Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 377-389). Available also in a digital version from Dissertation Abstracts.

Solution algorithms are developed for the nonlinear finite element equations, resulting from the discretization of governing incremental equations of equilibrium. The equations of equilibrium in the total Lagrangian formation are derived, based on continuum mechanics principles and by invoking the principle of virtual work. A general purpose computer program, modular in structure, and interactive in nature, is developed, based on the theoretical formulation presented. A brief review of some of the existing solution algorithms for nonlinear structural analysis using the finite element formulation is presented. Arc-length methods, which facilitate the tracing of the load-configuration path beyond limit points, are systematically examined. Specific emphasis is focussed on obtaining the complete structural response in an efficient and reliable way. The arc-length methods treat the load parameter as a variable in addition to the unknown displacements. A constraint equation forms the supplemental equation for the determination of the additional variable. Attention is directed to the constraint equation, comprising the displacements and loads. Realising that the loads and displacements have different magnitudes, several authors had addressed the issue of including a scaling parameter, however, inadequately. In this research, several well formulated automatic means of computing the scaling parameter are suggested. A constant scaling parameter, which remains unchanged throughout all the load steps, and a variable scaling parameter, which is recalculated at each load step are introduced. The latter parameter is related to the current stiffness parameter. In the present investigation, the spherical constraint, the normal plane constraint and the updated normal plane constraint equations are examined with the proposed scaling parameters. An automatic load step calculation, based on the arc-length is suggested. The load step is rendered adaptive by including the load term with the scaling parameter in the constraint equation. Examples from large displacement problems, that exhibit severe geometric nonlinearities, are included to evaluate the proposed algorithms and substantiate their efficacies in tracing the complete load-configuration path. The relative performances of the proposed algorithms reveal their cost-effectiveness.

The research work presented here deals with the problems of geometrically nonlinear analysis of thin shell structures. The specific objective was to develop geometrically nonlinear formulations, using Discrete-Kirchhoff Curved Triangular (DKCT) thin shell elements. The DKCT elements, formulated in the natural curvilinear coordinates, based on arbitrary deep shell theory and representing explicit rigid body modes, were successfully applied to linear elastic analysis of composite shells in an earlier research work. A detailed discussion on the developments of classical linear and nonlinear shell theories and the Finite Element applications to linear and nonlinear analysis of shells has been presented. The difficulties of developing converging shell elements due to Kirchhoff's hypothesis have been discussed. The importance of formulating shell elements based on deep shell theory has also been pointed out. The development of shell elements based on Discrete-Kirchhoff's theory has been discussed. The development of a simple 3-noded curved triangular thin shell element with 27 degrees-of-freedom in the tangent and normal displacements and their first-order derivatives, formulated in the natural curvilinear coordinates and based on arbitrary deep shell theory, has been described. This DKCT element has been used to develop geometrically nonlinear formulation for the nonlinear analysis of thin shells. A detailed derivation of the geometrically nonlinear (GNL) formulation, using the DKCT element based on the Total Lagrangian approach and the principles of virtual work has been presented. The techniques of solving the nonlinear equilibrium equations, using the incremental methods has been described. This includes the derivation of the Tangent Stiffness matrix. Various Newton-Raphson solution algorithms and the associated convergence criteria have been discussed in detail. Difficulties of tracing the post buckling behavior using these algorithms and hence the necessity of using alternative techniques have been mentioned. A detailed numerical evaluation of the GNL formulation has been carried out by solving a number of standard problems in the linear buckling and GNL analysis. The results compare well with the standard solutions in linear buckling cases and are in general satisfactory for the GNL analysis in the region of large displacements and small rotations. It is concluded that this simple and economical element will be an ideal choice for the expensive nonlinear analysis of shells. However, it is suggested that the element formulation should include large rotations for the element to perform accurately in the region of large rotations.

published_or_final_version / abstract / toc / Industrial and Manufacturing Systems Engineering / Doctoral / Doctor of Philosophy

No description available.

Unplanned ore dilution or stope overbreak, which has a direct and large influence on the cost of a stope, and ultimately on the profitability of a mining operation, can be attributed to both the mining process and to geologic setting. The research undertaken in this document, applicable to a wide range of underground mines employing the blasthole mining method to extract tabular orebodies, focuses on examining factors attributable to the generation of unstable stope hanging-walls. / The primary objective of the research undertaken is to establish new models for stope and orezone design, with respect to anticipated stope overbreak, focusing on the position and type of stope within the orezone extraction sequence. Identified factors influencing unplanned dilution, such as: induced stress environment, stope geometry, and the setting of individual stopes are considered. / The research undertaken incorporates a variety of components, including (i) parametric 3-D numerical modelling to examine influences of individual factors on hanging-wall overbreak, (ii) case example analysis, and (iii) orezone extraction sequence simulation, using 3-D elastic numerical modelling. Design criteria, developed from the parametric modelling, was applied to the orezone sequence modelling to develop trends for stope dilution, as functions of stope design and construction. / It was found that hanging-wall overbreak is not significantly influenced by depth alone, and that stopes with large vertical and short horizontal dimensions or stopes having long horizontal and short vertical dimensions are more stable than large square-like stopes. Also, through parametric and case studies, it was demonstrated that, in addition to stope dimension, the amount of unplanned dilution differed according to stope type. Five stope types were identified, based on their position within a tabular blasthole mining sequence. Measured overbreak varies with stope type, with secondary stopes generating a greater volume of hanging-wall dilution than do primary stopes. A pillarless mining sequence will generate less overall dilution than a primary stope: secondary pillar mining sequence.

No description available.

No description available.

No description available.

Reliability characteristics of new devices are usually demonstrated by life testing. When lifetime data are sparse, as is often the case with highly reliable devices, expensive devices, and devices for which accelerated life testing is not feasible, reliability models that are based on a combination of degradation and lifetime data represent an important practical approach. This thesis presents reliability models based on the combination of degradation and lifetime data or degradation data alone, with and without the presence of covariates. Statistical inference methods associated with the models are also developed. / The degradation process is assumed to follow a Wiener process. Failure is defined as the first passage of this process to a fixed barrier. The degradation data of a surviving item are described by a truncated Wiener process and lifetimes follow an inverse Gaussian distribution. Models are developed for three types of data structures that are often encountered in reliability studies, terminal point data (a combination of degradation and lifetime data) and mixed data (an extended case of terminal point data); conditional degradation data; and covariate data. / Maximum likelihood estimators (MLEs) are derived for the parameters of each model. Inferences about the parameters are based on asymptotic properties of the MLEs and on the likelihood ratio method. An analysis of deviance is presented and approximate pivotal quantities are derived for the drift and variance parameters. Predictive density functions for the lifetime and the future degradation level of either a surviving item or a new item are obtained using empirical Bayes methods. Case examples are given to illustrate the applications of the models.