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At Saab Training & Simulation, there are set strength requirements in the form of quality testing for its products through vibration testing. This is done to ensure the quality of the products, but the vibration machine can only test products up to a set weight limit. The purpose is to investigate the possibility of weight reduction for a fixture used in vibration testing through simulation, with the goal of testing heavier products. As part of this, the tools of topology optimization and design of experiments have been explored in an iterative process to develop design proposals. These design proposals have been evaluated through finite element analysis. The result is the development of three design proposals, out of which the proposal that advanced is presented with a weight reduction of 32,41%.

Wind turbines have been utilized for centuries to harness energy from the wind. Commercial wind turbine blades are typically made from composite materials, which are difficult to recycle, leading to blades ending up in landfills at the end of their lifecycle. Additionally, these materials contribute to microplastic pollution. In response to growing environmental concerns, there has been an increased focus on addressing such issues. The Swedish company SeaTwirl AB develops offshore vertical-axis wind turbines (VAWT), and this study focuses on optimizing the weight of a blade from a new 10-15 MW VAWT concept using steel as the material. Steel has long been recyclable, making it an interesting material for wind turbine blades. The specific steel used in this study is the ultra-high-strength steel "Strenx 1300" from SSAB, which is not only extremely durable but is also expected to be fossil-free by 2026, by implementation of the manufacturing technology HYBRIT. The study found that a single blade made from Strenx 1300, when designed and optimized for 35 years of operational use, would weigh approximately 193.4 tonnes and would require 6016.8 meters of welds with a fatigue class of FAT 125. A rough estimation of the weight of a fiberglass VAWT of the same size resulted in approximately 300 tonnes. Therefore, this study concludes that it may be feasible to construct a commercially competitive VAWT blade using environmentally friendly, fossil-free steel. This approach would make wind energy a more sustainable energy source without the problems of recyclability and microplastic pollution. / Vindkraftverk har använts i århundraden för att utvinna energi från vinden. Kommersiella vindkraftverksblad tillverkas vanligtvis av kompositmaterial, vilket är svårt att återvinna och leder till att bladen hamnar på soptippar vid slutet av deras livscykel. Dessutom bidrar dessa material till mikroplastföroreningar. Som svar påväxande miljöproblem har det därför blivit ett ökat fokus på denna typ av frågor. Det svenska företaget SeaTwirl AB utvecklar vertikalaxliga vindkraftverk (VAWT) för offshore-användning, och denna studie fokuserar på att optimera vikten av ett blad från ett nytt 10-15 MW VAWT-koncept med stål som material. Stål har länge varit återvinningsbart, vilket gör det till ett intressant material för vindkraftverksblad. Det specifika stål som används i denna studie är det höghållfasta stålet "Strenx1300" från SSAB, som inte bara är extremt hållbart, men också förväntas bli fossilfritttill 2026, tack vare implementeringen av tillverkningsteknologin HYBRIT. Studien visade att ett enskilt blad tillverkat av Strenx 1300, när det är utformat och optimerat för 35 års driftstid, skulle väga cirka 193,4 ton och kräva 6016,8 meter svets med en utmattningsklass FAT 125. En grov uppskattning av vikten av en VAWT av samma storlek i glasfiber resulterade i cirka 300 ton. Därför drar denna studie slutsatsen att det kan vara möjligt att konstruera ett kommersiellt konkurrenskraftigt VAWT-blad med miljövänligt, fossilfritt stål. Detta tillvägagångssätt skulle göra vindenergi till en mer hållbar energikälla utan problemen associerade med återvinning och mikroplaster.

[pt] Otimização topológica (OT) é uma técnica de otimização estrutural capaz de gerar projetos incrivelmente detalhados para uma grande gama de problemas. No entanto, a maioria dos trabalhos de OT presentes na literatura está focada em problemas de minimização de flexibilidade, que não consideram a resistência dos materiais durante o processo de otimização, levando a soluções que não satisfazem limites de falha do material. Neste trabalho, focamos em problemas de OT baseados em tensão no qual introduzimos restrições de tensão no problema de otimização, para garantir a integridade estrutural do projeto final. A formulação de tensão de OT nos leva a um problema de engenharia muito mais natural que nos remete à seguinte pergunta: Qual a estrutura mais leve capaz de suportar as cargas as quais será submetida? Para ajudar a responder essa pergunta e para trazer a OT para mais próximo de aplicações reais, neste trabalho foi desenvolvido um sistema computacional em paralelo, baseado em GPU, considerando uma carga que pode variar a sua direção continuamente e capaz de resolver problemas de larga escala. A implementação em GPU apresenta soluções eficientes para os principais problemas de OT de larga escala, como o filtro, o algoritmo de otimização e a solução das equações de equilíbrio. Ao mesmo tempo, ao considerar uma carga variando continuamente que mais se aproxima das condições reais de carregamento usando uma estratégia de pior cenário, obtém-se soluções mais robustas e mais adequadas a aplicações de engenharia. Várias soluções numéricas são apresentadas, incluindo problemas 3D com mais de 45 milhões de restrições de tensão, que demonstram a efetividade das técnicas desenvolvidas neste trabalho. O sistema de larga escala baseado em GPU combinado com as soluções analíticas para a variação contínua de carga, tem o potencial de expandir o uso da OT na engenharia levando a novas e mais eficientes estruturas. / [en] In the field of structural optimization, Topology Optimization (TO) is one of the most general techniques because it is able to generate complex structures with intricate details for a wide range of problems. However, most of the works in TO have focused on compliance-based design that does not consider material strength in the design process leading to structures that do not satisfy material failure requirements. In this work, we focus on the stress-based design approach. We introduce stress constraints in the optimization procedure to guarantee the structural integrity of the final optimized design. This leads to a more natural formulation that addresses a simple engineering question: What is the lightest structure able to withstand its loads? We developed a large-scale GPU-based parallel stress-constrained TO framework considering a continuous range of varying load directions to answer this question and close the gap between TO and practical application. The developed GPU-based C++/CUDA framework efficiently addresses the main challenges of large-scale TO, filtering, optimization algorithm, and the solution of the equilibrium equations, only requiring a moderately affordable GPU hardware. At the same time, we obtain designs that are more suitable for engineering applications by considering a continuous variable range of load directions that more closely resemble real-life service loads using a worstcase analytical approach. We present several numerical results, including 3D problems with over 45 million local constraints providing detailed optimal structures that demonstrate the capabilities of the techniques developed in this work. The large-scale GPU framework, combined with the analytical solutions for continuously varying load cases, has the potential to expand the applications of TO techniques leading to improved engineering designs.

[pt] Materiais feitos com microestruturas arquitetadas possuem propriedades mecânicas ajustáveis e podem ser usados na obtenção de estruturas leves e, ao mesmo tempo, com máxima rigidez. Em estruturas celulares formadas por rede de treliças, por exemplo, pode-se variar o tipo de topologia e porosidade de modo que o material seja eficientemente distribuído no domínio de projeto. Devido às geometrias complexas destas estruturas, projetá-las usando ferramentas de desenho assistido por computador é uma tarefa desafiadora. Neste trabalho, foi desenvolvida uma modelagem paramétrica no programa Rhinoceros usando a extensão Grasshopper para auxiliar na construção de modelos de sólidos celulares com estrutura interna treliçada de densidade variável. A modelagem paramétrica desenvolvida permite definir a topologia e o diâmetro das barras das treliças que simplificam em muito a geração de modelos de sólidos porosos. Modelos de microestrutura foram gerados e fabricados em poliamida 12 por meio de sinterização seletiva a laser para avaliar se é viável imprimir as treliças a partir dos parâmetros estabelecidos. O problema de uma viga biapoiada com carga concentrada no centro foi resolvido utilizando-se o método de otimização topológica e o campo de densidades foi usado para geração do modelo de densidade variável. Considerando a mesma massa final dos modelos otimizados, modelos com densidade constante foram gerados e fabricados juntamente com os modelos de densidade variável. Foram realizadas análises experimentais por meio de ensaios de flexão em três pontos e os resultados mostram que a solução usando densidade variável tem um grande aumento da rigidez quando comparadas com as soluções com densidade uniforme. / [en] Materials made with architected microstructures present tunable mechanical properties and can be used to obtain light structures and, at the same time, with maximum stiffness. In lattice structures, for example, the type of topology and porosity can be varied so that the material is efficiently distributed in the design domain. Due to the complex geometries of these structures, designing them using computer-aided design tools is a challenging task. In this work, a parametric modeling was developed in the Rhinoceros program using the Grasshopper extension to assist in the construction of models of lattice structures with varying truss diameters. The developed parametric modeling allows defining the topology and the diameter of the truss bars, which greatly simplifies the generation of models of porous solids. Microstructure models were generated and manufactured in polyamide 12 through selective laser sintering to assess whether it is feasible to print the trusses from the established parameters. The problem of a simply supported beam with a concentrated load at the center was solved using the topology optimization method and the density field was used to generate the variable density model. Considering the same final mass of the optimized models, models with constant density were generated and manufactured together with the models with variable density. Experimental analyzes were carried out using three-point bending tests and the results show that the solution using variable density has a large increase in stiffness when compared to solutions with uniform density.

[pt] Sabe-se que a maioria das estruturas reais estão sujeitas à diferentes casos de carregamentos, relacionadas à diferentes solicitações estruturais e à ação de forças naturais, como ventos e ondas. Neste contexto, é importante levar em consideração o efeito da maior quantidade de cenários possíveis que possam atuar em uma estrutura ao realizar um estudo de otimização topológica. A maneira tradicional de solução deste tipo de probema envolve uma análise caso a caso dos cenários, o que no contexto de um algoritmo de otimização estrutural requer a solução de um problema de elementos finitos para cada cenário em cada passo do algoritmo, ficando limitada pelo elevado custo computacional associado. Esta limitação abre espaço para abordagens baseadas em redução de dimensões como a aproximação estocástica e a decomposição em valores singulares. Este trabalho verifica a viabilidade do uso destes dois métodos na solução de problemas de otimização topológica estrutural com muitos casos de carga. Duas aplicações são apresentadas, otimização robusta e o problema de cargas dinâmicas usando o método do carregamento estático equivalente. Com isso, situações envolvendo carregamentos mais complexos podem ser estudadas através de algoritmos eficientes de otimização topológica. Para ambos os casos, são mostrados resultados comparando os resultados obtidos através da metodologia desenvolvida neste trabalho com resultados da literatura. / [en] It is known that most real structures are subject to different loading scenarios, related to different structural solicitations and the action of natural forces, such as winds and sea waves. In this context, it is important to consider the effect of the largest number of possible scenarios that can act on a structure when performing a topology optimization study. The traditional way of solving this type of problem involves a case-by-case analysis of the scenarios, which in the context of a structural optimization algorithm requires the solution of one finite element problem for each scenario and at each step of the algorithm, being limited by the high associated computational cost. This limitation leave room for approaches based on dimenson reduction such as stochastic approximation and decomposition into singular values. This work verifies the feasibility of using these two approaches to solve structural topology optimization problems with many load cases. Two applications are presented, robust optimization and the problem of dynamic loads using the equivalent static loading method. Thus, situations involving more complex loads can be studied through efficient topology optimization algorithms. For both cases, comparisons are established between the results obtained through the methodology developed in this work and the ones from the literature.

This project was conducted as a case study at Öhlins Racing AB, a manufacturer of suspension systems for automotive applications. Öhlins usually manufacture their components by traditional methods such as forging, casting, and machining. The project aimed to investigate how applicable Additive Manufacturing (AM) is to manufacture products for suspension systems to add value to suspension system components. For this, a proof of concept was designed and manufactured. The thesis was conducted at Öhlins in Upplands Väsby via the consultant firm Combitech.  A product catalog was searched, screened, and one part was selected. The selected part was used as a benchmark when a new part was designed for AM, using methods including Topology Optimization (TO) and Design for Additive Manufacturing (DfAM). Product requirements for the chosen part were to reduce weight, add functions, or add value in other ways.  Methods used throughout the project were based on traditional product development and DfAM, and consisted of three steps: Product Screening, Concept Development, and Part Design. The re-designed part is ready to be manufactured in titanium by L-PBF at Amexci in Karlskoga.  The thesis result shows that at least one of Öhlin's components in their product portfolio is suitable to be chosen, re-designed, and manufactured by AM. It is also shown that value can be added to the product by increased performance, in this case mainly by weight reduction. The finished product is a fork bottom, designed with hollow structures, and is ready to print by L-PBF in a titanium alloy.

La conception assistée par ordinateur (CAO), les effets visuels, la robotique et de nombreux autres domaines tels que la biologie computationnelle, le génie aérospatial, etc. reposent sur la résolution de problèmes mathématiques. Dans la plupart des cas, des méthodes de calcul sont utilisées pour résoudre ces problèmes. Le choix et la construction de la méthode de calcul ont un impact important sur les résultats et l'efficacité du calcul. La structure du problème peut être utilisée pour créer des méthodes, qui sont plus rapides et produisent des résultats qualitativement meilleurs que les méthodes qui n'utilisent pas la structure. Cette thèse présente trois articles avec trois nouvelles méthodes de calcul s'attaquant à des problèmes de simulation et d'optimisation contraints par des équations aux dérivées partielles (EDP). Dans le premier article, nous abordons le problème de la dissipation d'énergie des solveurs fluides courants dans les effets visuels. Les solveurs de fluides sont omniprésents dans la création d'effets dans les courts et longs métrages d'animation. Nous présentons un schéma d'intégration temporelle pour la dynamique des fluides incompressibles qui préserve mieux l'énergie comparé aux nombreuses méthodes précédentes. La méthode présentée présente une faible surcharge et peut être intégrée à un large éventail de méthodes existantes. L'amélioration de la conservation de l'énergie permet la création d'animations nettement plus dynamiques. Nous abordons ensuite la conception computationelle dont le but est d'exploiter l'outils computationnel dans le but d'améliorer le processus de conception. Plus précisément, nous examinons l'analyse de sensibilité, qui calcule les sensibilités du résultat de la simulation par rapport aux paramètres de conception afin d'optimiser automatiquement la conception. Dans ce contexte, nous présentons une méthode efficace de calcul de la direction de recherche de Gauss-Newton, en tirant parti des solveurs linéaires directs épars modernes. Notre méthode réduit considérablement le coût de calcul du processus d'optimisation pour une certaine classe de problèmes de conception inverse. Enfin, nous examinons l'optimisation de la topologie à l'aide de techniques d'apprentissage automatique. Nous posons deux questions : Pouvons-nous faire de l'optimisation topologique sans maillage et pouvons-nous apprendre un espace de solutions d'optimisation topologique. Nous appliquons des représentations neuronales implicites et obtenons des résultats structurellement sensibles pour l'optimisation topologique sans maillage en guidant le réseau neuronal pendant le processus d'optimisation et en adaptant les méthodes d'optimisation topologique par éléments finis. Notre méthode produit une représentation continue du champ de densité. De plus, nous présentons des espaces de solution appris en utilisant la représentation neuronale implicite. / Computer-aided design (CAD), visual effects, robotics and many other fields such as computational biology, aerospace engineering etc. rely on the solution of mathematical problems. In most cases, computational methods are used to solve these problems. The choice and construction of the computational method has large impact on the results and the computational efficiency. The structure of the problem can be used to create methods, that are faster and produce qualitatively better results than methods that do not use the structure. This thesis presents three articles with three new computational methods tackling partial differential equation (PDE) constrained simulation and optimization problems. In the first article, we tackle the problem of energy dissipation of common fluid solvers in visual effects. Fluid solvers are ubiquitously used to create effects in animated shorts and feature films. We present a time integration scheme for incompressible fluid dynamics which preserves energy better than many previous methods. The presented method has low overhead and can be integrated into a wide range of existing methods. The improved energy conservation leads to noticeably more dynamic animations. We then move on to computational design whose goal is to harnesses computational techniques for the design process. Specifically, we look at sensitivity analysis, which computes the sensitivities of the simulation result with respect to the design parameters to automatically optimize the design. In this context, we present an efficient way to compute the Gauss-Newton search direction, leveraging modern sparse direct linear solvers. Our method reduces the computational cost of the optimization process greatly for a certain class of inverse design problems. Finally, we look at topology optimization using machine learning techniques. We ask two questions: Can we do mesh-free topology optimization and can we learn a space of topology optimization solutions. We apply implicit neural representations and obtain structurally sensible results for mesh-free topology optimization by guiding the neural network during optimization process and adapting methods from finite element based topology optimization. Our method produces a continuous representation of the density field. Additionally, we present learned solution spaces using the implicit neural representation.

Die neuen Fertigungsmöglichkeiten durch die Additive Fertigung ermöglicht es nicht nur topologisch neuartige Bauteile herzustellen, sondern auch Bauteile mit inneren Strukturen zu versehen, die der Bauteilbelastung angepasst sind oder anderen Funktionen Freiräume bieten. Ein Ansatz ist es durchlässige innere Strukturen, z. B. Gitterstrukturen (auch als Lattice Strukturen bezeichnet) einzusetzen und durch die damit geschaffenen großen inneren Flächen eine effiziente Bauteilkühlung zu realisieren. Anhand eines einfachen Beispiels wird durch Simulation und Experiment die Wirkung einer solchen Kühlung gezeigt. Als weiteres Anwendungsbeispiel wird der Einsatz verschiedener innere Strukturen zur festigkeitsgerechten Gestaltung gewichtsoptimierter Bauteile vorgestellt. In beiden Fällen wird die Gestaltung mit Hilfe von FE-Modellen experimentell begleitet. / The new manufacturing possibilities offered by additive manufacturing not only allows to produce topologically novel components, but also enables to provide components with internal structures that are adapted to the component load or offer new possibilities for other functions. One approach is to use permeable internal structures, e. g. lattice structures, to realize efficient component cooling through the large internal surfaces created thereby. The effect of such a cooling is demonstrated by simulations and experiments using a simple example. As a further application example, the use of various internal structures for the strength-oriented design of weight-optimized components will be presented. In both cases the design is experimentally accompanied by FE models.

[pt] Este trabalho apresenta aplicações da técnica de otimização topológica para problemas de escoamento com fluidos não Newtonianos, usando o método dos elementos virtuais (VEM) em domínios bidimensionais arbitrários. O objetivo é projetar a trajetória ótima, a partir da minimização da energia dissipativa, de um escoamento governado pelas equações de Navier-Stokes-Brinkman e do modelo não Newtoniano de Carreau-Yasuda. A abordagem de porosidade proposta por (Borrvall e Petersson, 2003) [1] é usada na formulação do problema de otimização topológica. Para resolver este problema numericamente é usado o método VEM, recentemente proposto. A principal característica que diferencia o VEM do método dos elementos finitos (FEM) é que as funções de interpolação no interior dos elementos não precisam ser computadas explicitamente. Isso ocorre porque a integração é feita em funções polinomiais e bases de ordem inferior, permitindo assim uma grande flexibilidade no que diz respeito ao uso de elementos não convexos. Portanto, o cálculo das matrizes e vetores elementares se reduz à avaliação de grandezas geométricas nos contornos desses elementos. Finalmente, são apresentados exemplos numéricos representativos para demonstrar a eficiência do VEM em comparação com o FEM e a aplicabilidade da otimização topológica para esta classe de problemas de escoamento. / [en] This work presents selected applications of topology optimization for non-Newtonian fluid flow problems using the virtual element method (VEM) in arbitrary two-dimensional domains. The objective is to design an optimal layout into a fluid flow domain to minimize dissipative energy governed by the Navier-Stokes-Brinkman and non-Newtonian Carreau-Yasuda model equations. The porosity approach proposed by (Borrvall and Petersson, 2003) [1] is used in the topology optimization formulation. To solve this problem numerically, the recently proposed VEM method is used. The key feature that distinguishes VEM from the standard finite element method (FEM) is that the interpolation functions in the interior of the elements do not need to be computed explicitly. This is because the integration is on lower-order polynomial and basis functions, and there is great flexibility by using a non-convex element. Therefore, the computation of the main element matrices and vectors are reduced to the evaluation of geometric quantities on the boundary of the elements. Finally, several numerical examples are provided to demonstrate the efficiency of the VEM compared to FEM and the applicability of the topology optimization to fluid flow problems.