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Modelling of elastically coupled rigid bodies is an important research topic in multibody dynamics. We consider the problem of modelling what can be called flexural joints, where two essentially rigid bodies are coupled by a substantially more elastic body. For modelling general elastic couplings one would like to have generically applicable, lumped parameter, intuitive, Euclidean geometric, accurate models with desirable physical symmetries. The model constitutive equations should be easily and quickly computable. For purely elastic coupling the constitutive equations should be truly energy conservative: the configuration-wrench equations should be derivable from a potential function. Linear and angular momentum should be conserved. Quaternion-based and twist-based modelling methods are presented. The constitutive equations to calculate the configuration-wrench behavior are derived via geometric potential energy functions. Wrenches are computable given the configurations of the rigid bodies and all the stiffness matrices of the compliant element. For an arbitrary pair of elastically coupled rigid bodies there exist coincident, unique points on the bodies known as centers of stiffness at which translation and rotation are minimally coupled. At the center of stiffness there exist three sets of orthonormal principal axes and corresponding principal stiffnesses. These parameters are useful in both analysis and numerical simulation. A finite-element-based method for computing canonical stiffness parameters of elastically coupled rigid bodies is presented. The method is applied to notch hinges and Remote Center of Compliance (RCC) hinges. Standard procedures are presented on how to determine canonical stiffness parameters at the center of stiffness of a spatial compliance. Series of canonical stiffness parameters can be generated automatically using the methods provided. Key program listings are provided which can be used to duplicate the results presented.

The mixing of compounds in a highly viscous medium is important in many industrial settings; from food processing to the manufacturing of rocket fuel and drugs. Experts in mixing have long been aware of how things become mixed in a nonturbulent flow, but there has been little quantitative analysis of such mixing processes. As recent developments in chaos theory have found their way into the engineering literature, there have been some attempts to apply these ideas toward numerically quantifying nonturbulent mixing processes. Chaos theory is a new name for an old subject in mathematics, dynamical systems theory which includes ergodic theory. By examining the older literature of ergodic theory, one can determine what is necessary to quantify nonturbulent mixing processes. This has led to the methods which are suggested in this dissertation. After discussing some principles of ergodic theory, the design of a bladeless mixer is presented. The philosophy of this design is to adopt an abstract mathematically mixing system around which to design and build an actual machine. Ergodic theory is then used to develop methods for quantifying nonturbulent mixing processes by both experimental and numerical means. These methods are then applied to the bladeless mixer.

Typically, the problem of a plate on an elastic foundation has been approached by assuming that the foundation modulus (or modulus of subgrade reaction for a soil) remains constant as the plate deforms the foundation. If one were dealing with soil as the foundation material, it can be seen from a load-deformation plot for a particular soil, that this modulus would not be constant but would decrease as the deformations increase. The purpose of this thesis is to obtain an accurate solution that uses a more realistic model for the effect of the foundation behavior in the problem. When larger deflections of the plate are encountered, the results of the analysis using a non-linear model for the foundation differ substantially when compared to results using a linear model.

The exact three-dimensional transient solution of a multi-layer orthotropic panel subjected to transverse loading is presented. The finite geometry panel, supported by rollers, is subjected to an arbitrarily distributed surface load. Governing equations, derived from Reissner's functional, are solved by applying Fourier or Laplace transformation in time and enforcing the continuity of traction and displacement components between the adjacent layers. Material damping is incorporated into the analysis through complex material constants. The accuracy of the present analysis is established by considering a thick and thin laminate under quasi-static and transient loading, respectively. The solution of the static analysis is compared with a known exact solution and the transient analysis is compared with a finite element analysis. Transient responses of a thick laminate and a composite sandwich panel are also investigated. Material damping is found to significantly affect the transient stress and displacement fields of a laminate.

All welding processes can give rise to defects, which weakens the joint and can eventually lead to the failure of the welded structure. In order to inspect welds for detects, without affecting the usability of the product, non-destructive testing (NDT) is needed. NDT includes a wide range of different techniques, based on different physical principles, each with its advantages and disadvantages. The testing is often performed manually by a skilled operator and in many cases only as spot-checks. Today the trend in industry is to move towards thinner material, in order to save weight for cost and for environmental reasons. The need for inspection of a larger portion of welds therefore increases and there is an increasing demand for fully automated inspection, including both the mechanised testing and the automatic analysis of the result. Compared to manual inspection, an automated solution has advantages when it comes to speed, cost and reliability. A comparison of several NDT methods was therefore first performed in order to determine which methods have most potential for automated weld inspection. Automated analysis of NDT data poses several difficulties compared to manual data evaluation. It is often possible for an operator to detect defects even in noisy data, through experience and knowledge about the part being tested. Automatic analysis algorithms on the other hand suffer greatly from both random noise as well as indications that originate from geometrical variations. The solution to this problem is not always obvious. Some NDT techniques might not be suitable for automated inspection and will have to be replaced by other, better adapted methods. One such method that has been developed during this work is thermography for the detection of surface cracks. This technique offers several advantages, in terms of automation, compared to existing methods. Some techniques on the other hand cannot be easily replaced. Here the focus is instead to prepare the data for automated analysis, using various pre-processing algorithms, in order to reduce noise and remove indications from sources other than defects. One such method is ultrasonic testing, which has a good ability for detecting internal defects but suffers from noisy signals with low spatial resolution. Work was here done in order to separate indications from corners from other indications. This can also help to improve positioning of the data and thereby classification of defects. The problem of low resolution was handled by using a deconvolution algorithm in order to reduce the effect of the spread of the beam.The next step in an automated analysis system is to go beyond just detection and start characterising defects. Using knowledge of the physical principles behind the NDT method in question and how the properties of a defect affect the measurement, it is sometimes possible to develop methods for determining properties such as the size and shape of a defect. This kind of characterisation of a defect is often difficult to do in the raw data, and is therefore an area where automated analysis can go beyond what is possible for an operator during manual inspection. This was shown for flash thermography, where an analysis method was developed that could determine the size, shape and depth of a defect. Similarly for laser ultrasound, a method was developed for determining the size of a defect. / <p>Godkänd; 2014; 20140415 (mike); Nedanstående person kommer att disputera för avläggande av teknologie doktorsexamen. Namn: Patrik Broberg Ämne: Experimentell mekanik/Experimental Mechanics Avhandling: Imaging and Analysis Methods for Automated Weld Inspection Opponent: Professor Tadeusz Stepinski, Signaler och system, Institutionen för teknikvetenskaper, Uppsala universitet, Ordförande: Professor Mikael Sjödahl, Avd för strömningslära och experimentell mekanik, Institutionen för teknikvetenskap och matematik, Luleå tekniska universitet Tid: Fredag den 13 juni 2014, kl 10.00 Plats: E243, Luleå tekniska universitet</p>

Why copy the best athletes? When you finally learn their technique, they may have already moved on. Using muscluloskeletal biomechanics you might be able to add the "know-why" so that you can lead, instead of being left in the swells. This dissertation presents the theoretical framework of musculoskeletal modeling using inverse dynamics with static optimization. It explores some of the possibilities and limitations of musculoskeletal biomechanics in cross-country skiing, especially double-poling. The basic path of the implementation is shown and discussed, e.g. the issue of muscle model choice. From that discussion it is concluded that muscle contraction dynamics is needed to estimate individual muscle function in double-poling. Several computer simulation models, using The Anybody Modeling System™, have been created to study different cross-country skiing applications. One of the applied studies showed that the musculoskeletal system is not a collection of discrete uncoupled parts because kinematic differences in the lower leg region caused kinetic differences in the other end of the body. An implication of the results is that the kinematics and kinetics of the whole body probably are important when studying skill and performance in sports. Another one of the applied studies showed how leg utilisation may affect skiing efficiency and performance in double-poling ergometry. Skiing efficiency was defined as skiing work divided by metabolic muscle work, performance was defined as forward impulse. A higher utilization of the lower-body increased the performance, but decreased the skiing efficiency. The results display the potential of musculoskeletal biomechanics for skiing efficiency estimations. The subject of muscle decomposition is also studied. It is shown both analytically and with numerical simulations that muscle force estimates may be affected by muscle decomposition depending on the muscle recruitment criteria. Moreover, it is shown that proper choices of force normalization factors may overcome this issue. Such factors are presented for two types of muscle recruitment criteria. To sum up, there are still much to do regarding both the theoretical aspects as well as the practical implementations before predictions on one individual skier can be made with any certainty. But hopefully, this disseration somewhat furthers the fundamental mechanistic understanding of cross-country skiing, and shows that musculoskeletal biomechanics will be a useful complement to existing experimental methods in sports biomechanics. / Varför ska man kopiera de som är bäst inom sin idrottsgren? När man väl har lärt sig deras teknik så har de antagligen redan gått vidare. Vore det inte bättre att öka sin förståelse så att man kan ligga i framkant, istället för i svallvågorna? Med biomekaniska simuleringar som ett komplement till traditionella experimentella metoder finns möjligheten att få veta varför prestationen ökar, inte bara hur man ska göra för att öka sin prestation. Längdskidåkning innehåller snabba och kraftfulla helkroppsrörelser och därför behövs en beräkningsmetod som kan hantera helkroppsmodeller med många muskler. Avhandlingen presenterar flera muskeloskelettära simuleringsmodeller skapade i The AnyBody Modeling System™ och är baserade på inversdynamik och statisk optimering. Denna metod tillåter helkroppsmodeller med hundratals muskler och stelkroppssegment av de flesta kroppsdelarna. Avhandlingen visar att biomekaniska simuleringar kan användas som komplement till mer traditionella experimentella metoder vid biomekaniska studier av längdskidåkning. Exempelvis går det att förutsäga muskelaktiviteten för en viss rörelse och belastning på kroppen. Detta nyttjas för att studera verkningsgrad och prestation inom dubbelstakning. Utifrån experiment skapas olika simuleringsmodeller. Dessa modeller beskriver olika varianter (eller stilar) av dubbelstakning, alltifrån klassisk stil med relativt raka ben och kraftig fällning av överkroppen till en mer modern stil där åkaren går upp på tå och använder sig av en kraftig knäböj. Resultaten visar först och främst att ur verkningsgradsynpunkt är den klassiska stilen att föredra då den ger mest framåtdrivande arbete per utfört kroppsarbete, dvs den är energisnål. Men ska en längdlöpare komma så fort fram som möjligt (utan att bry sig om energiåtgång) verkar det som en mer modern stil är att föredra. Denna studie visar också att för att kunna jämföra kroppens energiåtgång för skelettmusklernas arbete mellan olika rörelser så krävs det en modell där muskler ingår. Andra studier som presenteras är hur muskelantagonister kan hittas, hur lastfördelningen mellan muskler eller muskelgrupper förändras när rörelsen förändras samt effekter av benproteser på energiåtgång. Några aspekter av metoden presenteras också. Två muskelmodeller och dess inverkan på olika simuleringsresultat visas. En annan aspekt är hur muskeldekomposition och muskelrekryteringskriterium påverkar beräkningarna. Normaliseringsfaktorer för olika muskelrekryteringskriterium presenteras. / Beräkningsbaserad biomekanik inom längdskidåkningen - möjligheter och begränsningar

This dissertation concerns structural topology optimization in conceptual design stages. The objective of the project has been to identify and solve problems that prevent structural topology optimization from being used in a broader sense in the avionic industry; therefore the main focus has been on stress and fatigue constraints and robustness with respect to load uncertainties. The thesis consists of two parts. The first part gives an introduction to topology optimization, describes the new contributions developed within this project and motivates why these are important. The second part includes five papers. The first paper deals with stress constraints and a clustered approach is presented where stress constraints are applied to stress clusters, instead of being defined for each point of the structure. Different approaches for how to create and update the clusters, such that sufficiently accurate representations of the local stresses are obtained at a reasonable computational cost, are developed and evaluated. High-cycle fatigue constraints are developed in the second paper, where loads described by a variable-amplitude load spectrum and material data from fatigue tests are used to determine a limit stress, for which below fatigue failure is not expected. A clustered approach is then used to constrain the tensile principal stresses below this limit. The third paper introduces load uncertainties and stiffness optimization considering the worst possible loading is then formulated as a semi-definite programming problem, which is solved very efficiently. The load is due to acceleration of point masses attached to the structure and the mass of the structure itself, and the uncertainty concerns the direction of the acceleration. The fourth paper introduces an extension to the formulated semi-definite programming problem such that both fixed and uncertain loads can be optimized for simultaneously. Game theory is used in the fifth paper to formulate a general framework, allowing essentially any differentiable objective and constraint functions, for topology optimization under load uncertainty. Two players, one controlling the structure and one the loads, are in conflict such that a solution to the game, a Nash equilibrium, is a design optimized for the worst possible load.

Today’s rules and regulations regarding emissions from combustion vehicles are very strict and the travel range per tank and/or charge, especially for electric vehicles, is a crucial factor which will always be considered by the customers. Hence, automotive manufacturers strive to boost fuel and battery economy. This can, to a great extent, be done by improving the aerodynamics of the vehicle for lower drag. The conventional CFD process for aerodynamic development is relatively time consuming and there is rarely enough timeor resources to find the optimal design in all regions of the vehicle. Hence, the adjoint solver was investigated to make the aerodynamic development process more efficient by providing sensitivities of the geometry with respect to drag force. The adjoint solver was investigated both through a literature review as well as by performing CFD and adjoint simulations. The CFD and adjoint simulations were performed using Fluent 2019 R1 and the realizable k-ε turbulence model. It was found that it is important to monitor surface sensitivities during the solution in addition to the adjoint residuals to assess convergence of the adjoint simulation. It is also recommended to analyse regions of high residuals in the domain to ensure that they are far away from the surface(s) of interest. Investigations regarding different stabilization schemes as well different meshes for the adjoint solver were performed. It was concluded that the residual minimization scheme (RMS) is the preferred stabilization scheme. It was found that a coarser mesh can be used to reduce localized transient behaviour if the adjoint solver has trouble converging. It was found that a simplified model of a fully detailed car geometry is necessary to reduce the complexity and the resolution of the mesh to be able to use the RMS and to avoid local instabilities. A proposed CFD and adjoint procedure with guidelines and recommendation was developed.

In this Licentiate of Engineering thesis, a method is proposed that identifies the mechanical properties of arteries in vivo. The mechanical properties of an artery are linked to the development of cardiovascular diseases. The possibility to identify the mechanical properties of an artery inside the human body could, thus, facilitate disease diagnostization, treatment and monitoring. Supplied with information obtainable in the clinic, typically limited to time- resolved pressure-radius measurement pairs, the proposed in vivo parameter identi- fication method calculates six representative parameters by solving a minimization problem. The artery is treated as a homogeneous, incompressible, residual stress- free, thin-walled tube consisting of an elastin dominated matrix with embedded collagen fibers referred to as the constitutive membrane model. To validate the in vivo parameter identification method, in silico arteries in the form of finite element models are created using published data for the human abdominal aorta. With these in silico arteries which serve as mock experiments with pre-defined material parameters and boundary conditions, in vivo-like pressure-radius data sets are generated. The mechanical properties of the in silico arteries are then determined using the proposed parameter identification method. By comparing the identified and the pre-defined parameters, the identification method is quantitatively validated. The parameters for the radius of the stress-free state and the material constant associated with elastin show high agreement in case of healthy arteries. Larger differences are obtained for the material constants associated with collagen, and the largest discrepancy occurs for the in situ axial prestretch. For arteries with a pathologically small elastin content, incorrect parameters are identified but the presence of a diseased artery is revealed by the parameter identification method. Furthermore, the identified parameters are used in the constitutive membrane model to predict the stress state of the artery in question. The stress state is thereby decomposed into an isotropic and an anisotropic component which are primarily associated with the elastin dominated matrix and the collagen fibers, respectively. In order to assess the accuracy of the predicted stress, it is compared to the known stress state of the in silico arteries.  The comparison of the predicted and the in silico decomposed stress states show a close agreement for arteries exhibiting a low transmural stress gradient. With increasing transmural stress gradient the agreement deteriorates. The proposed in vivo parameter identification method is capable of identifying adequate parameters and predicting the decomposed stress state reasonably well for healthy human abdominal aortas from in vivo-like data. / In diesem Lizentiat der Ingenieurwissenschaften wird eine Methode zur Identifikation der mechanischen Eigenschaften von Arterien in vivo vorgestellt. Die mechanischen Eigenschaften einer Arterie sind mit der Ausbildung kardiovaskulärer Krankheiten verknüpft und deren Identifikation hat daher das Potenzial die Diagnose, die Behandlung und die Überwachung dieser Krankheiten zu verbessern. Basierend auf klinisch möglichen Messungen, die üblicherweise auf ein zeitaufgelöstes Druck-Radiussignal limitiert sind, werden sechs repräsentative Parameter durch Lösen eines Minimierungsproblems berechnet. Die sechs Parameter sind dabei die Eingangsparameter des zur Hilfe gezogenen konstitutiven Schalenmodells welches eine Arterie als eine homogene, inkompressible, restspannungsfreie und dünnwandige Röhre beschreibt. Weiterhin wird angenommen, dass die Arterienwand aus einer elastindominierten Matrix mit eingebetteten Kollagenfasern besteht. Um die in vivo Parameteridentifikationsmethode zu validieren, werden in silico Arterien in Form von Finite Elemente Modellen erstellt. Diese in silico Arterien beruhen auf publizierten Materialparametern der menschlichen Abdominalaorta und dienen als Pseudoexperimente mit vordefinierten mechanischen Eigenschaften und Randbedingungen. Mit diesen Arterien werden in vivo-ähnliche Druck-Radiussignale erstellt und anschliesend werden ihre mechanischen Eigenschaften mit Hilfe der Parameteridentifikationsmethode bestimmt. Der Vergleich der identifizierten und der vordefinierten Parameter ermöglicht die quantitative Validierung der Methode. Die Parameter des spannungsfreien Radius und der Materialkonstanten für Elastin weisen hohe Übereinstummung im Falle gesunder Arterien auf. Die Abweichung der Materialkonstanten für Kollagen sind etwas gröser und der gröste Unterschied tritt beim axialen in situ Stretch auf. Für Arterien mit einem pathologisch geringen Elastinbestandteil werden falsche Parameter identifiziert, wobei die Parameteridentifikationsmethode eine krankhafte Arterie offenlegt. Weiterhin werden mit Hilfe der identifizierten Parameter und des konstitutiven Schalenmodells der Spannungszustand in der Arterienwand berechnet. Dieser ist dabei aufgeteilt in einen isotropen und einen anisotropen Anteil. Der isotrope Anteil wird mit der elastindomierten Matrix und der anisotrope Anteil mit den Kollagenfasern verknüpft. Um die Genauigkeit des berechneten Spannungszustandes beurteilen zu können, wird dieser mit dem Zustand in den in silico Arterien verglichen. Im Fall von Arterien, die einen geringen transmuralen Spannungsgradienten aufweisen, entspricht der berechnete Spannungszustand dem in silico Zustand. Mit zunehmendem transmuralen Spannungsgradienten lässt die Übereinstimmung nach. Für die gesunde menschliche Abdominalaorta ist die entwickelte in vivo Parameteridentifikationsmethode in der Lage, basierend auf in vivo-ähnlichen Messsignalen, adäquate Parameter zu identifizieren und einen zufriedenstellenden Spannungszustand zu berechnen. / I denna licentiatavhandling föreslås en metod för att identifiera mekaniska egenskaper hos artärer in vivo. De mekaniska egenskaperna är kopplade till utvecklingen av hjärt-kärlsjukdomar, och möjligheten att identifiera dessa egenskaper skulle således kunna underlätta diagnostisering, behandling och uppföljning av dessa sjukdomar. Den förslagna metoden använder kliniskt mätbara tryck-radie-signaler och löser ett minimeringsproblem för att bestämma sex parametrar som beskriver kärlets mekaniska egenskaper. Artären modelleras som ett homogent, inkompressibelt och spänningsfritt tunnväggigt rör där kärlväggen utgörs av en elastindominerad matris armerad med inbäddade kollagenfibrer. För att validera parameteridentifieringen skapas en uppsättning representativa, virtuella artärer med hjälp av finita element. Dessa in silico-artärer baseras på publicerade data för mänsklig bukaorta och används för att generera fiktiva tryckradie-signaler vilka sedan matas in i den förslagna modellen. Genom att parametrar och randvillkor för in silico-artärerna är kända fungerar dessa som en kontroll mot vilka resultatet från parameteridentifieringen kan jämföras. Parametrarna som beskriver den icke trycksatta radien och den elastindominerade matrisen visar god överensstämmelse med de in silico-artärerna för friska kärl. Större diskrepans erhålls för de parametrar som associeras med kollagenet, och den största avvikelsen erhålls för den parameter som beskriver den axiella försträckningen. För artärer med patologiskt lågt elastininnehåll identifieras felaktiga parametrar, men resultatet avslöjar ändå tydligt en sjuk artär. De identifierade parametrarna har också använts för att jämföra spänningstillst åndet i membranmodellen och in silico-artäreren. Spänningstillståndet har delats upp i en isotrop och en anisotrop komponent svarande mot, i huvudsak, den elastindominerade matrisen samt kollagenfibrerna. Resultatet visar en mycket god överensstämmelse för bägge komponenterna hos in silico-artärer med låg spänningsgradient genom väggen. Med ökande spänningsgradient försämras dock överensstämmelsen. Resultatet visar att den förslagna metoden är kapabel att identifiera adekvata parametrar och att förutsäga spänningskomponenterna i en frisk aorta.