In this work, a design platform for the modeling, simulation and optimization of fluidic components and their interactions in larger systems is developed. A hydrogel-based stimulus-sensitive microvalve is the core element of the microfluidic toolbox. Essential material properties as swelling-stimuli functions and the cooperative diffusion are extracted from measurements. The results provide necessary input data for finite element simulations in order to extract characteristic properties of the mechanical and fluid domains. Finally, the behavior of the microvalve and other fluidic library elements is implemented in Matlab Simscape for component and system simulations. Case studies and design optimization can be realized in a very short time with high accuracy. The toolbox is suitable for research and development and as software for academic education. The library elements are evaluated for a chemofluidic NAND gate, a chemofluidic decoder and a chemofluidic oscillator.:1 Introduction to Microfluidic Systems 1.1 Chemofluidic Enables Scalable and Logical Microfluidics 1.2 Focus of this Work 2 Fundamentals for Hydrogel-based Lab-on-Chip Systems 2.1 Basic Hydrogel Material Behavior 2.1.1 Basic Swelling Behavior 2.1.2 General Properties of Hydrogels 2.2 Overview of the used Microtechnology 2.2.1 Synthesis of P(NIPAAm-co-SA) 2.2.2 Microfabrication of a Microfluidic Chip 2.3 Introduction to Modeling and Simulation Techniques 2.3.1 Computer-aided Design Methodologies 2.3.2 Model Abstraction Levels for Computer-Aided Design 2.3.3 Modeling Techniques for Microvalves in a Fluidic System 3 Analytical Descriptions of Swelling 3.1 Quasi-Static Description 3.1.1 Physical Static Chemo-Thermal Description 3.1.2 Finite Element Routine for Static Thermo-Elastic Expansion 3.1.3 Static System Level Design for Hydrogel Swelling 3.2 Transient Description 3.2.1 Physical Dynamic Chemo-Thermal Description 3.2.2 Finite Element Routine for Dynamic Thermo-Elastic Expansion 3.2.3 Transient System Level Design for Hydrogel Swelling 3.3 Swelling Hysteresis Effect 3.3.1 Quasi-static Hysteresis 3.3.2 Transient Hysteresis 4 Characterization of Hydrogel 4.1 Data Acquisition through Automated Measurements 4.1.1 Measuring the Swelling of Hydrogels 4.1.2 Contactless Measurement Concept to Determine the Core Stiffness of Hydrogels 4.2 Data Evaluation with Image Recognition 4.3 Data Fitting and Model Adaption 4.3.1 Quasi-static Response 4.3.2 Transient Response 4.3.3 Hysteresis Response 5 Modeling Swelling in Finite Elements 5.1 Validity of the Model and Simulation Approach 5.2 Thermo-Mechanical Model of the Hydrogel Expansion Behavior 5.2.1 Change of the Length by Thermal Expansion 5.2.2 Stress-Strain Relationship for Hydrogels 5.2.3 Thermal Volume Expansion and Parameter Adaptation 5.2.4 Heat Transfer Coefficient 5.3 Volume Phase-Transition of a Hydrogel implemented in ANSYS 5.4 Computational Fluid Dynamics 5.4.1 Analytic Mesh Morphing 5.4.2 One-way Fluid Structure Interaction Modeling 5.4.3 Towards a Two-way Fluid Structure Interaction Model in CFX 6 Lumped Modeling 6.1 The Chemical Volume Phase-transition Transistor Model 6.1.1 Static Hysteresis 6.1.2 Equilibrium Swelling Length – Quasi-static Behavior 6.1.3 Kinematic Swelling Length - Transient Behavior 6.1.4 Stiffness and Maximum Closing Pressure 6.1.5 Calculation of the Fluidic Conductance 6.1.6 Modeling of the Fluid Flow through the Valve 6.2 Circuit Descriptions Analogy for Microfluidic Applications 6.2.1 Advantages and Limitations of Combined Simulink-Simscape Models 6.2.2 Requirements for Microfluidic Circuits 6.2.3 Graphical User Interfaces and Library Element Management 6.3 Modeling Techniques for the Chemical Volume Phase-transition Transistor (CVPT) 6.3.1 Network Description of CVPT 6.3.2 Signal Flow Description of CVPT 6.3.3 Mixed Signal Flow and Network Model for CVPT 7 Micro-Fluidic Toolbox 7.1 Microfluidic Components 7.1.1 Fluid Sources and Stimuli Sources 7.1.2 Fluidic Resistor with Bidirectional Stimulus Transport 7.1.3 Junctions 7.1.4 Chemical Volume Phase-transition Transistor 7.2 Microfluidic Matlab Toolbox 7.3 Modeling Chemofluidic Logic Circuits 7.3.1 Chemofluidic NAND Gate 7.3.2 Chemofluidic Decoder Application 7.3.3 Chemo-Fluidic Oscillator 7.4 Layout Synthesis 8 Summary and Outlook Appendix A 2D Thermo-Mechanical Solid Element for the Finite Element Method B Thermal Expansion Equation for ANSYS C Linear Regression of the Thermal Expansion Equation for ANSYS D Comparing different Mechanical Strain Definitions E Supporting Documents E.1 Analytic Static Swelling E.2 FEM - Matrix Method E.3 8 Node Finite Element Routine E.4 FEM - Script to create the CTEX table data E.5 Comparison of Solid Mechanics / In dieser Arbeit wird eine Entwurfsplattform für die Modellierung, Simulation und Optimierung von fluidischen Komponenten und deren Wechselwirkungen in größeren Systemen entwickelt. Ein Mikroventil auf der Basis von stimuli-sensitiven Hydrogelen ist das Kernelement des Entwurfstools. Wesentliche Materialeigenschaften wie das Quellverhalten und der kooperative Diffusionskoeffizient werden zu Beginn mit Messungen ermittelt. Mit Finite-Elemente-Simulationen werden aus diesen Daten charakteristische Kennwerte für das mechanische und fluidische Verhalten bestimmt. Sie bilden die Basis für komplexe Systemmodelle in Matlab Simscape, welche das Mikroventil und weitere fluidische Grundelemente in ihrem Zusammenwirken beschreiben. Verschiedene Konzepte können in kurzer Zeit und mit hoher Genauigkeit analysiert, optimiert und verglichen werden. Die Toolbox eignet sich für die Forschung und Entwicklung sowie als Software für die akademische Ausbildung. Sie wurde für den Entwurf eines chemofluidischen NAND-Gatters, für einen chemofluidischen Decoder und für einen chemofluidischen Oszillator eingesetzt.:1 Introduction to Microfluidic Systems 1.1 Chemofluidic Enables Scalable and Logical Microfluidics 1.2 Focus of this Work 2 Fundamentals for Hydrogel-based Lab-on-Chip Systems 2.1 Basic Hydrogel Material Behavior 2.1.1 Basic Swelling Behavior 2.1.2 General Properties of Hydrogels 2.2 Overview of the used Microtechnology 2.2.1 Synthesis of P(NIPAAm-co-SA) 2.2.2 Microfabrication of a Microfluidic Chip 2.3 Introduction to Modeling and Simulation Techniques 2.3.1 Computer-aided Design Methodologies 2.3.2 Model Abstraction Levels for Computer-Aided Design 2.3.3 Modeling Techniques for Microvalves in a Fluidic System 3 Analytical Descriptions of Swelling 3.1 Quasi-Static Description 3.1.1 Physical Static Chemo-Thermal Description 3.1.2 Finite Element Routine for Static Thermo-Elastic Expansion 3.1.3 Static System Level Design for Hydrogel Swelling 3.2 Transient Description 3.2.1 Physical Dynamic Chemo-Thermal Description 3.2.2 Finite Element Routine for Dynamic Thermo-Elastic Expansion 3.2.3 Transient System Level Design for Hydrogel Swelling 3.3 Swelling Hysteresis Effect 3.3.1 Quasi-static Hysteresis 3.3.2 Transient Hysteresis 4 Characterization of Hydrogel 4.1 Data Acquisition through Automated Measurements 4.1.1 Measuring the Swelling of Hydrogels 4.1.2 Contactless Measurement Concept to Determine the Core Stiffness of Hydrogels 4.2 Data Evaluation with Image Recognition 4.3 Data Fitting and Model Adaption 4.3.1 Quasi-static Response 4.3.2 Transient Response 4.3.3 Hysteresis Response 5 Modeling Swelling in Finite Elements 5.1 Validity of the Model and Simulation Approach 5.2 Thermo-Mechanical Model of the Hydrogel Expansion Behavior 5.2.1 Change of the Length by Thermal Expansion 5.2.2 Stress-Strain Relationship for Hydrogels 5.2.3 Thermal Volume Expansion and Parameter Adaptation 5.2.4 Heat Transfer Coefficient 5.3 Volume Phase-Transition of a Hydrogel implemented in ANSYS 5.4 Computational Fluid Dynamics 5.4.1 Analytic Mesh Morphing 5.4.2 One-way Fluid Structure Interaction Modeling 5.4.3 Towards a Two-way Fluid Structure Interaction Model in CFX 6 Lumped Modeling 6.1 The Chemical Volume Phase-transition Transistor Model 6.1.1 Static Hysteresis 6.1.2 Equilibrium Swelling Length – Quasi-static Behavior 6.1.3 Kinematic Swelling Length - Transient Behavior 6.1.4 Stiffness and Maximum Closing Pressure 6.1.5 Calculation of the Fluidic Conductance 6.1.6 Modeling of the Fluid Flow through the Valve 6.2 Circuit Descriptions Analogy for Microfluidic Applications 6.2.1 Advantages and Limitations of Combined Simulink-Simscape Models 6.2.2 Requirements for Microfluidic Circuits 6.2.3 Graphical User Interfaces and Library Element Management 6.3 Modeling Techniques for the Chemical Volume Phase-transition Transistor (CVPT) 6.3.1 Network Description of CVPT 6.3.2 Signal Flow Description of CVPT 6.3.3 Mixed Signal Flow and Network Model for CVPT 7 Micro-Fluidic Toolbox 7.1 Microfluidic Components 7.1.1 Fluid Sources and Stimuli Sources 7.1.2 Fluidic Resistor with Bidirectional Stimulus Transport 7.1.3 Junctions 7.1.4 Chemical Volume Phase-transition Transistor 7.2 Microfluidic Matlab Toolbox 7.3 Modeling Chemofluidic Logic Circuits 7.3.1 Chemofluidic NAND Gate 7.3.2 Chemofluidic Decoder Application 7.3.3 Chemo-Fluidic Oscillator 7.4 Layout Synthesis 8 Summary and Outlook Appendix A 2D Thermo-Mechanical Solid Element for the Finite Element Method B Thermal Expansion Equation for ANSYS C Linear Regression of the Thermal Expansion Equation for ANSYS D Comparing different Mechanical Strain Definitions E Supporting Documents E.1 Analytic Static Swelling E.2 FEM - Matrix Method E.3 8 Node Finite Element Routine E.4 FEM - Script to create the CTEX table data E.5 Comparison of Solid Mechanics

Lineare hyperbolische partielle Differentialgleichungen in homogenen Medien, beispielsweise die Wellengleichung, die die Ausbreitung und die Streuung akustischer Wellen beschreibt, können im Zeitbereich mit Hilfe von Randintegralgleichungen formuliert werden. Im ersten Hauptteil dieser Arbeit stellen wir eine effiziente Möglichkeit vor, numerische Approximationen solcher Gleichungen zu implementieren, wenn das Huygens-Prinzip nicht gilt. Wir nutzen die Faltungsquadraturmethode für die Zeitdiskretisierung und eine Galerkin-Randelement-Methode für die Raumdiskretisierung. Mit der Faltungsquadraturmethode geht eine diskrete Faltung der Faltungsgewichte mit der Randdichte einher. Bei Gültigkeit des Huygens-Prinzips konvergieren die Gewichte exponentiell gegen null, sofern der Index hinreichend groß ist. Im gegenteiligen Fall, das heißt bei geraden Raumdimensionen oder wenn Dämpfungseffekte auftreten, kann kein Verschwinden der Gewichte beobachtet werden. Das führt zu Schwierigkeiten bei der effizienten numerischen Behandlung. Im ersten Hauptteil dieser Arbeit zeigen wir, dass die Kerne der Faltungsgewichte in gewisser Weise die Fundamentallösung im Zeitbereich approximieren und dass dies auch zutrifft, wenn beide bezüglich der räumlichen Variablen abgeleitet werden. Da die Fundamentallösung zudem für genügend große Zeiten, etwa nachdem die Wellenfront vorbeigezogen ist, glatt ist, schließen wir Gleiches auch in Bezug auf die Faltungsgewichte, die wir folglich mit hoher Genauigkeit und wenigen Interpolationspunkten interpolieren können. Darüber hinaus weisen wir darauf hin, dass zur weiteren Einsparung von Speicherkapazitäten, insbesondere bei Langzeitexperimenten, der von Schädle et al. entwickelte schnelle Faltungsalgorithmus eingesetzt werden kann. Wir diskutieren eine effiziente Implementierung des Problems und zeigen Ergebnisse eines numerischen Langzeitexperimentes. Im zweiten Hauptteil dieser Arbeit beschäftigen wir uns mit Transmissionsproblemen der Wellengleichung im Freiraum. Solche Probleme werden gewöhnlich derart behandelt, dass der Freiraum, wenn nötig durch Einführen eines künstlichen Randes, in ein unbeschränktes Außengebiet und ein beschränktes Innengebiet geteilt wird mit dem Ziel, eventuelle Inhomogenitäten oder Nichtlinearitäten des Materials vollständig im Innengebiet zu konzentrieren. Wir werden eine Lösungsstrategie vorstellen, die es erlaubt, die aus der Teilung resultierenden Teilprobleme so weit wie möglich unabhängig voneinander zu behandeln. Die Kopplung der Teilprobleme erfolgt über Transmissionsbedingungen, die auf dem ihnen gemeinsamen Rand vorgegeben sind. Wir diskutieren ein Kopplungsverfahren, das auf verschiedene Diskretisierungsschemata für das Innen- und das Außengebiet zurückgreift. Wir werden insbesondere ein explizites Verfahren im Innengebiet einsetzen, im Gegensatz zum Außengebiet, bei dem wir ein auf ein Mehrschrittverfahren beruhendes Faltungsquadraturverfahren nutzen. Die Kopplung erfolgt nach der Strategie von Johnson und Nédélec, bei der die direkte Randintegralmethode zum Einsatz kommt. Diese Strategie führt auf ein unsymmetrische System. Wir analysieren das diskrete Problem hinsichtlich Stabilität und Konvergenz und unterstreichen die Einsatzfähigkeit des Kopplungsalgorithmus mit der Durchführung numerischer Experimente.

This thesis aims to reduce the reinforcement areas in lattice girder elements after large amounts have been observed in several projects. Existing handbooks and materials for designing lattice girder elements have been analyzed. A revised calculation model for design that is adapted to Eurocode and the Swedish national annex EKS 11 has then been developed. The calculation model should be seen as a proposal to how lattice girder elements can be designed. A reference project has laid the basis for testing the calculation model. Simultaneously two finite element models have been established in FEM-Design and smaller calculations have been performed in WIN-Statik: Concrete Beam.  The results show that the reinforcement areas have been reduced. An effective method of designing lattice girder elements is to extract forces and moments from a finite element program. These are then inserted into the calculation model together with other required data and by making the desired adjustments. The calculation model then designs the lattice girder element. Alternatively, the lattice girder element is designed using the FEM-software whilst the lattice girder is designed using the calculation model. Numerous methods of finding the design-moments have been studied. The results show that it is not satisfactory to calculate the moments with respect to a lattice girder element or a single strip. Thus, the whole slab must be taken into consideration.

De nombreux phénomènes physiques peuvent être étudiés au moyen de modélisations et de simulations numériques, courantes dans les applications scientifiques. Pour être calculable sur un ordinateur, des techniques de discrétisation appropriées doivent être considérées, conduisant souvent à un ensemble d’équations linéaires dont les caractéristiques dépendent des techniques de discrétisation. D’un côté, la méthode des éléments finis conduit généralement à des systèmes linéaires creux, tandis que les méthodes des éléments finis de frontière conduisent à des systèmes linéaires denses. La taille des systèmes linéaires en découlant dépend du domaine où le phénomène physique étudié se produit et tend à devenir de plus en plus grand à mesure que les performances des infrastructures informatiques augmentent. Pour des raisons de robustesse numérique, les techniques de solution basées sur la factorisation de la matrice associée au système linéaire sont la méthode de choix utilisée lorsqu’elle est abordable. A cet égard, les méthodes hiérarchiques basées sur de la compression de rang faible ont permis une importante réduction des ressources de calcul nécessaires pour la résolution de systèmes linéaires denses au cours des deux dernières décennies. Pour les systèmes linéaires creux, leur utilisation reste un défi qui a été étudié à la fois par la communauté des matrices hiérarchiques et la communauté des matrices creuses. D’une part, la communauté des matrices hiérarchiques a d’abord exploité la structure creuse du problème via l’utilisation de la dissection emboitée. Bien que cette approche bénéficie de la structure hiérarchique qui en résulte, elle n’est pas aussi efficace que les solveurs creux en ce qui concerne l’exploitation des zéros et la séparation structurelle des zéros et des non-zéros. D’autre part, la factorisation creuse est accomplie de telle sorte qu’elle aboutit à une séquence d’opérations plus petites et denses, ce qui incite les solveurs à utiliser cette propriété et à exploiter les techniques de compression des méthodes hiérarchiques afin de réduire le coût de calcul de ces opérations élémentaires. Néanmoins, la structure hiérarchique globale peut être perdue si la compression des méthodes hiérarchiques n’est utilisée que localement sur des sous-matrices denses. Nous passons en revue ici les principales techniques employées par ces deux communautés, en essayant de mettre en évidence leurs propriétés communes et leurs limites respectives, en mettant l’accent sur les études qui visent à combler l’écart qui les séparent. Partant de ces observations, nous proposons une classe d’algorithmes hiérarchiques basés sur l’analyse symbolique de la structure des facteurs d’une matrice creuse. Ces algorithmes s’appuient sur une information symbolique pour grouper les inconnues entre elles et construire une structure hiérarchique cohérente avec la disposition des non-zéros de la matrice. Nos méthodes s’appuient également sur la compression de rang faible pour réduire la consommation mémoire des sous-matrices les plus grandes ainsi que le temps que met le solveur à trouver une solution. Nous comparons également des techniques de renumérotation se fondant sur des propriétés géométriques ou topologiques. Enfin, nous ouvrons la discussion à un couplage entre la méthode des éléments finis et la méthode des éléments finis de frontière dans un cadre logiciel unique. / Many physical phenomena may be studied through modeling and numerical simulations, commonplace in scientific applications. To be tractable on a computer, appropriated discretization techniques must be considered, which often lead to a set of linear equations whose features depend on the discretization techniques. Among them, the Finite Element Method usually leads to sparse linear systems whereas the Boundary Element Method leads to dense linear systems. The size of the resulting linear systems depends on the domain where the studied physical phenomenon develops and tends to become larger and larger as the performance of the computer facilities increases. For the sake of numerical robustness, the solution techniques based on the factorization of the matrix associated with the linear system are the methods of choice when affordable. In that respect, hierarchical methods based on low-rank compression have allowed a drastic reduction of the computational requirements for the solution of dense linear systems over the last two decades. For sparse linear systems, their application remains a challenge which has been studied by both the community of hierarchical matrices and the community of sparse matrices. On the one hand, the first step taken by the community of hierarchical matrices most often takes advantage of the sparsity of the problem through the use of nested dissection. While this approach benefits from the hierarchical structure, it is not, however, as efficient as sparse solvers regarding the exploitation of zeros and the structural separation of zeros from non-zeros. On the other hand, sparse factorization is organized so as to lead to a sequence of smaller dense operations, enticing sparse solvers to use this property and exploit compression techniques from hierarchical methods in order to reduce the computational cost of these elementary operations. Nonetheless, the globally hierarchical structure may be lost if the compression of hierarchical methods is used only locally on dense submatrices. We here review the main techniques that have been employed by both those communities, trying to highlight their common properties and their respective limits with a special emphasis on studies that have aimed to bridge the gap between them. With these observations in mind, we propose a class of hierarchical algorithms based on the symbolic analysis of the structure of the factors of a sparse matrix. These algorithms rely on a symbolic information to cluster and construct a hierarchical structure coherent with the non-zero pattern of the matrix. Moreover, the resulting hierarchical matrix relies on low-rank compression for the reduction of the memory consumption of large submatrices as well as the time to solution of the solver. We also compare multiple ordering techniques based on geometrical or topological properties. Finally, we open the discussion to a coupling between the Finite Element Method and the Boundary Element Method in a unified computational framework.

This thesis investigates the numerical simulation of three-dimensional, mechanical deformation problems in the context of large deformations. The main focus lies on the prediction of non-linearly elastic, incompressible material. Based on the equilibrium of forces, we present the weak formulation of the large deformation problem. The discrete version can be derived by using linearisation techniques and an adaptive mixed finite element method. This problem turns out to be a saddle point problem that can, among other methods, be solved via the Bramble-Pasciak conjugate gradient method or the minimal residual algorithm. With some modifications the resulting simulation can be improved but we also address remaining limitations. Some numerical examples show the capability of the final FEM software. In addition, we briefly discuss the special case of linear elasticity with small deformations. Here we directly derive a linear weak formulation with a saddle point structure and apply the adaptive mixed finite element method. It is shown that the presented findings can also be used to treat the nearly incompressible case.

In dem Vortrag wird die Entwicklung einer Finiten-Elemente-App für Android dargelegt, sowie die Vorteile im Postprozessing von einfachen Strukturen bei der Verwendung der Gestensteuerung erörtert.

Im Vortrag wird das Vorgehen zur Konstruktionsoptimierung mittels parametrischer FE-Simulation beschrieben. Die einzelnen Schritte werden dargestellt und am Beispiel eines Übertragungselements für Klauenkupplungen erläutert. Zunächst wird der Optimierungsgegenstand vorgestellt und die Festlegung der Entwurfsvariablen und Zielfunktionen beschrieben. Im Anschluss werden die Erstellung des FE-Modells und die Durchführung der Optimierungsrechnung schrittweise erläutert. Abschließend folgen ein Vergleich verschiedener Optimierungsmethoden und die Zusammenfassung. Als Software wurden ANSYS und Autodesk Inventor verwendet.

In this thesis singularly perturbed convection-diffusion equations in the unit square are considered. Due to the presence of a small perturbation parameter the solutions of those problems exhibit an exponential layer near the outflow boundary and two parabolic layers near the characteristic boundaries. Discretisation of such problems on standard meshes and with standard methods leads to numerical solutions with unphysical oscillations, unless the mesh size is of order of the perturbation parameter which is impracticable. Instead we aim at uniformly convergent methods using layer-adapted meshes combined with standard methods. The meshes considered here are S-type meshes--generalisations of the standard Shishkin mesh. The domain is dissected in a non-layer part and layer parts. Inside the layer parts, the mesh might be anisotropic and non-uniform, depending on a mesh-generating function. We show, that the unstabilised Galerkin finite element method with bilinear elements on an S-type mesh is uniformly convergent in the energy norm of order (almost) one. Moreover, the numerical solution shows a supercloseness property, i.e. the numerical solution is closer to the nodal bilinear interpolant than to the exact solution in the given norm. Unfortunately, the Galerkin method lacks stability resulting in linear systems that are hard to solve. To overcome this drawback, stabilisation methods are used. We analyse different stabilisation techniques with respect to the supercloseness property. For the residual-based methods Streamline Diffusion FEM and Galerkin Least Squares FEM, the choice of parameters is addressed additionally. The modern stabilisation technique Continuous Interior Penalty FEM--penalisation of jumps of derivatives--is considered too. All those methods are proved to possess convergence and supercloseness properties similar to the standard Galerkin FEM. With a suitable postprocessing operator, the supercloseness property can be used to enhance the accuracy of the numerical solution and superconvergence of order (almost) two can be proved. We compare different postprocessing methods and prove superconvergence of above numerical methods on S-type meshes. To recover the exact solution, we apply continuous biquadratic interpolation on a macro mesh, a discontinuous biquadratic projection on a macro mesh and two methods to recover the gradient of the exact solution. Special attentions is payed to the effects of non-uniformity due to the S-type meshes. Numerical simulations illustrate the theoretical results.

A new simple design approach will be described that utilizes test results from the Repeated Load Triaxial Apparatus to establish the risk level of permanent deformations in the unbound granular layers (UGL) in pavement constructions under consideration of the seasonal effects. From this data a serviceability limit line (plastic shakedown limit) stress boundary for the unbound granular materials (UGM) was defined for different moisture contents. Below this line the material will have stable behavior. The serviceability limit line was applied in a finite-element (FE)-program FENLAP to predict whether or not stable behavior occurs in the UGM. To calculate the stress in the UGL, a nonlinear elastic model (Dresden Model), which is described in the paper, was implemented into the FE-program. The effects of changing moisture content during Spring-thaw period and asphalt temperature on pavement structural response were investigated. Additionally, permanent deformation calculations for the UGL were performed taking the stress history into consideration. The results clearly demonstrate that, for pavement constructions with thick asphalt layers, there is no risk of rutting in the granular base, even at high number of load repetitions. The study showed that the proposed design approach is a very satisfactory simple method to assess the risk against rutting in the UGL, even without the calculation of the exact permanent deformation of the pavement construction.

Betongpelare är en vanlig del i konstruktioner inom bygg-och anläggningsbranschen och kräver normalt en stor mängd armeringsjärn för att säkerställa dess styrka och stabilitet. Vid dimensionering av slanka betongpelare ska hänsyn inte bara tas till första ordningens moment och deformationer utan även andra ordningens teori ska beaktas. För att dimensionera förandra ordningens moment beskriver Eurokoderna tre olika metoder, en generell metod samt två förenklade metoder: nominell styvhet och nominell krökning. Dimensionering kan ske förhand eller med datorprogram. FEM-Design, som är ett avancerat analysprogram, baseras på finita elementmetoden som är en numerisk analysmetod och ett av de vanligaste sätten att beräkna fysikaliska fenomen. FEM-Design kan ofta ge ett bättre och säkrare resultat då handberäkningar approximerar för att de ska vara hanterbara.I arbetet jämförs beräknad armeringsmängd mellan handberäkningar med nominell styvhet,nominell krökning samt analysprogrammet FEM-Design. Arbetet har gjorts för att undersöka skillnaden i armering och därmed kunna avgöra vilken metod som ger minst respektive mest mängd armering. Betongpelarna som undersöks är slanka och har tre olika upplagsförhållanden, varje upplag belastas med tre olika belastningsfall. Beräkningarna är utförda enligt Eurokod 2 och resultatet blev att FEM-Design gav i sju av nio fall lägst andra ordningens moment. I åtta av nio fall gav FEM-Design lägst mängd armering medan nominell styvhet gav störst andra ordningens moment och störst mängd armering i samtliga fall. Nominell krökning gav ett andra ordningens moment som var nära FEM-Designs resultat medstörsta skillnaden på 30%. Beräknad armering för nominell krökning växlade mellan attstämma överens mest med nominell styvhet och FEM-Design. Utifrån resultatet har även skillnaden i pris på armering beräknats fram där nominell styvhet är det dyraste alternativet.FEM-Design är 61% billigare än nominell styvhet medan nominell krökning är 51% billigareän nominell krökning.Jämförelsen visar att nominell krökning kan i dessa belastningsfall som har undersökts ansesvara den bästa metoden av handberäkningarna men FEM-Design anses vara den bästa av samtliga metoder i detta arbete. Slutsatsen som kunde dras var att båda de förenklade handberäkningsmetoderna överdimensionerar armeringsmängden i pelarna och därmed anses FEM-Design som det bästa alternativet. FEM-Design gav inte bara minst armering och därmed lägsta armeringskostnaden utan dimensioneringen tog också kortast tid. / When designing slender concrete columns where the second-order theories need to be considered, the Eurocodes describe three different methods; a general method and two simplified methods - nominal stiffness and nominal curvature. Designing can be done manually or with programs. FEM-design, an advanced analysis program, is based on the finiteelement method, which is a numerical analysis method and is one of the most common ways to calculate big and complex problems. FEM-Design often provides more reliable results compared to calculations done by hand, which involve approximations to make them manageable.In this study the calculated reinforcement quantities are compared with hand calculationsusing the nominal stiffness, nominal curvature and FEM-Design. The purpose is to investigatethe difference in reinforcement and determine which method requires the least amount of reinforcement. The investigated columns are slender and have three different boundary conditions, each subject to three different load cases. The calculations are performed according to the Eurocode 2. The results show that in seven out of nine cases the FEM-Design method produced the lowest second-order moments. In eight out of nine cases, FEM-Design resulted in least amount of reinforcement, while nominal stiffness resulted in the highest second-order moments and greatest amount of reinforcement in all cases. Nominal curvature generally produced second-order moments that were close to FEM-Design, the largest difference being 30%. Regarding the calculated reinforcement , nominal curvature varied in agreement with nominal stiffness and FEM-Design. The cost of reinforcement was also analyzed, with nominal stiffness being 51% more expensive than nominal curvature and 61% more expensive than FEM-Design. Nominal curvature was the preferred manual method, but FEM-Design emerged as the best overall method, offering both minimal reinforcement and shorter design time.