Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references (leaves 207-211). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references (leaves 207-211). Also available on the Internet.

The present study involves analysis and design optimisation of lattice composite structures using symbolic computation. The concept of a homogenised model is used to represent heterogeneous composite isogrid structure as a homogeneous structure with the stiffness equivalent to the original grid structure. A new homogenisation technique is developed and used in the present study. The configuration of a unit cell and the geometrical parameters of the ribs of a composite isogrid cylinder are optimised subject to a strength criterion in order to maximise externally applied loading to provide maximum strength and stiffness of the structure as a whole. The effects of tension and torsion on the optimum design are investigated. Special purpose computation routines are developed using the symbolic computation package Mathematica for the calculation of equivalent stiffness of a structure, failure analysis and calculation of optimum design parameters. The equivalent stiffness homogenisation approach, in conjunction with optimum search routines, is used to determine the optimal values of the design variables. The numerical approach employed in the present study was necessitated by the computational inefficiency and conventional difficulties of linking the optimiser and the FEM analysis package for calculating the stress resultants used in the optimisation process. These drawbacks were successfully overcome by developing special purpose symbolic computation routines to compute stress resultants directly in the program using a new homogenisation approach for the model with equivalent stiffness. In the design optimisation of cylindrical isogrids the computational efficiency of the optimisation algorithm is improved and good accuracy of the results has been achieved. The investigation on the basis of failure analysis shows that the difference in the value of the maximum load applied to the optimal and non-optimal isogrid structure can be quite substantial, emphasising the importance of optimisation for the composite isogrid structures. The computational efficiency of optimisation algorithms is critical and therefore special purpose symbolic computation routines are developed for its improvement. A number of optimal design problems for isogrid structures are solved for the case of maximum applied load design. / Thesis (Ph.D.)-University of Natal, Durban, 2000.

Most of the current optimization techniques for the design of light-weight structures are unable to generate structural alternatives at the concept stage of design. This research tackles the challenge of developing an optimization method for the early stage of design. The main goal is to propose a procedure to optimize material and shape of stiff shafts in torsion. / Recently introduced for bending stiffness design, shape transformers are presented in this thesis for optimizing the design of shafts in torsion. Shape transformers are geometric parameters defined to classify shapes and to model structural efficiency. The study of shape transformers are centered on concept selection in structural design. These factors are used to formulate indices of material and shape selection for minimum mass design. An advantage of the method of shape transformers is that the contribution of the shape can be decoupled from the contribution of the size of a cross-section. This feature gives the designer insight into the effects that scaling, shape, as well as material have on the overall structural performance. / Similar to the index for bending, the performance index for torsion stiffness design is a function of the relative scaling of two cross-sections. The thesis examines analytically and graphically the impact of scaling on the torsional efficiency of alternative cross-sections. The resulting maps assist the selection of the best material and shape for cross-sections subjected to dimensional constraints. It is shown that shape transformers for torsion, unlike those for bending, are generally function of the scaling direction. / The efficiency maps ease the visual contrast among the efficiency of open-walled cross-sections and that of close-walled cross-sections. As expected, the maps show the relative inefficiency of the former compared to the latter. They can also set the validity range of thin- and thick-walled theory in torsion stiffness design. The analytical results are validated with the numerical data obtained from ANSYS to guarantee the consistency of the models. The thesis concludes with three case studies that demonstrate the method.

The understanding of the masticatory apparatus including its functional and structural relationship with other components of the cranium increasingly requires an interdisciplinary approach. Recently, "traditional biological sciences" such as anatomy, comparative biology, anthropology and evolution have increasingly meshed with elements from other domains, such as mechanical engineering and material sciences, which has resulted in new and exciting paradigms to be explored. This is particularly true in the field of craniofacial biomechanics yet there are still many unexplored issues and numerous questions that remain unanswered. Numerical modelling in general and Finite Element Analysis (FEA) in particular, represent a numerical experimental procedure to generate such information. Originally derived from the field of structural engineering, FEA has steadily permeated its way into craniofacial biomechanics and has proven itself as a most useful scientific tool. The present study introduces an engineering-based workframe for applying FEA to craniofacial biomechanical research in a comprehensive manner to cover the entire analytical spectrum, from developing questions to providing their solutions. The study is composed of two major experimental parts addressing both the linear elastic and the non-linear behaviour of some biomaterials encountered in the craniofacial arena. In the first part I analysed mandibular biomechanics using linear elastic models while in the second part I used nonlinear discrete models to determine the optimal elastic properties of the cervical restorative materials. Modern humans have a number of anatomical features that set us apart from our ancestors. Amongst these perhaps the most striking is the emergence of a protruding chin, otherwise absent in other archaic humans and hominids. While it has been shown that the chin has its embryological origins in the postnatal remodelling of bone in the area around the mandibular symphysis which produces the midline keel in the form of an inverted �T� the functional significance of this novel evolutionary feature is still obscure. It is accepted that the mandible is optimally designed for resisting masticatory stress, whereby optimal is seen as maximual strength at the lowest biological cost. Here, I tested the currently most accepted theory, namely that the chin provides mechanical resistance to the mandible during mastication. In other words, I tested the hypothesis that a chinned mandible would be stiffer and hence experience lower strains when compared to a non-chinned counterpart under identical loadings. My functional analysis consisted firstly of three simple models which reproduce a simian shelf, a flat and a chinned symphysis, loaded using two unidirectional loadcases (torsion and wishboning) to represent a distortion similar to that which occurs in the mandible during mastication. Secondly, I developed complex geometrical models which incorporated the cortical bone, medullary bone and teeth. The models were then analysed using the same loadcases as those used for the first theoretical models. Additionally, I incorporated the coronal bending and also a coupled loadcase which simulated the complex deformation of the mandible during biting. The aim here was to test the hypothesis that the presence of a chin changed the strain pattern in the mastication-loaded mandible. The results were then interpreted using Frost�s mechanostat theory which relates in a more precise manner the mechanical loading environment to the adaptive response of the bone. My results showed that the calculated strain values for both the chinned and flat mandibles were within the normal bone maintenance levels of the mechanostat during molar biting. In other words, variation in bone strain magnitude across the mandible, which should differ between the chinned and the non-chinned mandibles if the hypothetical mechanical role of the chin is true, is similar in both forms. I concluded that the development of the human chin is thus unrelated to the functional demands placed upon it by mastication. I suggested a new functional demand associated with pronounced tongue activity during speech. I hypothesise that it is the resistance to stresses induced by strong, repetitive contractions of the tongue and perioral musculature during, phonation that shaped the modern human chin. I tested my hypothesis by loading the symphyseal region with two principal nonmasticatory, muscle systems; firstly, the tongue and secondly the peri-oral muscular curtain, anterior to the symphysis. My results suggested that the flat, non-chinned symphysis when subjected to speech-related genioglossal movements will undergo adaptive changes which would result in an optimised (chinned) shape, such as that found in the modern human symphysis. These results thus offer a new foundation to an old hypothesis and a solution to the longstanding controversy over the origin of the human chin. I conclude that forces generated by speech rather than those generated by mastication, shaped the chin in anatomically modern humans. Prompted by an earlier observation I further investigated the apparent cross-over distribution of strains on the mandibular corpora during mastication. In doing so, I tested the hypothesis that this cross-over may be linked with another particular anatomical feature of the mandible that of the postcanine cortical asymmetry, which appears to be stereotypical among anthropoids. The results of my study hence suggest that strain patterns within the human mandible are more complex than previously thought. Not only do strains differ between lingual and buccal aspects of working and non-working sides, but they also differ within these areas (i.e. from alveolus to corpus, to lower border regions). I conclude that postcanine cortical asymmetry may be a retained evolutionary trait rather than the result of masticatory biomechanics. In the second section of the thesis I introduced a different analysis regime which allows the prediction of fracture initiation and propagation. In this part I analysed the mechanics underlying the failure of the restorations placed in non-carious cervical lesions and suggested changes in the material properties of the restorations used to treat them. Non-carious cervical lesions (NCCL) include those entities characterised by the cervical loss of hard dental tissue that occurs in the absence of any carious process. To distinguish between lesions that occur due to excessive occlusal load and other non-carious cervical lesion (i.e. erosion and abrasion) the clinical term "abfraction" has been adopted. Although a common clinical issue, failure of restoration placed in these lesions has not been subjected to a rigorous biomechanical analysis. To determine which of the material�s parameters should be changed and to what extent, I employed a combined numerical approach. Here I introduced a novel approach in simulating the cracking of restorative materials and tooth tissues which is based on a simpler material formulation and can be used in an advanced nonlinear numerical analysis. The material model I used allows automatic crack insertion and growth and also uniquely accounts for the microdamage which precedes the instalment of macroscopic cracks. The first step was to balance the factors that may affect failure employing a linear analysis with a stress-based approach to failure. Here, the aim was to investigate the influence of lesion shape and depth as well as the direction of occlusal loading on the mechanical response of the cervical glass-ionomer cements restoration in a lower first premolar. This analysis showed that the direction of loading was the major contributor to the failure of the restoration. The next step was to apply this fracture model to the restorations of the NCCL in order to verify if the material is able to accurately simulate the location and type of mechanical failure. The data for this problem, i.e. the geometry and the loadcase were derived from the conclusions of linear analysis, that is I chose the "worst case scenario" as the upper boundary of material endurance. My results showed that under the action of para-functional loadings the GIC failed on the cervical margin. I also showed that prior to fracture the restorative material undergoes strain softening, which in turn introduces damage and weakens the materials involved. After successfully testing the proposed model, the final step was to determine which material properties and restorative techniques would be most reliable under given biomechanical conditions. The present work relied on the hypothesis that a more flexible material would partially buffer the local stress concentration and hence reduce the likelihood of mechanical failure of the restoration. My study, a first of its kind, proposes a radical approach to address the problems of material improvement, namely: numerical-based material optimisation engineering. That is, I aimed to identify the "most favourable" selection of elastic modulus or E value for the restorative material, which will allow it to survive under the unfavourable occlusal loading conditions that may prevail. Two filling techniques were considered; firstly a single bulk material, namely glass-ionomer (GIC) and secondly a layered technique. The latter consisted of a layer of GIC supporting a composite bulk restorative. I chose two thicknesses for the GIC layer, 50 and 150 microns. My results showed that the restorative materials currently used in cervical non-carious lesions are largely unsuitable in terms of resistance to fracture of the restoration mostly because of their relative high stiffness irrespective of the filling technique. The best results are obtained for a bulk filling with a 1GPa elastic modulus material case in which the tensile stresses are about 50% of the failure limit. This approach in determining the mechanical properties of the restorative is novel and unique so far in the dental literature. The direct benefit of this study was the improvement of the restorative material, as it can be engineered to withstand the conditions identified as major cause of failure. This is consonant with the call for new materials better tailored for some specific needs.

This dissertation aims to advance the field of structural optimization by creating and demonstrating new methodologies for the explicit inclusion of manufacturing issues. The case of composite aerospace structures was a main focus of this work as that field provides some of the greatest complexities in manufacturing yet also provides the greatest incentives to optimize structural performance. Firstly, the possibilities for modifying existing FEA based structural optimization methods to better capture manufacturing constraints are investigated. Examples of brick-based topology optimization, shell-based topology optimization, parametric sizing optimization and manufacturing process optimization are given. From these examples, a number of fundamental limitations to these methods were observed and are discussed. The key limitation that was uncovered related to a dichotomy between analytical methods (such as FEA) and CAD-type methods. Based on these observations, a new Knowledge-Based framework for structural optimization was suggested whereby manufacturing issues are integrally linked to the more conventional structural issues. A prototype system to implement this new framework was developed and is discussed. Finally, the validity of the framework was demonstrated by application to a generic composite rib design problem.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 72-74). Also available via the Internet.

Thesis (M.E.E.)--University of Delaware, 2007. / Principal faculty advisor: Dennis W. Prather, Dept. of Electrical & Computer Engineering. Includes bibliographical references.

Thesis (Ph.D.(Mechanical Engineering))--University of Pretoria, 2003. / Summaries in Afrikaans and English. Includes bibliographical references.

Thesis (M.Eng.(Mechanical Engineering))--University of Pretoria, 1999. / Summaries in Afrikaans and English. Includes bibliographical references.