Finite element models are used frequently in both engineering and scientific research. While they can provide useful information as to the performance of materials, as length scales are decreased more sophisticated model descriptions are required. It is also important to develop methods by which existing models may be verified against experimental findings. The present study evaluates the ability of various finite element models to predict materials behaviour at length scales ranging from several microns to tens of nanometers. Considering this motivation, this thesis is provided in manuscript form with the bulk of material coming from two case studies. Following an overview of relevant literature in Chapter 2, Chapter 3 considers the nucleation of delta-zirconium hydrides in a Zircaloy-2 matrix. Zirconium hydrides are an important topic in the nuclear industry as they form a brittle phase which leads to delayed hydride cracking during reactor start-up and shut-down. Several FE models are used to compare present results with literature findings and illustrate the weaknesses of standard FE approaches. It is shown that standard continuum techniques do not sufficiently capture the interfacial effects of an inclusion-matrix system. By using nano-scale material descriptions, nucleation lattice strains are obtained which are in good agreement with previous experimental studies. The motivation for Chapter 4 stems from a recognized need to develop a method for modeling corrosion behaviour of materials. Corrosion is also an issue for reactor design and an ability to predict failure points is needed. Finite element models could be used for this purpose, provided model accuracy is verified first. In Chapter 4 a technique is developed which facilitates the extraction of sub-micron resolution strain data from correlation images obtained during in-situ tensile deformation. By comparing image correlation results with a crystal plasticity finite element code it is found that good agreement between the two exists. The method outlined is material independent and could be applied to most metallurgical studies. Chapter 5 reviews the findings of each case study and makes suggestions as to the direction of future research. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2013-09-30 16:05:52.934

Size effects play a significant role in metal processing when the specimen dimensions are reduced. In this study, influence of size effects were investigated on two problem specific processes. First, numerical simulations of a small-scale forward extrusion with varying grain size were performed for both 2D and 3D cases. Here, grains were assigned to non-homogeneous properties in a random fashion. The computational geometry was obtained from Voronoi tessellation in MATLAB, and python-scripting in ABAQUS. Then the effects of size and property non-homogeneity were investigated. Second, a numerical model was simulated to predict final form shapes, punch load requirement, and thickness distribution of hemispherical bowl-shaped forming. The die, punch and cover plate were fabricated using stereolithographic apparatus (SLA). Numerically obtained punch load requirement, thickness distribution, von-Mises contours, and equivalent plastic strain contours were compared for different thickness specimens. Finally, the models were validated by experimental results.

Background: Most traffic safety research projects require accurate real world data which is collected in different databases around the world. This is especially important since the results of these projects form the basis for new crash test procedures and standards. In many of these databases the involvement of the frontal structures of the car in frontal crashes is coded by using the SAE J224 practice (Society of Automobile Engineers). There were indications that by using this practice the database would contain an overestimate of the car frontal structure involvement in real world crashes. One purpose of this thesis is therefore to develop a new method for real world crash investigations to better address this issue. One purpose was also to adopt this method in a data collection of fatal crashes in Sweden and examine injury causation mechanisms. Studies shows that the commonly used Hybrid III dummy is not fully reproducing the kinematical behavior observed in frontal sled test with belted PMHS (Post Mortem Human Subject). A human FE-model (Finite Element) might be able to reproduce the behavior evidenced with the PMHS in order to study upper body kinematics in certain types of frontal collision events. Method: A new data collection method was developed with the purpose to examine actual load paths active in the car front during a frontal crash. An important purpose was to examine if there was a relation between these load paths and injury producing mechanisms. This was done in an examination and analysis of 61 fatally injured occupants in 53 car frontal crashes in a sample area covering 40 % of the population of Sweden. Sample period was one year (1st October 2000 to 30th September 2001). An existing human FE-model was developed and validated with respect to upper body kinematics by using existing frontal belted PMHS tests. This was done by building a FE-model of the seat and seat belt used in the PMHS tests. Results: A generic car structure was developed which was used in the data collection methodology. By adopting this new method, Small Overlap (SO) crashes emerged as the most common crash configuration (48 %) among belted frontal fatalities. The injury producing mechanism in SO crashes is characterized by occupant upper body impacts in the side structure (door, a-pillar) of the car. This upper body kinematics is induced by both the crash pulse and the asymmetrical three point belt system. Current crash test procedures are not designed to fully estimate the performance of neither car structures nor restraints in SO crashes. In order to develop a better tool for reproducing this kinematical behavior a FE-model of a human body was refined and validated for belted conditions. This validation was performed with satisfying result. Conclusions: This study showed that by adopting new methods of data collecting new areas of traffic safety could be considered. In this study SO (48 %) crashes emerged as the most common crash configuration for belted frontal fatalities. Approximately ¼ of the fatalities occurred in a crash configuration comparable to current barrier crash test procedures. The body kinematics of PMHS in the SO crashes can be replicated and studied by using a FE-model of a human body in the collision load case model. With this tool possible collision counter measures could be evaluated for the SO crash configuration.

Les nouveaux composants à semi-conducteur de type grand gap ont été développés pour des applications de conversion de puissance en raison de leurs hautes fréquences de commutation (de centaine kHz à quelques MHz) et pertes faibles. Afin de bien profiter ses avantages, la technologie des circuits imprimés (PCB) est intéressante pour une intégration à haute densité de puissance grâce à sa flexibilité et son faible coût. Cependant, à cause de la mauvaise conductivité thermique du matériau FR-4 utilisé pour le substrat PCB et la haute densité de puissance réalisée, il est primordial de trouver des solutions thermiques pour améliorer les performances thermiques de la structure de PCB. Dans cette thèse, trois solutions thermiques pour les structures de PCB ont été proposées, y compris des solutions avec des vias thermiques, de cuivre épais sur le substrat de PCB ainsi que des dispositifs de refroidissement thermoélectrique (TEC). Nos études sont basées sur la modélisation électrothermique et la méthode d’éléments finis en 3D. Tout d’abord, l’optimisation des paramètres des vias (diamètre, épaisseur de placage, surface formée par des vias, la distance entre des vias etc.) a été réalisée pour optimiser l’effet de refroidissement. Ensuite, on constate que les performances thermiques des structures de PCB peuvent être améliorées en utilisant cuivre épais sur le substrat de PCB. Cuivre épais augmente le flux thermique latéral dans la couche de cuivre. Les influences de l’épaisseur de cuivre (35 à 500 µm) ont été étudiées. Cette solution est facile à réaliser et peut être combinée à d’autres solutions de refroidissement. Enfin, le dispositif thermoélectrique comme les modules Peltier est une technologie de refroidissement local. Les influences des paramètres de Peltier (Propriétés du matériau thermoélectrique, nombre d’éléments Peltier, distance entre la source de chaleur et les dispositifs Peltier, etc.) ont été identifiées. Il est démontré que des modules Peltier ont l’application potentielle pour le développement d’intégration de PCB attendu que son active contrôle des températures. / The emerging wide bandgap (WBG) semiconductor devices have been developed for power conversion applications instead of silicon devices due to higher switching frequencies (from few 100 kHz to several MHz) and lower on-state losses resulting in a better efficiency. In order to take full advantage of the WBG components, PCB technology is attractive for high power density integration thanks to its flexibility and low cost. However, due to poor thermal conductivity of the commonly used material Flame Retardant-4 (FR4), efficient thermal solutions are becoming a challenging issue in integrated power boards based on PCB substrates. So it is of the first importance to seek technological means in order to improve the thermal performances. In this thesis, three main thermal management solutions for PCB structures have been investigated including thermal vias, thick copper thickness on the PCB substrate as well as thermoelectric cooling (TEC) devices. Our studies are based on the electro-thermal modeling and 3D finite element (FE) methods. Firstly, optimization of the thermal via parameters (via diameter, via plating thickness, via-cluster surface, via pattern, pitch distance between vias etc.) has been realized to improve their cooing performances. We presented and evaluated thermal performances of the PCB structures by analyzing the thermal resistance of the PCB substrate with different thermal vias. Secondly, it is found that thermal performances of the PCB structures can be enhanced by using thick copper thickness on top of the PCB substrate, which increases the lateral heat flux along the copper layer. Influences of the copper thickness (35 µm to 500 µm) has been discussed. This solution is easy to realize and can be combined with other cooling solutions. Thirdly, thermoelectric cooler like Peltier device is a solid-state cooling technology that can meet the local cooling requirements. Influences of Peltier parameters (Thermoelectric material properties, number of Peltier elements, distance between the heating source and the Peltier devices etc.) have been identified. All these analyses demonstrate the potential application of Peltier devices placed beside the heating source for PCB structures, which is a benefit for developing the embedding technology in such structures.

To design a bridge, different typologies of construction materials can be used. All materials have in common that deformations occur due to different events, such as externalloading, temperature- and moisture variations. To allow these kinds of deformations,Expansion Joints (EJs) are used in the structure. In timber bridges, these joints haveturned out to be a complex construction detail, due to problems related to their strengthand moisture capacity. The purpose of this thesis is to overview design codes and tostudy the mechanical behavior of Nosing EJs in a roadway timber bridge under externalloading. The aim is to identify critical actions and provide an alternative design of thestudied EJ. The aim is also to create a Finite Element (FE) model of the EJs and carryout calculations according to the design codes. To achieve this, literature studies, designcalculations and FE-simulations were performed. It turned out that there were lack ofearlier studies within this field. Therefore, studies which treats EJs in bridges with othermaterial than timber were considered. The results from the simulations indicated thatthe steel components in EJs are the most exposed parts in the detail. It also turned outthat an eventual failure can transferred away from the screws to the parts consideredmore favorable in the EJ.

L'importance croissante de l'évaluation de la performance des structures soumis au chargement sismique souligne la nécessité d'estimer le risque de liquéfaction. Dans ce scénario extrême de la liquéfaction du sol, des conséquences dévastatrices sont observées, par exemple des tassements excessifs et des instabilités de pentes. Dans le cadre de cette thèse, la réponse dynamique et l'interaction d'un système ouvrage en terre-fondation sont étudiées, afin de déterminer quantitativement le mécanisme de ruine dû à la liquéfaction du sol de la fondation. Par ailleurs, les chargements sismiques peuvent induire dans les ouvrages en terre un mode de rupture générant des bandes de cisaillement. Une étude de sensibilité aux maillages a donc été engagée pour quantifier la dépendance des résultats de l'analyse dynamique. Par conséquent, l'utilisation d'une méthode de régularisation est évaluée au cours des analyses dynamiques. Le logiciel open-source Code_Aster, basé sur la méthode des Eléments Finis et développé par EDF R&D, est utilisé pour les simulations numériques, tandis que le comportement du sol est représenté par le modèle de comportement de l'ECP, développé à CentraleSupélec. En premier lieu, un modèle simplifié de propagation 1D des ondes SH dans une colonne de sol avec comportement hydromécanique couplé non linéaire a été simulé. L'effet des caractéristiques du signal sismique et de la perméabilité du sol sur la liquéfaction est évalué. Le signal sismique d'entrée est un élément important pour l'apparition de la liquéfaction, puisque la durée du choc principal peut conduire à de fortes non linéarités et à un état de liquéfaction étendu. En outre, quand une variation de perméabilité en fonction de l'état de liquéfaction est considérée, des changements significatifs sont observés pendant la phase de dissipation de la surpression interstitielle de l'eau et au comportement du matériau. En revanche, ces changements ne suivent pas une tendance unique. Puis, l'effet d'une méthode de régularisation avec cinématique enrichie, appelée premier gradient de dilatation, sur la propagation des ondes SH est étudié au travers d'une solution analytique. Des problèmes à la réponse dynamique du sol sont observés et discutés quand cette méthode de régularisation est appliquée. Ensuite, un modèle 2D d'un déblai est simulé et sa réponse dynamique est évaluée en conditions sèches, complètement drainées et hydromécanique couplées. Deux critères sont utilisés pour définir le début de la rupture de la structure. Le travail du second ordre est utilisé pour décrire l'instabilité locale à des instants spécifiques du mouvement sismique, tandis que l'estimation d'un facteur de sécurité locale est proposée prenant en compte la résistance résiduelle du sol. En ce qui concerne le mode de ruine, l'effet de la surpression interstitielle de l'eau est de grande importance, puisqu'un déblai stable en conditions sèches et complètement drainées, devient instable lors de l'analyse couplée à cause de la liquéfaction de la fondation. Enfin, un système digue-fondation est simulé et l'influence de la perméabilité du sol, la profondeur de la couche liquéfiable, ainsi que, les caractéristiques du séisme sur la ruine induite par la liquéfaction du sol est évaluée. Pour ce modèle de digue, le niveau de dommages est fortement lié à la fois à l'apparition de la liquéfaction dans la fondation et la dissipation de la surpression d'eau. Une surface d'effondrement circulaire est générée à l'intérieur de la couche du sol liquéfié et se propage vers la crête dans les deux côtés de la digue. Pourtant, lorsque la couche liquéfiée est située en profondeur, la digue n'est pas affectée par la liquéfaction de la fondation pour ce cas particulier de chargement. Ce travail de recherche se concentre sur une étude de cas de référence pour l'évaluation sismique des ouvrages en terre soumis à un séisme et fournit des méthodes et outils de calculs numériques performants accessibles aux ingénieurs. / The increasing importance of performance-based earthquake engineering analysis points out the necessity to assess quantitatively the risk of liquefaction. In this extreme scenario of soil liquefaction, devastating consequences are observed, e.g. excessive settlements, lateral spreading and slope instability. The present PhD thesis discusses the global dynamic response and interaction of an earth structure-foundation system, so as to determine quantitatively the collapse mechanism due to foundation’s soil liquefaction. As shear band generation is a potential earthquake-induced failure mode in such structures, the FE mesh dependency of results of dynamic analyses is thoroughly investigated and an existing regularization method is evaluated. The open-source FE software developed by EDF R&D, called Code_Aster is used for the numerical simulations, while soil behavior is represented by the ECP constitutive model, developed at CentraleSupélec. Starting from a simplified model of 1D SH wave propagation in a soil column with coupled hydromechanical nonlinear behavior, the effect of seismic hazard and soil’s permeability on liquefaction is assessed. Input ground motion is a key component for soil liquefaction apparition, as long duration of mainshock can lead to important nonlinearity and extended soil liquefaction. Moreover, when a variation of permeability as function of liquefaction state is considered, changes in the dissipation phase of excess pore water pressure and material behavior are observed, which do not follow a single trend. The effect of a regularization method with enhanced kinematics approach, called first gradient of dilation model, on 1D SH wave propagation is studied through an analytical solution. Deficiencies of the use of this regularization method are observed and discussed, e.g. spurious waves apparition in the soil’s seismic response. Next, a 2D embankment-type model is simulated and its dynamic response is evaluated in dry, fully drained and coupled hydromechanical conditions. Two criteria are used to define the onset of the structure’s collapse. The second order work is used to describe the local instability at specific instants of the ground motion, while the estimation of a local safety factor is proposed by calculating soil’s residual strength. Concerning the failure mode, the effect of excess pore water pressure is of great importance, as an otherwise stable structure-foundation system in dry and fully drained conditions becomes unstable during coupled analysis. Finally, a levee- foundation system is simulated and the influence of soil’s permeability, depth of the liquefiable layer, as well as, characteristics of input ground motion on the liquefaction-induced failure is evaluated. For the current levee model, its induced damage level (i.e. settlements and deformations) is strongly related to both liquefaction apparition and dissipation of excess pore water pressure on the foundation. A circular collapse surface is generated inside the liquefied region and extends towards the crest in both sides of the levee. Even so, when the liquefied layer is situated in depth, no effect on the levee response is found. This research work can be considered as a reference case study for seismic assessment of embankment-type structures subjected to earthquake and provides a high-performance computational framework accessible to engineers.

Refill Friction Stir Spot Welding (RFSSW) is a new solid-state joining technology, which is suitable for joining similar and dissimilar overlap sheets connections, particularly in aluminium and magnesium alloys. This welding method is expected to have wide applications in joining of body parts in the automotive industry. In the present study, RFSSW has been used to join 1.0 mm gauge sheets of two material combinations: similar AA6111-T4 automotive aluminium alloy joints and a dissimilar aluminium AA6111-T4 to magnesium AZ31-H24 alloy combinations. The performance of the joints was investigated in terms of the effect of the welding parameters (including tool rotation rate, sleeve plunge depth, and welding time etc.) to improve current understanding and allow optimisation of the process for short welding-cycles when joining similar and dissimilar light alloys. The results of the investigations on similar AA6111 welds showed the ability to use a wide window of process parameters that resulted in joints with a successfully refilled keyhole and flat weld surface, even when using a welding time as short as 0.5 s. The joints in the as-welded condition showed strengths as high as 4.2 kN, when using welding parameters of 1500 rpm, 1.0 mm with a range of welding times from 0.55 to 2.0 s. All joints showed a nugget pull-out failure mode when using a sleeve plunge depth of 0.8 mm or more, as a result of increasing the joint area. The strength of the joints further improved and reached peak loads of 5.15 and 6.43 kN after natural and artificial ageing, respectively, for welds produced using optimised welding parameters of a 2500 rpm tool rotation rate, a 1.5 s welding time and a 1.0 mm plunge. This improvement in strength resulted from the improvement in the local mechanical properties in the HAZ and other regions, which results from a minimal HAZ due to the rapid weld cycle and the re-precipitation of GPZs and clustering on natural ageing, or β on artificial ageing. A modification to the RFSSW process was developed in this project to solve the problems faced when dissimilar welding Mg to Al. This modified process involved adding a final brief pin plunge stage to consolidate refill defects and it was successful in producing nearly defect-free joints with improved mechanical properties, using a wide range of the process parameters. The average peak load of the joints increased with increasing tool rotation rate, to reach a maximum value at 2500 rpm due to eliminating the weld defects by increasing the material plasticity. However, increasing the tool rotation rate further to 2800 rpm led to a decrease in the average peak failure load due to eutectic melting at the weld interface. The optimum welding condition was thus found to be: 2500 rpm, 1.0 s, and 1.0 mm, which gave an average peak failure load of 2.4 kN and average fracture energy of 1.3 kN.mm. These values represent an improvement of about 10 % and 27 %, respectively, compared to welds produced with the conventional RFSSW process, and about 112 % and 78 % of the Mg-Mg similar joints produced using the same welding conditions. A FE model developed in this project was successful in increasing understanding of the behaviour of the RFSSW joints when subjected to lap tensile-shear loading. The stress and strain distribution in the modelled samples showed that the highest concentration occurring in the region of the confluence of the SZ with the two sheets. With increasing extension, these regions of highest stress and strain propagated to the outer surfaces of the two sheets and then annularly around the weld nugget. This annular ring of high strain concentration agreed well with the failure path and results in the full plug pull-out fracture mode shown by the experimentally tested samples. The predicted force-extension curves showed high agreement with the experimental results, especially when including the effect of the hook defect and correction of compliance in the experimental results.

Timber is a building material that is becoming more common and of interest for use in high-rise buildings. One of the reasons is that timber requires less energy input for the manufacturing process of the material compared to non-wood based materials. When designing high- rise timber buildings it is of great significance to understand the dynamic behavior of the structure. One method to obtain the dynamic properties is to use Operational Modal Analysis, which is based on the structural response from operational use. Finite element (FE) analysis is a tool which can be used for dynamic analysis for large structures. In this study an Operation Modal Analysis (OMA) was conducted on a four-story timber building in Växjö. A finite element model was created of the same building using commercial FE packages. Based on the mode shapes and natural frequencies obtained from the OMA, the FE model was fine-tuned. The purpose of this thesis is to gain knowledge of which parameters that might have a significant role in finite element modelling for a structural dynamic analysis. The aim is to develop a finite element model that accurately simulates the dynamic behavior of the tested building. It was shown from the result that is possible with an enough detailed FE model to capture the dynamic behaviour of a structure. The parameters that had the largest effect on the result can be pointed to the mass and the stiffness of the structure. / Trä är ett byggnadsmaterial som börjar bli allt mer vanligt och är av intresse att använda som stommaterial för höga byggnader. En anledning till detta är att det krävs mindre energi i tillverkningsfasen för trä jämfört med stål och betong. Vid dimensionering av höga träbyggnader är det essentiellt att förstå byggnadens dynamiska egenskaper. För att ta fram en byggnads dynamiska egenskaper kan en metod som benämns Operational Modal Analysis (OMA) tillämpas vilken baseras på byggnadens rörelser vid daglig användning. Finita element (FE) metoden är ett verktyg som kan användas vid dynamisk analys för större byggnader. I detta arbete genomfördes en OMA för ett fyravåningshus med trästomme beläget i Växjö. Genom användning av kommersiella FE-mjukvaror togs en finita element modell av samma byggnad fram. Baserat på de egenfrekvenser och egenmoder erhållna från OMA, uppdaterades FE-modellen därefter. Syftet med detta arbete är att erhålla kunskap kring vilka parametrar som har betydelse vid FE-modellering med hänsyn till dynamisk analys. Syftet är även att validera den prototyp av datainsamlingsenhet som använts vid fältmätningen. Målet med arbetet är att ta fram en FE-modell som på ett korrekt sätt beskriver den testade byggnadens dynamiska beteende. Resultatet av arbetet påvisar att med en tillräckligt detaljerad FE-modell är det möjligt att erhålla en byggnads dynamiska egenskaper. De parametrar som har störst inverkan på resultatet är byggnadens styvhet och inkluderad massa.

Vibrations in staircases have during the last decades become an important issue in design. The main reasons are current architectural trends aiming for innovative, slender and high staircases, together with developments in material properties and building technique, making these aims possible. The improved material properties and slender design of the staircase makes the structure lightweight and have great impact on the flexibility and dynamic performance of the staircase. This have resulted in that vibration serviceability criteria increasingly often are becoming governing in design. The performance of staircases in serviceability under dynamic loads is however very hard to predict. In many cases hand calculations will not be sufficient, and a computerized model, e.g. a finite element model, need to be created. Creating a finite element model that performs well when subjected to dynamic loads is however not simple. Especially boundary conditions, connections and the effect of non-structural elements are hard to adequately represent. The formulation of the load is also a complex question. The main dynamic load that staircases are subjected to, that causes uncomfort for the user, is the load that the user themselves apply on the structure, when ascending or descending.  The main part of this master thesis project is a case study of two lightweight, steel staircases. To form a basis for the case study, current research have been summarized in a literature survey. An introduction of elementary dynamics is also made for less conversant reader. The literature survey reviews previous research about loads introduced by humans and how these can be formulated, both for single human excitation and group loading. How vibrations arise and how humans percept vibrations is also reviewed. The view and recommendations of standards and regulations about load formulation and vibration acceleration limits is presented. Recommendations in research for finite element modeling of staircases and dynamic loads is also reviewed. The case study consists of measurements and analyzing of finite element models of the staircases. Measurements of vibrations and the dynamic response of the staircases under human introduced loads have been conducted. The human introduced loads included are an impulse load created by a jump, ascent at a moderate pace of a single subject and descent at a moderate pace by a single subject. The measurements have been recreated in finite element models. Different modeling choices and formulations for ascending, descending, and impulse loads are studied.  The aim is to investigate how different modeling choices in connections, boundary conditions and adjacent structure, affects the natural frequencies and mode shapes of the staircase. Different load formulations for the loads are analyzed, both for the impulse load and for the loads created by a subject ascending and descending. With these results as a basis, some general recommendations about construction a finite element mode of a staircase and achieving appropriate load formulation for dynamic loads are made. / Vibrationer i trappor har under de senaste årtiondena blivit en viktig fråga vid projekteringen av trappor. De främsta anledningar är dagens arkitektoniska trender som eftersträvar innovativa, slanka och långa trappor, tillsammans med utveckling i material egenskaper och förbättrade byggmetoder som möjliggör dessa trender. De förbättrade materialegenskaperna samt den slanka designen av trappan gör konstruktionen lätt och har stor påverkan på styvheten samt det dynamiska gensvaret hos trappan. Detta har resulterat i att vibrationer i bruksgränstillståndet allt oftare är dimensionerande i designen av trappan.    Responsen under dynamiska laster i bruksgränstillståndet hos trappan är dock väldigt svårt att förutbestämma. I de flest fall är handberäkningar inte tillräckliga för att förutsäga detta beteende och en dator modell, t.ex. en finita element modell, behöver utvecklas. Att utveckla en finita element modell som genererar tillförlitliga respons är dock inte enkelt. Speciellt randvillkoren, kopplingar och effekten av icke bärande element är svårt att modellera tillförlitligt. Hur man formulerar lasten kan också vara en svår fråga. Den främst dynamiska lasten som trappor utsätts för som skapar obekväma vibrationer för användaren, är också skapade av användaren själv eller andra användare som går upp eller ner i trappan.  Huvuddelen av detta arbete består av en fallstudie av två lätta ståltrappor. För att få en bas för fallstudien har rådande forskning gåtts igenom och summerats i en litteraturstudie. En introduktion av grundläggande dynamik har även gjorts för den mindre insatta läsaren.  Litteraturstudien har gått igenom forsning om dynamiska laster orsakade av människor och hur dessa kan beskrivas, både för laster orsakade av en människa, samt även för en grupp av människor. Hur vibrationer uppkommer och hur människor uppfattar vibrationer har också undersökts. Standarders uppfattning och rekommendationer, samt regelverk om lastformulering och gränsvärden för vibrationer presenteras. Rekommendationer från forskning av finita element modeller av trappor och dynamiska laster i dessa gås också igenom. Fallstudien består av mätningar i de verkliga trapporna, och av uppbyggnad och analysering av finita element modeller av trapporna. Mätningar av vibrationer och den dynamiska responsen hos trapporna när de utsätts för dynamiska laster orsakade av människor har utförts. De studerade lasterna inkluderar en impulslast skapad av ett hopp, last från en människa som går upp i trappan och last från en människa som går ner i trappan. Mätningarna har sedan försökts återskapas i finita element modellerna. Olika modellerings val och formuleringar för gång och impuls lasterna har studerats. Syftet är att undersöka hur olika modelleringsval hos kopplingar, randvillkor samt närliggande struktur påverkar egenfrekvenserna och modeformen hos trapporna. Olika beskrivningar på lasterna analyseras, både för impuls lasten, samt lasten från en människa som gå upp eller ner i trappan. Med hjälp av dessa resultat kommer några generella rekommendationer om hur finita element modeller av trappor kan konstrueras och hur en tillbörlig lastformulering för dynamiska laster uppnås.

Higher speeds and higher capacity will cause the Swedish rail network to be exposed to disturbing dynamic effects. Higher speeds cause higher vertical acceleration levels of the bridge deck. In this thesis, a numerical analysis of a three span end-frame bridge subjected to train induced vibrations is performed. The aim is to identify which structural components and boundary conditions that affect the dynamic behavior of the bridge. Furthermore, the influence of soil structure interaction (SSI) will be investigated as it may have contribution to the stiffness and damping of the structural system.  In order to capture the dynamic response of the bridge, an analysis in the frequency domain was preformed where frequency response functions (FRF) and acceleration envelopes were obtained. For this purpose, a detailed FE-model in 3D was created. Three different cases were studied, model subjected to ballast, model subjected to soil and model subjected to both ballast and soil in coherence. A high speed load model (HSLM) was used to create simulation of train passages at different speeds and applied to all cases so that the bridge deck accelerations could be studied. A simplified 2D-model with impedance functions representing the soil-structure interaction was created to validate the results from the detailed 3D-model and for practical design purposes.  The result of this numerical analysis showed that the vertical accelerations were within acceptable levels of the maximum allowed limits given in governing publications. Considering the surrounding soil, the results revealed an increase of the dynamic response in the midspan at resonant frequency. However, it was identified that this behavior is not explained by the influence of soil structure interaction but rather the change in boundary conditions of the end-shields. The same dynamic behavior was identified for the simplified 2D-model, with a slight underestimation of the vertical accelerations at resonance.