by changing the machining sequence and the shape of the material to be removed. This would reduce the timescales involved to correct the problems of distortion and eliminate material wastage.

Environmental factors, such as noise and emissions have begun to play a significant role in the design of new aircraft. Although advances in propulsion technology have reduced source noise levels significantly over the past few decades, it is becoming increasingly difficult to project similar advances for the next few decades. It is likely however that some noise benefits may come from improvements in aircraft performance and from changes in operational procedures. In order for such developments to be analysed at the conceptual design stage, an integrated conceptual aircraft design and aircraft noise model is required that enables the designer to rapidly assess the effect of key design parameters on reference noise levels and noise contour area.

In principal component analysis (PCA), the principal components (PC) are linear combinations of the variables that minimize some objective function. In the classical setup the objective function is the variance of the PC's. The variance of the PC's can be easily upset by outlying observations; hence, Chen and Li (1985) proposed a robust alternative for the PC's obtained by replacing the variance with an M-estimate of scale. This approach cannot achieve a high breakdown point (BP) and efficiency at the same time. To obtain both high BP and efficiency, we propose to use MM- and τ-estimates in place of the M-estimate. Although outliers may cause bias in both the direction and the size of the PC's, Chen and Li looked at the scale bias only, whereas we consider both. All proposed robust methods are based on the minimization of a non-convex objective function; hence, a good initial starting point is required. With this in mind, we propose an orthogonal version of the least median of squares (Rousseeuw and Leroy, 1987) and a new method that is orthogonal equivariant, robust and easy to compute. Extensive Monte Carlo study shows promising results for the proposed method. Orthogonal regression and detection of multivariate outliers are discussed as possible applications of PCA. / Science, Faculty of / Statistics, Department of / Graduate

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Motivated by dimension reduction in regression analysis and signal detection, we investigate order determination for large dimensional matrices with spiked structures in which the dimensions of the matrices are proportional to the sample sizes. Because the asymptotic behaviors of the estimated eigenvalues differ completely from those in fixed dimension scenarios, we then discuss the largest possible order, say q, we can identify and introduce criteria for different settings of q. When q is assumed to be fixed, we propose a "valley-cliff" criterion with two versions - one based on the original differences of eigenvalues and the other based on the transformed differences - to reduce the effect of ridge selection in the criterion. This generic method is very easy to implement and computationally inexpensive, and it can be applied to various matrices. As examples, we focus on spiked population models, spiked Fisher matrices and factor models with auto-covariance matrices. For the case of divergent q, we propose a scale-adjusted truncated double ridge ratio (STDRR) criterion, where a scale adjustment is implemented to deal with the bias in scale parameter for large q. Again, examples include spiked population models, spiked Fisher matrices. Numerical studies are conducted to examine the finite sample performances of the method and to compare it with existing methods. As for theoretical contributions, we investigate the limiting properties, including convergence in probability and central limit theorems, for spiked eigenvalues of spiked Fisher matrices with divergent q. Keywords: Auto-covariance matrix, factor model, finite-rank perturbation, Fisher matrix, principal component analysis (PCA), phase transition, random matrix theory (RMT), ridge ratio, spiked population model.

Published Article / This paper looks at the development of composite materials in layered manufacturing. It is known that Rapid Prototyping (RP) using a single material compares poorly with other conventional manufacturing processes when making parts from similar materials. For example, injection moulded parts are over 30% stronger than RP fabricated parts of the same material. The incorporation of secondary materials can result in a composite that can improve this situation. This paper will discuss different composites that are commercially available as well as some into which research is being conducted. An advantage of RP is that composites do not have to be manufactured in a homogeneous manner. Functionally graded parts may be fabricated where reinforcing material can be added in appropriate locations and in required orientations.