This thesis is a numerical study of the coupled Burgers equation. The coupled Burgers equation is motivated by the Boussinesq equations that are often used to model the thermal-fluid dynamics of air in buildings. We apply Finite Element Methods to the coupled Burgers equation and conduct several numerical experiments. Based on these results, the Group Finite Element method (GFE) appears to be more stable than the standard Finite Element Method. The design and implementation of controllers heavily relies on rapid solutions to complex models such as the Boussinesq equations. Thus, we further examine the feasibility and efficiency of the Proper Orthogonal Decomposition (POD) for the coupled Burgers equation. Using POD, we reduce the system to a "minimal" number of ODE's and conduct numerous numerical studies comparing the POD and GFE method. Further numerical experiments consider an application where the dynamics are projected on a POD basis and then the governing parameters of the system are varied. / Master of Science

Traveling to space requires a great deal of energy. This then limits the size of spacecraft accessible to transport to space. An optimization of a flexible tube that could be used as a satellite deployable structure was conducted by varying the cross section of the tube and its composite material properties. The material properties manipulated include the selection of a fiber, matrix, filler volume ratio, and orientation. HEEDS, a commercially available software, conducts the optimization process using the SHERPA algorithm. In the optimization, the finite element code, ABAQUS, iteratively performs two simulations. First, ABAQUS determines the stress distribution along the tube when wrapping the tube in its stored configuration. Second, ABAQUS finds the first natural frequency of the deployed structure. The objective function driving the optimization process is minimizing the weight and strain energy of the tube to create a light but highly flexible tube. This provides benefits of avoiding a violent deployment and lowering the dynamic response of the spacecraft during deployment. Three optimizations were performed with 1000 iterations each, using different initial geometries. While all three produce very similar results, one design converges to a clear best result. Using the best design, a series of deployment simulations are performed, using different boundary conditions to represent various scenarios. These boundary conditions include a free body dynamic response to deployment, a restricted response to only allow for rotation about the direction of deployment, and an increased damping deployment. Energy is dissipated differently comparing the results, showing that the most realistic case, being a free body deployment, has the lowest effect on the system. The spacecraft can dissipate energy by oscillating in the other axis. While damping does reduce the settling time for the deployed tube, there is notable oscillation in the middle of the tube seen in the transient state. / Master of Science / The size and weight of a spacecraft is important when considering its feasibility to launch to space. By creating a spacecraft that can be stowed in a small configuration and deploy, new parameters arise, thus new designs can be created. This paper observes using different shapes and materials to create an expandable tube, providing a support structure for a satellite or spacecraft. HEEDS, an optimization software, uses the SHERPA code to select the shape of the cross section and create a composite material. Composite material selection is comprised of a fiber, a matrix, a filler volume ratio, and an angle for the fibers to lay at. After selecting these parameters, HEEDS calls a finite element software, ABAQUS, to perform two simulations. The first simulation wraps the tube around a central hub and observes stress at each timestep. The second simulation finds the first mode of natural frequency of the deployed model. Using user defined constraints that revolve around the safety factor of the stress and minimum frequency, each iteration is marked as feasible or infeasible. An objective function is used to evaluate the best design. This paper focuses on minimizing the weight of the tube and the strain energy inside of the objective function. By minimizing the strain energy, the tube will deploy less violently and cause less rotation due to deployment. HEEDS performs 1000 iterations on three different initial geometry. While there are similar defining factors of each final design, there is one design that is better than the other two. Using the best design, ABAQUS runs three different deployment simulations to observe the deployment behavior. These scenarios encompass different dynamic simulations and show that a realistic deployment where the spacecraft is free to rotate on all axis is safe.

Spännhjulen på den av BAE Systems Hägglunds tillverkade midjestyrda bandvagn BvS10 har nått sin belastningsgräns, eftersom vagnens vikt numera uppgår till 16 000 kg. I det här arbetet undersöks om det skulle vara möjligt att tillverka ett hjul dimensionerat för 17 000 kg, utan att ändra hjulets diameter, lagring eller bandstyrning. Eftersom hjulet även borde gå att använda som bärhjul tas viss hänsyn till att vikten bör hållas nere. Huvudspåret för undersökningen är att hjulen ska gjutas i aluminium och därför görs försök att utforma geometrin för att utnyttja gjutmetodens fördelar till fullo. Relevanta lastfall tas fram för hjulen som sedan beräknas med hjälp av finita element-metoden för att undersöka om de besitter tillräckliga hållfasthetsegenskaper. Undersökningen visar att det borde gå att tillverka aluminiumhjul som kombinerar tillräcklig hållfasthet med de geometriska kraven, som dessutom inte behöver väga mer än nuvarande hjul. Hjulens slutgiltiga design är relativt simpel vilket öppnar upp för möjligheten att svarva fram hjulen istället för att gjuta dem. / The tension wheel on the BAE Systems Hägglunds BvS10 has reached its load carrying limit. The cause of this is the current vehicle weight now reaching 16 000 kg. This report examines the possibility to increase the load carrying capability of the tension wheel so that it will withstand the forces applied from a vehicle weighing 17 000 kg. No changes are to be made regarding the wheels outer diameter, bearing or track guide. The wheel should also be able to see use as a road wheel, which means that the weight of the wheel should be held at a minimum. The primary approach is to make the wheel out of cast aluminium. This dictates that efforts should be made to take full advantage of the benefits of different casting methods, when designing the wheel geometry. Finite element analysis for relevant load cases is performed on the wheels to see if they possess the required mechanical properties. The results indicate that it is possible to produce aluminium wheels that combine sufficient mechanical strength with the geometrical requirements. The study also shows that the weight of these wheels would be comparable or only slightly higher than the weight of the current wheels. The final design of the wheels suggested is relatively simple, which provides the possibility to produce it using lathe machining instead of casting.

Ett självständigt arbete på grundnivå inom produktutveckling av kälkhockeykälken / An independent degree project in product development of the sledge hockey sledge

Cette thèse traite de la modélisation numérique de la réponse vibro-acoustique de structures sandwiches-composites avec matériaux viscoélastiques intégrés soumises à différents types d’excitations mécaniques et acoustiques. Dans une première phase, nous avons utilisé une approche de synthèse modale pour calculer les principaux indicateurs vibro-acoustiques de la structure : la vitesse quadratique, la puissance rayonnée, la perte par transmission…Ensuite, l’intégrale de Rayleigh a été exploitée pour calculer la puissance rayonnée de chaque structure. L’obstacle majeur que nous avons alors surmonté, était de gérer efficacement la dépendance en fréquence des propriétés de la couche viscoélastique dans l’approche de synthèse modale. Dans une second phase, en partant du champ vibratoire calculé dans la première étape, nous avons développé une méthode hybride FEM-TMM (méthode des éléments finis – méthode de matrices de transfert) pour prédire avec précision et en un temps de calcul acceptable, et jusqu’en hautes fréquences, les principaux paramètres de conception vibro-acoustique de ces structures, notamment l’amortissement équivalent et les nombres d’ondes suivant les deux directions spatiales x et y de propagation de l’onde acoustique. Les validations numériques que nous avons effectuées, montrent bien la robustesse de l'algorithme que nous avons développé. Ce dernier reste toutefois limité à des structures planes. Dans une troisième phase de ce travail, une étude paramétrique sur l’effet de l’emplacement et de la forme de la couche viscoélastique a été réalisée. Cette étude a été faite en se servant de la méthode hybride FEM-TMM pour calculer la réponse acoustique (puissance transmise et perte par transmission).

ABSTRACTAs the industry becomes more efficient all the time and the budgets narrower the demand forsafety equipment has also increased to minimize downtime and injuries. With the efficienciesgrowing in Swedish industry the supplier of this project has also seen an increased demand forsafety equipment. One product that has increased is their “Industryprotection” a productcreated to protect forklifts from colliding with walls in industry spaces.The purpose of this project is to generate a concept for a new design of the“Industryprotection”. It also involves creating a static FEM analysis of a collision between aforklift and the “Industryprotection”. The goal for the analysis is to create a steady modelwhich easily could be applied to different concepts. A study of the different calculationsmethods will also be executed.The project is split into two phases one conceptual phase and one calculation phase, the laststep of the project is to analyze the recommended concept versus the current one using theanalysis created.The work is limited to only go as far as a recommended concept is created, the dimensioning,final drawing, manufacturing preparation and validating is given to the supplier of the projectThe theory for this project is gathered from studying literature from market evaluation,computer aided calculation and design process. After theory for each phase of the project hasbeen gathered they have been modified to suit the phase. Also a large study of everyparameter in the FEM analysis has been executed to secure a stable model for the analysis.The output of the model became a simple and steady model which easily could be applied todifferent concepts. The study of different calculation methods of the model generated a fivetime increase of the amount of momentum the “Industryprotection” could endure. / SAMMANFATTNINGDå industrin hela tiden utvecklas mot att bli mer effektiv och budgeterna blir allt snävareställs också högre krav på att minimera driftstopp och skador. I takt med att arbetet aveffektiviseringar inom svensk industri har ökat har uppdragsgivaren EAB, sett en störreefterfrågan av säkerhetsutrustning .En kategori som har ökat är deras industriskydd som ärskapat för skydda väggar i industrilokaler.Syftet med projektet är att generera ett rekommenderat koncept över hur ett nytt industriskyddkan konstrueras. Vidare skall även en statisk analysmodell skapas över ett kollision scenariomellan truck och industriskyddet. Målet med analysen är att skapa en stabil modell som enkeltkan appliceras på olika koncept. Vidare skall även en studie kring olika beräkningsmetoderutföras.Arbetet är uppdelat i två olika faser en konceptfas samt en beräkningsfas. Som sista steg iprojektet används den skapade beräkningsmodellen för att utvärdera det rekommenderadekonceptetProjektet är begränsat till det stadie där ett rekommenderat koncept är framtaget. Slutligdimensionering, detaljkonstruktion, tillverkningsberedning och verifiering överlämnas tilluppdragsgivaren.Teorin kring projektet har samlats in genom att studera relevant litteratur inommarknadsundersökningar, datorstödberäkningshjälp samt konstruktionsprocessen. Efterstudien har teori anpassats och applicerats för detta specifika projekt. Under beräkningsfasenhar en omfattande studie kring samtliga parametrar utförts för att skapa en stabilberäkningsmodell.Utfallet av modellen blev en enkel och stabil beräkningsmodell som kan appliceras på olikakoncept med goda resultat. Utvärdering av beräkningsmetoder genererade en ökning av denabsorberade energin med en faktor på fem.

The present thesis shows the analysis, calibration, and application of the stress modified criticai strain criterion to predict ductile failure for an A285 steel. To obtain the mechanical behavior of the material, experimental tests were carried out by implementation of 5 different types of geometries: smooth round bar, notched round bar (R=1 , 2, 3 mm), and, deep and shallow cracked SE(B) specimens. Then, for the calibration process of the mechanical properties finite element models were generated, using 30 solid elements with 8 nodes (C308), matching the geometry and the properties of the tested specimens. To calibrate the elastoplastic behavior was used the experimental and numerical response obtained from the smooth and notched round bar specimens; and, for the damage calibration was used the responses obtained from both deep and shallow crack SE(B) specimens. Once the mechanical properties were calibrated, then there were obtained the SMSC criterion factors represented by the equation ..... and, the damage condition which is represented by the displacement at failure (.......) and exponential factor (....). This calibrated model was able to recover the SE(B) experimental responses that validate the use of the characterized material in a complex structure. Then, the fully characterized material was applied in two pipelines which have externai initial circumferential elliptical crack; being the first one pipe with shallow crack and the second one with deep crack. Finally, both pipes were submitted to tension loads to predict the ductile damage behavior, obtaining the necessary load to the crack start growing, and the evolution of the failure. / A presente dissertação apresenta o processo de análise, calibração e aplicação das propriedades mecânicas, incluindo o comportamento elastoplástico e de dano, para o aço A285, utilizando o critério \"Stress modified criticai strain\" (SMCS). Para obter o comportamento mecânico do material, testes experimentais foram realizados com a implementação de 5 tipos diferentes de geometrias: barra cilíndrica sem entalhe, barra cilíndrica com entalhe (R = 1, 2, 3 mm) e corpos de prova SE(B) com trinca inicial profunda e rasa. Para o processo de calibração das propriedades mecânicas foram gerados modelos de elementos finitos, utilizando elementos sólidos 30 com 8 nós (C3D8), que representam de forma adequada a geometria e as propriedades dos corpos de prova testados. Para calibrar o comportamento elastoplástico e iniciação do dano, utilizou-se a resposta experimental e numérica obtida para as amostras de barra cilíndrica com e sem entalhe; e, para a calibração da evolução do dano, foram utilizadas as respostas obtidas para os espécimes SEB de trincas profundas e rasa. Este modelo calibrado foi capaz de recuperar as respostas experimentais dos corpos de prova SE(B), o que valida o uso do material caracterizado em uma estrutura complexa. Uma vez calibradas as propriedades mecânicas, foram obtidos os fatores do critério SMSC representados pela equação ....... , e, a condição de dano que é representada pelo deslocamento na falha .... e o fator de amolecimento exponencial .... . Depois, o material totalmente caracterizado foi aplicado em dois dutos que possuem trinca elíptica circunferencial inicial externa; sendo o primeiro tubo com trinca superficial e o segundo com trinca profunda. Finalmente, ambos os tubos foram submetidos a cargas de tensão para prever o comportamento do dano dúctil, obtendo a carga necessária para o início do crescimento da trinca e a evolução da falha.

In this thesis, we study a numerical tool named multi-mesh method within the framework of the adaptive finite element method. The aim of this method is to minimize the size of the linear system to get the optimal performance of simulations. Multi-mesh methods are typically used in multi-physics problems, where more than one component is involved in the system. During the discretization of the weak formulation of partial differential equations, a finite-dimensional space associated with an independently refined mesh is assigned to each component respectively. The usage of independently refined meshes leads less degrees of freedom from a global point of view. To our best knowledge, the first multi-mesh method was presented at the beginning of the 21st Century. Similar techniques were announced by different mathematics researchers afterwards. But, due to some common restrictions, this method is not widely used in the field of numerical simulations. On one hand, only the case of two-mesh is taken into scientists\' consideration. But more than two components are common in multi-physics problems. Each is, in principle, allowed to be defined on an independent mesh. Besides that, the multi-mesh methods presented so far omit the possibility that coefficient function spaces live on the different meshes from the trial and test function spaces. As a ubiquitous numerical tool, the multi-mesh method should comprise the above circumstances. On the other hand, users are accustomed to improving the performance by taking the advantage of parallel resources rather than running simulations with the multi-mesh approach on one single processor, so it would be a pity if such an efficient method was only available in sequential. The multi-mesh method is actually used within local assembling process, which should not be conflict with parallelization. In this thesis, we present a general multi-mesh method without the limitation of the number of meshes used in the system, and it can be applied to parallel environments as well. Chapter 1 introduces the background knowledge of the adaptive finite element method and the pioneering work, on which this thesis is based. Then, the main idea of the multi-mesh method is formally derived and the detailed implementation is discussed in Chapter 2 and 3. In Chapter 4, applications, e.g. the multi-phase flow problem and the dendritic growth, are shown to prove that our method is superior in contrast to the standard single-mesh finite element method in terms of performance, while accuracy is not reduced.

In this thesis I argue that science fiction is not a genre exclusively made up of written texts but a community or series of communities. I examine the science fiction community's engagement with questions of femeninity, masculinity, sex and sexuality over the past seventy years, that is from 1926 until 1996. My examination of this engagement is centred on the battle of the sexes, the lives of James Tiptree, Jr. and the Award named in Tiptree's honour. I make connections between contemporary feminist science fiction and the earliest pulp science fiction engagements with sex and sexuality.

Der Vortrag demonstriert am Beispiel eines Designraumes die Kombination aus einem FE-Werkzeug mit parametrischen Untersuchungen.