Este trabalho apresenta a aplicação do Método de Otimização Topológica (MOT) considerando restrição de tensão mecânica em dois problemas de Engenharia: o projeto de estruturas mecânicas sujeitas a restrição de tensão e o projeto da distribuição de material em estruturas constituídas por Materiais com Gradação Funcional (MsGF). O MOT é um método numérico capaz de fornecer de forma automática o leiaute básico de uma estrutura mecânica para que esta atenda a um dado requisito de projeto, como o limite sobre a máxima tensão mecânica no componente. Os MsGF são materiais cujas propriedades variam gradualmente com a posição. Este gradiente de propriedades é obtido através da variação contínua da microestrutura formada por dois materiais diferentes. Neste trabalho o MOT foi implementado utilizando o modelo de material Solid Isotropic Microstructure with Penalization (SIMP) e o campo de densidades foi parametrizado utilizando a abordagem Aproximação Contínua da Distribuição de Material (ACDM). O modelo de material e utilizado em conjunto com um localizador de tensões, de modo a representar as tensões nas regiões com densidade intermediária. O projeto de estruturas tradicionais através do MOT possui dois problemas centrais aqui tratados: o fenômeno das topologias singulares, que consiste na incapacidade do algoritmo de otimização de retirar material de certas regiões da estrutura, onde a tensão mecânica supera o limite de tensão quando os valores da densidade tendem a zero, e o problema do grande número de restrições envolvidas, pois que a tensão mecânica é uma grandeza local e deve ser restrita em todos os pontos da estrutura. Para tratar o primeiro problema é utilizado o conceito de relaxação. Para o segundo são utilizadas duas abordagens: uma é a substituição das restrições locais por uma restrição global e a outra é a aplicação do Método do Lagrangeano Aumentado. Ambas foram implementadas e aplicadas para o projeto de estruturas planas e axissimétricas. No projeto da distribuição de material em estruturas constituídas por MsGF é utilizado um modelo de material baseado na interpolação dos limites de Hashin-Shtrikman. A partir deste modelo as tensões em cada fase são obtidas a partir das matrizes localizadoras de tensão. Para tratar o fenômeno das topologias singulares é proposto um índice estimativo de falha, baseado nas tensões de von Mises em cada fase da microestrutura, que evita tal problema. O grande número de restrições é tratado através da restrição global de tensão. Em ambos os problemas as formulações são apresentadas e sua eficiência é discutida através de exemplos numéricos. / This work presents the Topology Optimization Method (TOM) with stress constraint applied to two Engineering problems: the design of mechanical structures subjected to stress constraint and the design of material distribution in structures made of Functionally Graded Materials (FGMs). The TOM is a numerical method capable of synthesizing the basic layout of a mechanical structure accomplishing to a given design requirement, for example the maximum stress in the structure. The FGMs are materials with spatially varying properties, which are obtained through a continuum change of the microstructuremade of two different materials. In this work, the TOM was implemented with Solid Isotropic Microstructure with Penalization (SIMP) material model and the density field was parameterized with the Continuous Approximations of Material Distribution. To obtain the intermediate density stresses, the material model is applied together with a stress localization matrix. The design of mechanical structures through the TOM has two major problems: the singular topology phenomenon, which is characterized by the optimization algorithm impossibility of removing material from certain regions, where the stress overpasses the limiting stress when the density goes to zero, and the large number of constraints, once the stress is a local value that must be constrained everywhere in the structure. To deal with the first problem, it is applied the \"-realaxation concept, and for the second one two approaches are considered: one is to change the local stress constraint into a global stress constraint and the other is to apply the Augmented Lagrangian Method. Both approaches were implemented and applied to the design of plane and axisymmetric structures. In the design of material distribution in structures made of FGMs a material model based on Hashin-Shtrikman bounds is applied. From this model, stresses in each phase are obtained by the stress localization matrix. To deal with the singular topology phenomenon it is proposed a modified von Mises failure criteria index that avoids such problem. A global stress constraint is applied to deal with the large number of constraints. In both problems formulations are presented and their performance are discussed through numerical examples.

Em sentido geral, a quimiotaxia é o movimento dirigido que desenvolvem alguns seres vivos em resposta aos gradientes químicos presentes no seu ambiente. Uma bactéria é um organismo unicelular que usa a quimiotaxia como mecanismo de mobilização para encontrar os nutrientes de que precisa para sobreviver e para escapar de ambientes nocivos. Evoluída durante milhões de anos pela natureza, a quimiotaxia de bactérias é um processo altamente otimizado de busca e exploração em espaços desconhecidos. Graças aos avanços no campo da computação, as estratégias quimiotácticas das bactérias e sua excelente capacidade de busca podem ser modeladas, simuladas e emuladas para desenvolver métodos de otimização inspirados na natureza que sejam uma alternativa aos métodos já existentes. Neste trabalho, desenvolvem-se dois algoritmos baseados em estratégias quimiotácticas de bactérias: o BCBTOA (Bacterial Chemotaxis Based Topology Optimization Algorithm) e o BCMOA (Bacterial Chemotaxis Multiobjective Optimization Algorithm) os quais são um algoritmo de otimização topológica e um algoritmo de otimização multi-objetivo, respectivamente. O desempenho dos algoritmos é avaliado mediante a sua aplicação à solução de diversos problemas de prova e os resultados são comparados com os de outros algoritmos atualmente relevantes. O algoritmo de otimização multi-objetivo desenvolvido, também foi aplicado na solução de três problemas de otimização de projeto mecânico de eixos. Os resultados obtidos e os analise comparativos feitos, permitem concluir que os algoritmos desenvolvidos são altamente competitivos e demonstram o potencial do processo de quimiotaxia de bactérias como fonte de inspiração de algoritmos de otimização distribuída, contribuindo assim, a dar resposta à constante demanda por técnicas de otimização mais eficazes e robustas. / In general, chemotaxis is the biased movement developed by certain living organisms as a response to chemical gradients present in their environment. A bacterium is a unicellular organism that uses chemotaxis as a mechanism for mobilization that allows it to find nutrients needed to survive and to escape from harmful environments. Millions of years of natural evolution became bacterial chemotaxis a highly optimized process in searching and exploration of unknown spaces. Thanks to advances in the computing field, bacterial chemotactical strategies and its excellent ability in searching can be modeled, simulated and emulated developing bio-inspired optimization methods as alternatives to classical methods. Two algorithms based on bacterial chemotactical strategies were designed, developed and implemented in this work: i) the topology optimization algorithm, BCBTOA (Bacterial Chemotaxis Based Topology Optimization Algorithm) and ii) the multi-objective optimization algorithm, BCMOA (Bacterial Chemotaxis Multiobjective Optimization Algorithm). Algorithms performances were evaluated by their applications in the solution of benchmark problems and the results obtained were compared with other algorithms also relevant today. The BCMOA developed here was also applied in the solution of three mechanical design problems. The results obtained as well as the comparative analysis conducted lead to conclude that the algorithms developed were competitive. This also demonstrates the potential of bacterial chemotaxis as a process in which distributed optimization techniques can be inspired.

Orientador: Francisco de Assis Magalhães Gomes Neto / Tese (doutorado )- Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-22T00:37:54Z (GMT). No. of bitstreams: 1 Senne_ThadeuAlves_D.pdf: 4979548 bytes, checksum: 0317347b212e7649dd09e5d5388e618e (MD5) Previous issue date: 2013 / Resumo: Nos últimos anos, a otimização topológica vem sendo amplamente adotada nas indústrias automotiva e aeroespacial, e no projeto de um tipo especial de estruturas, denominado mecanismo flexível. Grande parte dos trabalhos na área de otimização topológica considera que a estrutura possui uma relação linear entre deformações e deslocamentos, ou seja, supõe-se que os deslocamentos sofridos pela estrutura sejam pequenos. Todavia, para algumas estruturas, essa hipótese não é válida, sendo necessário supor que os deslocamentos são grandes, o que implica numa relação não linear entre deformações e deslocamentos. Nesse caso, dizemos que a estrutura está sob não linearidade geométrica. O objetivo desta tese de doutorado é a obtenção da topologia ótima de estruturas e de mecanismos flexíveis sob não linearidade geométrica através um novo algoritmo de otimização, denominado Programação Linear por Partes Sequencial (PLPS). Este método consiste na resolução de subproblemas de programação linear por partes convexas, onde são introduzidas informações sobre a diagonal da matriz Hessiana da função objetivo. Para acelerar o algoritmo, tais subproblemas são convertidos em problemas de programação linear. Provamos que a PLPS é globalmente convergente a pontos estacionários. Além disso, nossos experimentos numéricos realizados com estruturas e mecanismos flexíveis sujeitos a grandes deslocamentos mostram que a PLPS é eficiente e robusta / Abstract: In the last years, topology optimization has been broadly applied in the automotive and aerospatial industries, and to a special kind of structure, named compliant mechanism. Most papers on topology optimization consider that the structure has a linear relation between strains and displacements, meaning that the displacements of the structure are small. However, for some structures this assumption is not valid, and it is necessary to suppose that the displacements are large, implying in a nonlinear relation between strains and displacements. In this case, we say that the structure is under geometrical nonlinearity. The objective of this doctoral thesis is to obtain the optimum topology of structures and compliant mechanisms under geometrical nonlinearity through a new optimization algorithm, named Sequential Piecewise Linear Programming (SPLP). This method consists in the solution of convex piecewise linear programming subproblems that contain information about the diagonal of the Hessian matrix of the objective function. To speed up the algorithm, these subproblems are converted into linear programming ones. We prove that the SPLP is globally convergent to stationary points. Besides, our numerical experiments with structures and compliant mechanisms under large displacements also show that the SPLP is efficient and robust / Doutorado / Matematica Aplicada - Otimização / Doutor em Matemática Aplicada

Additive manufacturing (AM) is a particularly useful manufacturing method for components designed using topology optimization (TO) since it allows for a greater part complexity than any traditional manufacturing method. However, the AM process potentially leads to anisotropic material properties due to the layer-by-layer buildup of parts and the fast and directional cooling. For Ti6Al4V tensile specimens built using electron beam melting (EBM), it has been observed that flat built specimens show superior strength and elastic moduli compared to top built specimens. Designs with the loading direction parallel to the build layers are therefore expected to show greater reliability. In this thesis a procedure is developed to optimize the AM build orientation considering anisotropic elastic material properties. A transversely isotropic material model is used to represent the in-plane and out-of-plane characteristics of AM produced parts. Two additional design variables are added to the TO formulation in order to control the orientation of the material using a coordinate transformation. Sensitivity analysis for the material direction variables is conducted for compliance as well as maximum von-Mises stress using a -norm stress aggregation function. The procedures for the AM build orientation optimization and stress constraints are implemented in the finite element software TRINITAS and evaluated using a number of examples in 2D and 3D. It is found that the procedure works well for compliance as well as stress but that a combination of these may lead to convergence issues due to contradicting optimal material orientations. An evaluation of the -norm stress aggregation function showed that a single global stress measure in combination with a stress correction procedure works well for most problems given that the mesh is refined enough to resolve the stresses accurately.

[pt] Este trabalho apresenta uma formulação puramente baseada em plasticidade para ser aplicada à otimização topológica. A principal ideia da otimização topológica em mecânica dos sólidos é encontrar a distribuição de material dentro do domínio de forma a otimizar uma medida de performance e satisfazer um conjunto de restrições. Uma possibilidade é minimizar a flexibilidade da estrutura satisfazendo que o volume seja menor do que um determinado valor. Essa é a formulação clássica da otimização topológica, que é vastamente utilizada na literatura. Não obstante fornecer resultados interessantes, condições adicionais devem ser levadas em consideração para viabilizar sua aplicação prática. O projeto estrutural aborda dois aspectos principais: (i) a estrutura não deve colapsar, suportando os carregamentos aplicados (critério de segurança); e (ii) deverá se sujeitar a um valor máximo aceitável de deformação (critério de aceitabilidade). Consequentemente, a otimização topológica clássica deve ser modificada de forma a encontrar a distribuição de material correspondente ao menor volume possível tal que o critério de segurança seja verificado. O referido critério de segurança pode ser definido como limitar as tensões elásticas ao critério de plastificação em todo o domínio. Esta definição resultou em um novo ramo de pesquisa: a otimização topológica com restrições de tensões. Por outro lado, entende-se que o projeto estrutural plástico é preferível quando um projeto ótimo é almejado, uma vez que permite um maior aproveitamento da resistência do material. Dessa forma, este trabalho aborda a incorporação do projeto estrutural plástico à otimização topológica como método mais vantajoso do que a otimização topológica clássica e a com restrições de tensões. A formulação proposta é uma extensão da análise limite, que fornece uma estimativa da carga de colapso de uma estrutura diretamente por meio da programação matemática, assegurando a eficiência computacional da metodologia proposta. De forma a verificar a otimização topológica plástica e comparar a topologia final com as obtidas através da otimização topológica clássica e da com restrição de tensões, são apresentados exemplos numéricos. / [en] This work presents a full plastic formulation to be applied within topology optimization. The main idea of topology optimization in solid mechanics is to find the material distribution within the domain so that it optimizes a performance measure and satisfies a set of constraints. One might seek to minimize the compliance satisfying that the volume is less than a given value. The aforementioned formulation is the standard topology optimization which has been used widely in literature. Although it provides interesting results, additional requirements must be taken into account when practical application is concerned. Structures are designed considering two main aspects: (i) the structure must not collapse, supporting the applied loads (safety criterion); and (ii) its displacements must be lower than a prescribed bound (serviceability criterion). Consequently, the standard formulation shall be modified, finding the material distribution corresponding to the minimum volume such that the safety criterion is met. Said safety criterion may be defined as restraining the elastic stresses to the yield criterion in the entire domain. This definition has resulted in a new branch in this research field: the stress constrained topology optimization. On the other hand, it is understood that the plastic design criterion is preferable when optimization is intended, since it fully exploits the material strength. Therefore, this work addresses the incorporation of the plastic design criterion into topology optimization as a more advantageous method than standard and stress constrained topology optimization methods. The proposed formulation is an extension of limit analysis, which provides an estimative of the collapse load of a structure directly through mathematical programming, ensuring computational efficiency to the proposed methodology. Lastly, numerical examples are shown to verify plastic topology optimization and the final topology is compared with those provided by standard and stress constrained topology optimization methods.

“Development of a solar car body” is a bachelor thesis done at Jönköping University by two students studying mechanical engineering with a focus on product development and design. The project has been done for JU Solar Team, an organization where student develop and build a solar powered electric car with which they then use in the competition Bridgestone World Solar Challenge. The body of the 2019 solar car is made from a carbon fiber monocoque which means that the body and chassis is made from one integrated component. This type of construction is both costly and complex and it has created a lot of trouble in the post processing of the body after it is received from the developer. The following report is explaining a conceptual development process of module-based body construction. The purpose is to simplify the development and allow for easier modification. Furthermore, the aim of the project has been to make it possible to move most of the production in-house at Jönköping University and show a concept that JU Solar Team can use in the development of upcoming solar car projects. Initially the project studied earlier CFD-simulations that has been made on the solar car from 2019 which was used as a basis for dividing the car into different modules. Since the aim was to make it possible to move the production in-house at Jönköping University it was deemed that 3D-printing was a plausible method for this, which the rest of the project was based upon. Conventional product development methods were then used to generate possible solutions that developed into a finished concept. Different types of methods for joining modules together have been explored which meet the defined criteria. Since a low weight that maximizes energy efficiency is essential when designing a car like this, a topology optimization process was used to study where material could be removed. This optimized construction was then verified by studying the static stress in the body, as well as comparing different materials based on weight, maximum stress and safety factors. The project resulted in a topologically optimized and module-based prototype where 30% of the original volume has been removed. The report ends with recommendations of materials and joining techniques as well as comments for further development of upcoming solar car projects. / ”Konceptutveckling av solbilskaross” är ett examensarbete utfört vid Jönköpings Tekniska Högskola inom utbildningen maskinteknik, produktutveckling och design. Projektet har genomförts i samarbete med JU Solar Team, en organisation där studenter utvecklar och tillverkar en soldriven elbil som medverkar i tävlingen Bridgestone World Solar Challenge. 2019 års solbilskaross är av en kolfiber-monocoque konstruktion vilket innebär att kaross och chassi är integrerat i en komponent. Denna konstruktion har skapat begränsningar vid efterhandskonstruktioner samt medfört en komplex och resurskrävande tillverkning. Följande rapport behandlar en konceptutvecklingsprocess av en modulbaserad karosskonstruktion med syfte att underlätta vid produktförändringar samt simplifiera tillverkningen. Vidare har projektets mål även varit att möjliggöra en tillverkning vid Jönköping University och påvisa ett koncept som JU Solar Team kan utnyttja till kommande solbilsprojekt. Inledningsvis i projektet analyserades tidigare CFD-simuleringar av 2019 års solbil vilket lade grunden för modulindelningen av karossen. Med anledning av att möjliggöra en tillverkning vid Jönköping University bedömdes additiv tillverkning vara en tillämplig metod vilket projektet sedermera utgick ifrån. Konventionella produktutvecklingsmetoder tillämpades för att generera lösningsförslag som sedan kunde bedömas och vidareutvecklas. Olika sammanfogningstekniker undersöktes för att studera hur de framtagna modulerna kan monteras baserat på uppsatta kriterier. Eftersom en låg strukturvikt är essentiellt för att maximera energieffektiviteten genomfördes en topologioptimeringsprocess för att studera var material kan avlägsnas. Den optimerade konstruktionen verifierades sedan genom spänningsberäkningar och analys av olika material baserat på vikt, maxspänning och säkerhetsfaktor. Projektet resulterade i ett topologioptimerat och modulbaserat koncept av karossen där 30% av ursprungsvolymen har avlägsnats. Rapporten avslutas med rekommendationer av materialval och sammanfogningsmetod, samt kommentarer för vidare arbete till kommande solbilsprojekt.

This study proposes an approach for solving density-based multi-material topology optimization of cracked structures using Peridynamics. The alternating active-phase algorithm is utilized to transform the multi-material problem into a series of binary phase topology optimization sub-problems. Instead of the conventional mesh-based methods, the Peridynamics theory (PD) is used as a tool to model the behaviour of the materials and solve for the displacement field. The most significant advantage of PD is its ability to model discontinuities in a relatively straightforward manner. Thus, in the present work, the effect of cracks as a discontinuity is investigated on the optimal multi-material topologies. The Solid Isotropic Material with Penalty (SIMP) method is utilized to define the material properties as a function of the design variables. Also, the optimization problem is solved through the Optimality Criteria (OC) approach. The proposed method is compared to the results reported in the literature by executing three numerical examples that investigate the effect of the direction of an interior crack on the optimal topologies. Moreover, the efficiency of the proposed approach is verified by solving several examples where we aim at minimizing the compliance of the structure with and without initial cracks. / Graduate

Ålö is a supplier of products for agricultural tractors. They mainly develop and manufacture front loaders, which traditionally are used to handle hay, but today are employed also in various other application areas. Ålö's products revolve around the front loader, where one of the products is the subframe. The subframes are the mechanical adjustment required for the front loaders to fit different tractors. The design of the subframe can sometimes be difficult to develop since it is limited by the tractor and its attachment points. The Product Integration Department at Ålö wants to investigate a software called Generative Design to facilitate the process of developing new subframes. Three different tractor models with a plate-like geometry are investigated. In addition, a tractor model for which an alternative casting subframe should be developed is investigated. A total of three different methods for the development of subframes are applied. For two of the methods, separate load cases need to be simulated on the two different parts of the subframe. The load cases used for the simulations are obtained by hand calculation. For each method, the time it takes from modelling to optimized design is investigated. In addition, information about other optimization programs is obtained. The result of this project is that the software has too few adjustment possibilities and that the generated design becomes too complex to be successfully used in the development of new subframes with sheet structure. However, an optimized cast design was developed, which provides a weight reduction of 17 kg. The total time of the design process, from the introduction of scanned data to the final subframe concept, is about six hours. Two topology optimization programs are considered better suited for the project and a further study is recommended to explore the software Altaire Inspire. / Ålö är en leverantör av produkter till jordbrukstraktorer. De utvecklar och tillverkar i huvudsak frontlastare som i grunden används för att hantera hö, men som idag har flera olika användningsområden. Ålös produkter kretsar runt frontlastaren där en av produkterna är fundament. Fundamenten är den mekaniska anpassningen som krävs för att frontlastare ska passa till olika traktorer. Designen för fundamenten kan ibland vara svår att ta fram då konstruktionen är begränsad av traktorn och dess infästningspunkter. Avdelningen Produktintegration på Ålö vill undersöka om programmet Generative Design kan underlätta proceduren att ta fram nya fundament. Vid Projektarbetet så utvärderas tre olika traktormodeller där designen ska ha en plåtliknande geometri. Utöver det så undersöks en traktormodell där ett alternativt gjutet fundament ska framtas. Totalt tre olika metoder för framtagning av fundament appliceras. För två av metoderna så krävs det att separata lastfall simuleras på de två olika delarna av fundamentet. Lastfallen som används vid simulering framtas genom handberäkning. En tidsredovisning framtas från modellering till optimerad design och information om andra optimeringsprogram erhålls. Det projektet resulterat i är att Generative Design har för få inställningsmöjligheter och att den genererade designen blir för komplex för att kunna användas vid framtagning av nya fundament som har plåtstruktur. Däremot så har en optimerad gjuten design framtagits vilket ger en viktbesparing på 17 kg jämförd med den nuvarande designen. Tidsredovisningen ger en sammanlagd tid på sex timmar från införandet av inskannad data till konceptfundament. Två topologioptimeringsprogram anses bättre lämpad för projektet och en vidare undersökning rekommenderas inom mjukvaran Altaire Inspire.

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This diploma thesis deals with design of axle carrier for Formula Student. The axle carrier is topologically optimized and additively manufactured with Selective Laser Melting technology. Material for its production is aluminium alloy AlSi10Mg, which has worse mechanical properties than commonly used high-strength alloys. Therefore the aim was, by using topology optimization, to design a component, which would have comparable properties with milled component. The stress strain analysis was carried out by the finite element method and maximum deformation and safety coef-ficients were acquired. The prototype was made and its dimensions were controlled by optical digitization, which proved accuracy of manufacturing. The strength calcu-lations were verified by special testing device and photogrammetry measurement. The load during the tests was 20 % higher than in the analysis and no limit state was observed. This verified its safety and functionality.