Thesis (MScEng (Mechanical and Mechatronic Engineering))--University of Stellenbosch, 2009. / Although mass minimisation is an important application within structural optimisation, other applications include: (1) concept generation, (2) concept evaluation, (3) design for structural feasibility and (4) data matching. These applications, except data matching, are discussed and illustrated on a prototype design of the Karoo Array Telescope (KAT) antenna. The KAT passed through the design process and a full scale prototype was built, but was found to be too expensive. A detailed finite element model of the finalised design was considered as a test bed for reducing costs. Size-, shape- and topology optimisation are applied to three KAT components, while considering wind, temperature and gravity loads. Structural- and nonstructural constraints are introduced. Coupling of the structural optimisation code with an external analysis program to include non-structural responses and the parallelisation of the sensitivity calculations are presented. It is shown that if a finite element model is available, it is generally possible to apply structural optimisation to improve an existing design. A reduction of 2673 kg steel was accomplished for the existing KAT components. The total cost saving for the project will be significant, when considering that a large amount of antennas will be manufactured.

L’objectif de cette thèse est le développement de méthodes d’optimisation multi-objectif pour la résolution de problèmes de conception des structures mécaniques. En effet, la plupart des problèmes réels dans le domaine de la mécanique des structures ont plusieurs objectifs qui sont souvent antagonistes. Il s’agit, par exemple, de concevoir des structures en optimisant leurs poids, leurs tailles, et leurs coûts de production. Le but des méthodes d’optimisation multi-objectif est la recherche des solutions de compromis entre les objectifs étant donné l’impossibilité de satisfaire tout simultanément. Les métaheuristiques sont des méthodes d’optimisation capables de résoudre les problèmes d’optimisation multi-objective en un temps de calcul raisonnable sans garantie de l’optimalité de (s) solution (s). Au cours des dernières années, ces algorithmes ont été appliqués avec succès pour résoudre le problème des mécaniques des structures. Dans cette thèse deux métaheuristiques ont été développées pour la résolution des problèmes d’optimisation multi-objectif en général et de conception de structures mécaniques en particulier. Le premier algorithme baptisé MOBSA utilise les opérateurs de croisement et de mutation de l’algorithme BSA. Le deuxième algorithme nommé NNIA+X est une hybridation d’un algorithme immunitaire et de trois croisements inspirés de l’opérateur de croisement original de l’algorithme BSA. Pour évaluer l’efficacité et l’efficience de ces deux algorithmes, des tests sur quelques problèmes dans littérature ont été réalisés avec une comparaison avec des algorithmes bien connus dans le domaine de l’optimisation multi-objectif. Les résultats de comparaison en utilisant des métriques très utilisées dans la littérature ont démontré que ces deux algorithmes peuvent concurrencer leurs prédécesseurs. / The objective of this thesis is the development of multi-objective optimization methods for solving mechanical design problems. Indeed, most of the real problems in the field of mechanical structures have several objectives that are often antagonistic. For example, it is about designing structures by optimizing their weight, their size, and their production costs. The goal of multi-objective optimization methods is the search for compromise solutions between objectives given the impossibility to satisfy all simultaneously. Metaheuristics are optimization methods capable of solving multi-objective optimization problems in a reasonable calculation time without guaranteeing the optimality of the solution (s). In recent years, these algorithms have been successfully applied to solve the problem of structural mechanics. In this thesis, two metaheuristics have been developed for the resolution of multi-objective optimization problems in general and of mechanical structures design in particular. The first algorithm called MOBSA used the crossover and mutation operators of the BSA algorithm. The second one named NNIA+X is a hybridization of an immune algorithm and three crossover inspired by the original crossover operator of the BSA algorithm. To evaluate the effectiveness and efficiency of these two algorithms, tests on some problems in literature have been made with a comparison with algorithms well known in the field of multi-objective optimization. The comparison results using metrics widely used in the literature have shown that our two algorithms can compete with their predecessors.

Este trabalho trata da otimização de painéis alveolares e vigotas protendidas utilizando Algoritmos Genéticos (AGs). A proposta de tal algoritmo foi inspirada no princípio da seleção natural de indivíduos, onde o mais ‘apto’ tende a permanecer na população e se reproduzir, passando seu código genético para a próxima geração. Em alguns casos, esse método pode alcançar melhores soluções se comparados aos métodos tradicionais de otimização. O principal objetivo do trabalho é investigar o uso de AG como uma técnica para a minimização da função custo da aplicação de painéis alveolares e vigotas protendidas. Na análise estão incluídas as verificações dos elementos nas etapas transitórias referentes à produção, transporte e montagem. A função custo é avaliada considerando valores da realidade brasileira. O trabalho de pesquisa compara os resultados obtidos utilizando AGs com aqueles obtidos utilizando o método de otimização convencional conhecido como método do Lagrangiano Aumentado. Os resultados obtidos por ambos os métodos evidenciam a eficácia dos AGs com relação ao método convencional. Foram propostas e analisadas três famílias do AG simples, buscando identificar, dentre seus elementos, quais variantes mais adequados na busca da solução dos problemas. / This work aims to optimize the production cost of hollow core panels and prestressed joists using Genetic Algorithms (GAs). The proposal of such an algorithm was inspired by the principle of natural selection of individuals, where the most ‘capable’ tends to remain in the population and reproduce, passing its genetic code onto the next generation. In some cases, this method can achieve good solutions when compared with conventional methods of optimization. The main goal of the work is to investigate AG as a technique for the minimization of the function cost of hollow core panel and prestressed joist applications. The analysis takes account of the verifications of the precast elements in the transitory stages as production,transportation and erection. The function cost is evaluated within the Brazilian context. The research compares the results using GAs with those using a conventional method, the Augmented Lagrangian. The results provide evidence the effectiveness of the GAs with relation to a conventional method. The research considers three families of the simple GA, searching to identify, among them, the adjusted variant in the search of the solution of the problems.

A renewed commitment in the United States and abroad to electricity from renewable resources, such as wind, along with the recent deployment of very large turbines that rise to new heights, makes obtaining the most efficient and safe designs of the structures that support them ever more important. Towards this goal, the present research seeks to understand how optimization concepts and Microsoft Excel's optimization capabilities can be used in the design of wind turbine towers and foundations. Additionally, this research expands on the work of previous researchers to study how considering the tower and foundation as an integral system, where tower support conditions are not perfectly rigid, affects the optimal design. Specifically, optimization problems are formulated and solved with and without taking into account the effect of deflections, resulting from the foundation's rotational and horizontal stiffness, on natural frequency calculations. The general methodology used to transcribe the design of wind turbine towers and foundations into an optimization problem includes: 1) collecting information on design requirements and parameter values 2) deciding how to analyze the structure 3) formulating the optimization problem 4) implementation using Microsoft Excel. Key assumptions include: 1) use of an equivalent lumped mass method for estimating natural frequency 2) International Electrotechnical Commission (IEC) 61400-1 extreme loading condition controls design (i.e. fatigue loading condition is not considered) 3) extreme loads are obtained from manufacturer provided structural load document that satisfies loading cases outlined in IEC 61400-1 4) wind forces on the tower are calculated in accordance with IEC 61400-1 5) optimization variables are continuous. The sum of the tower material and fabrication cost and the total foundation cost is taken as the objective function. Important conclusions from this work include: 1) optimization concepts and Microsoft Excel's optimization capabilities can be used to obtain reasonable conceptual level designs and cost estimates 2) detailed designs and cost estimates could be achieved using a solver capable of handling discrete optimization problems 3) considering the tower and foundation as an integral system results in a more expensive, but safer, design 4) for the assumed parameter values, the constraint on the tower's natural frequency was found to control the tower design and the bearing capacity constraint was found to control the foundation design 5) relaxing or tightening the limit on the natural frequency will result in the greatest benefit or penalty, respectively, on the optimum solution.

Dans la perspective du présent scénario énergétique, ce travail de thèse propose une méthodologie qui associe la méthode du pincement à l’analyse exergétique de manière à dépasser leurs limitations individuelles aboutissant à une conception améliorée aux deux niveaux : paramètres opératoires et topologie. Une méthodologie globale, consistant à hybrider les deux méthodes thermodynamiques dans une approche entrelacée avec des règles heuristiques et une optimisation numérique, est donc évoquée. À l'aide de nouveaux critères d'optimisation basés sur l’exergie, l'analyse exergétique est utilisée non seulement pour évaluer les pertes d’exergie mais également pour guider les améliorations potentielles des conditions de fonctionnement et de structure des procédés industriels. En plus, au lieu de considérer uniquement l’intégration de la chaleur pour satisfaire des besoins existants, la méthodologie proposée étend la méthode de pincement pour inclure d’autres formes d’exergie récupérables et exploiter de nouvelles voies de synergie via des systèmes de conversion. Après avoir présenté les lignes directrices de la méthodologie proposée, l’approche est démontrée sur deux systèmes industriels, un procédé d’hydrotraitement de gasoil sous vide et un procédé de liquéfaction de gaz naturel. L’application du cadre méthodologique à des processus réalistes a montré comment ajuster les conditions opératoires de chaque procédé et comment mettre en œuvre des systèmes de conversion générant des économies d’énergie substantielles. / In the perspective of the prevailing and alarming energy scene, this doctoral work puts forward a methodology that couples pinch and exergy analysis in a way to surpass their individual limitations in the aim of generating optimal operating conditions and topology for industrial processes. A global methodology, a hybrid of the two thermodynamic methods in an intertwined approach with heuristic rules and numerical optimization, is therefore evoked. Using new optimizing exergy-based criteria, exergy analysis is used not only to assess the exergy losses but also to guide the potential improvements in industrial processes structure and operating conditions. And while pinch analysis considers only heat integration to satisfy existent needs, the proposed methodology allows including other forms of recoverable exergy and explores new synergy pathways through conversion systems. After exhibiting the guidelines of the proposed methodology, the entire approach is demonstrated on two industrial systems, a vacuum gasoil hydrotreating process and a natural gas liquefaction process. The application of the methodological framework on realistic processes demonstrated how to adjust each process operating conditions and how to implement conversion systems ensuing substantial energy savings.

This thesis attempts to resolve the contradictory relationship between the ecological merits of wood construction and the significant material intensity of recent free form timber surface structures. The building industry is now adept in the design and construction of freeform surface architecture, however new challenges have been introduced with the environmentally conscious desire to build these structures in wood. Lacking the formal versatility of steel and concrete, wood introduces a great deal of difficulty in the realization of complex form at an architectural scale. Powerful digital design and fabrication tools have recently made it possible to model, analyze and construct these buildings, but at the cost of heavy structural solutions that involve energy intensive fabrication processes and significant material waste. This approach contradicts the ecological benefits of wood, and raises the question of whether it is possible to achieve free and expressive form in timber surface architecture while maintaining an economy of means and material. This question is addressed through the development of a generative design tool for the creation of material conscious free form timber surface architecture. The formation of the tool is informed by the field of computational morphogenesis, which draws from the natural growth processes of biological structures in the virtual synthesis of form. The tool is conceived as a morphogenetic material system, which consists of a generative algorithm that integrates material, structure and form in a single computational process. Specific material saving techniques deployed in the algorithm draw from existing research in timber shell design and material optimization. Established methods in the use of geodesic lines for the structural patterning of wood shells and stress driven material distribution make up the core concepts deployed in the algorithm. The material system is developed, refined and tested through the design and construction of an experimental free form timber lattice.

Sonic boom annoyance is an important technical showstopper for commercial supersonic aircraft operations. It has been proposed that aircraft can be shaped to alleviate sonic boom. Choosing the right aircraft shape reflecting the design requirements is a fundamental and most important step that is usually over simplified in the conceptual stages of design by resorting to a qualitative selection of a baseline configuration based on historical designs and designers perspective. Final aircraft designs are attempted by minor shape modifications to this baseline configuration. This procedure may not yield large improvements in the objectives, especially when the baseline is chosen without a rigorous analysis procedure. Traditional analyses and implementations tend to have a complex algorithmic flow, tight coupling between tools used and computational limitations. Some of these shortcomings are overcome in this study and a diverse mix of tools is seamlessly integrated to provide a simple, yet powerful and automatic procedure for sonic boom minimization. A shape optimization procedure for supersonic aircraft design using better geometry generation and improved analysis tools has been successfully demonstrated. The geometry engine provides dynamic reconfiguration and efficient manipulation of various components to yield unstructured watertight geometries. The architecture supports an assimilation of different components and allows configuration changes to be made quickly and efficiently because changes are localized to each component. It also enables an automatic way to combine linear and non-linear analyses tools. It has been shown in this study that varying atmospheric conditions could have a huge impact on the sonic boom annoyance metrics and a quick way of obtaining probability estimates of relevant metrics was demonstrated. The well-accepted theoretical sonic boom minimization equations are generalized to a new form and the relevant equations are derived to yield increased flexibility in aircraft design process. Optimum aircraft shapes are obtained in the conceptual design stages weighing in various conflicting objectives. The unique shape optimization procedure in conjunction with parallel genetic algorithms improves the computational time of the analysis and allows quick exploration of the vast design space. The salient features of the final designs are explained. Future research recommendations are made.

When a mechanical system is subject to constraints its motion is in some way restricted. In accordance with Newton's second law, motion is a direct result of forces acting on a system; hence, constraint is inextricably linked to force. The presence of a constraint implies the application of particular forces needed to compel motion in accordance with the constraint; absence of a constraint implies the absence of such forces. The objective of this thesis is to formulate a comprehensive, consistent, and concise method for identifying a set of forces needed to constrain the behavior of a mechanical system modeled as a set of particles and rigid bodies. The goal is accomplished in large part by expressing constraint equations in vector form rather than entirely in terms of scalars. The method developed here can be applied whenever constraints can be described at the acceleration level by a set of independent equations that are linear in acceleration. Hence, the range of applicability extends to servo-constraints or program constraints described at the velocity level with relationships that are nonlinear in velocity. All configuration constraints, and an important class of classical motion constraints, can be expressed at the velocity level by using equations that are linear in velocity; therefore, the associated constraint equations are linear in acceleration when written at the acceleration level. Two new approaches are presented for deriving equations governing motion of a system subject to constraints expressed at the velocity level with equations that are nonlinear in velocity. By using partial accelerations instead of the partial velocities normally employed with Kane's method, it is possible to form dynamical equations that either do or do not contain evidence of the constraint forces, depending on the analyst's interests.

Steel has become widespread and now it can be accepted as the candidate of being main material for the structural systems with its excellent properties. Its high quality, durability, stability, low maintenance costs and opportunity of fast construction are the advantages of steel. The correct use of the material is important for steel&rsquo / s bright prospects. The need for weight optimization becomes important at this point. Available sources are used economically through optimization. Optimization brings material savings and at last economy. Optimization can be achieved with different ways. This thesis investigates the effect of the appropriate choice of column orientation on minimum weight design of steel frames. Evolution strategies (ESs) method, which is one of the three mainstreams of evolutionary algorithms, is used as the optimizer in this study to deal with the current problem of interest. A new evolution strategy (ES) algorithm is proposed, where design variables are considered simultaneously as cross-sectional dimensions (size variables) and orientation of column members (orientation variables). The resulting algorithm is computerized in a design optimization software called OFES. This software has many capabilities addressing to issues encountered in practical applications, such as producing designs according to TS-648 and ASD-AISC design provisions. The effect of column orientations is numerically studied using six examples with practical design considerations. In these examples, first steel structures are sized for minimum weight considering the size variables only, where orientations of the column members are initially assigned and kept constant during optimization process. Next, the weight optimum design of structures are implemented using both size and orientation design variables. It is shown that the inclusion of column orientations produces designs which are generally 4 to 8 % lesser in weight than the cases where only size variables are employed.

In this thesis, the optimum design algorithm is presented for reinforced concrete special moment frames. The objective function is considered as the total cost of reinforced concrete frame which includes the cost of concrete, formwork and reinforcing steel bars. The cost of any component is inclusive of material, fabrication and labor. The design variables in beams are selected as the width and the depth of beams in each span, the diameter and the number of longitudinal reinforcement bars along the span and supports. In columns the width and the depth of the column section, the number and the diameter of bars in x and y directions are selected as design variables. The column section database is prepared which includes the width and height of column section, the diameter and the number of reinforcing bars in the column section is constructed. This database is used by the design algorithm to select appropriate sections for the columns of the frame under consideration. The design constraints are implemented from ACI 318-05 which covers the flexural and shear strength, serviceability, the minimum and maximum steel percentage for flexural and shear reinforcement, the spacing requirements for the reinforcing bars and the upper and lower bound requirements for the concrete sections. The optimum design problem formulated according to ACI 318-05 provisions with the design variables mentioned above turns out to be a combinatorial optimization problem. The solution of the design problem is obtained by using the harmony search algorithm (HS) which is one of the recent additions to meta-heuristic optimization techniques which are widely used in obtaining the solution of combinatorial optimization problems. The HS algorithm is quite simple and has few parameters to initialize and consists of simple steps which make it easy to implement. Number of design examples is presented to demonstrate the efficiency and robustness of the optimum design algorithm developed.