Orientadores: Milton da Costa Lopes Filho, Helena Judith Nussenzveig Lopes / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-25T00:41:15Z (GMT). No. of bitstreams: 1 Albanez_DeboraAparecidaFrancisco_D.pdf: 3117782 bytes, checksum: 4f8e30c3d217ed3a6d26e9924d4df7ab (MD5) Previous issue date: 2014 / Resumo: Motivados pela existênca de um número finito de parâmetros determinantes (graus de liberdade), tais como modos, nós e médias espaciais locais para sistemas dinâmicos dissipativos, principalmente as equações de Navier-Stokes, apresentamos nesta tese um novo algoritmo de assimilação contínua de dados para o modelo tridimensional das equações Navier-Stokes-alpha, o qual consiste na introdução de um tipo geral de operador interpolante de aproximação (construído a partir de medições observacionais) dentro das equações de Navier-Stokes-alpha. O principal resultado garante condições sob a resolução espacial de dimensão finita dos dados coletados, suficientes para que a solução aproximada, construída a partir desses dados coletados, convirja para a referente solução que não conhecemos (realidade física) no tempo. Essas condições são dadas em termos de alguns parâmetros físicos, tais como a viscosidade cinemática, o tamanho do domínio e o termo de força / Abstract: Motivated by the presence of the finite number of determining parameters (degrees of freedom) such as modes, nodes and local spatial averages for dissipative dynamical systems, specially Navier-Stokes equations, we present in this thesis a new continuous data assimilation algorithm for the three-dimensional Navier-Stokes-alpha model, which consists of introducing a general type of approximation interpolation operator, (that is constructed from observational measurements), into the Navier-Stokes-alpha equations. The main result provides conditions on the finite-dimensional spatial resolution of the collected data, sufficient to guarantee that the approximating solution, that is obtained from these collected data, converges to the unkwown reference solution (physical reality) over time. These conditions are given in terms of some physical parameters, such as kinematic viscosity, the size of the domain and the forcing term / Doutorado / Matematica / Doutora em Matemática

In this work, a Representative Volume Element (RVE) generator based on the distance fields of arbitrary shaped inclusion packing is used to obtain morphologies of open-foam materials. When the inclusions are spherical, the tessellations of the resultant packing creates morphologies that are similar to physical foam samples in terms of their face-to-pore ratio, edge-to-face ratio and strut length distribution among others. Functions that combine the distance fields can be used to obtain the tessellations along with the necessary variations in the strut geometry and extract these open-foam morphologies. It is also possible to replace the inclusion packing with a predefined set of inclusions that are directly extracted from CT-scan based images.The use of discrete level-set functions results in steep discontinuities in the distance function derivatives. A multiple level-set based approach is presented that can appropriately capture the sharp edges of the open-foam struts from the resultant distance fields. Such an approach can circumvent the discontinuities presented by the distance fields which might lead to spurious stress concentrations in a material behavior analysis.The individual cells are then extracted as inclusion surfaces based on said combinations of the distance functions and their modifications. These surfaces can be joined together to obtain the final geometry of the open-foam morphologies. The physical attributes of the extracted geometries are compared to the experimental data. A statistical comparison is presented outlining the various features. The study is extended to morphologies that have been extracted using CT-scan images. With the help of mesh optimization tools, surface triangulations can be obtained, merged and developed as finite element (FE) models. The models are ready to use in a multi-scale study to obtain the homogenized material behavior. The upscaling can help assess the practical applications of these models by comparing with experimental data of physical samples. The material behavior of the RVEs are also compared with the experimental observations. To increase the computational efficiency of the study, a neural network based surrogate is presented that can replace the micro-scale boundary value problem (BVP) in the multi-scale analysis. The neural networks are built with the help of modules that are specifically designed to predict history dependent behavior and are called Recurrent Neural Networks (RNN). The surrogates are trained to take into account the randomness of the loading that complex material undergo during any given material behavior analysis. / Dans ce travail, un générateur de volumes élémentaires représentatifs (VER) basé sur les champs de distance d'un agrégat d'inclusions de forme arbitraire est développé dans le cadre de matériaux moussés à structure ouverte. Lorsque les inclusions sont sphériques, la tessellation de l'agrégat résulte en des morphologies similaires aux échantillons de mousse physique en termes de rapports des nombres de face par pores et de bords par faces, ainsi que de la distribution de la longueur des entretoises, entre autres. Les fonctions qui combinent les champs de distance peuvent être utilisées pour obtenir des tesselations avec les variations nécessaires aux géométries des entretoises et extraire ces morphologies de mousse ouverte. Il est également possible de remplacer l'agrégat d'inclusions par un ensemble prédéfini d'inclusions qui sont directement extraites d'images tomographiques.L'utilisation de fonctions de niveaux discrètes entraîne de fortes discontinuités dans les dérivées des champs de distance. Une approche basée sur des ensembles de niveaux multiples est présentée qui peut capturer de manière appropriée les arêtes vives des entretoises des mousses ouvertes à partir des champs de distance résultants. Une telle approche peut contourner les discontinuités présentées par les champs de distance qui pourraient conduire à des concentrations de contraintes parasites dans une analyse ducomportement des matériaux.Les pores individuels sont ensuite extraits en tant que surfaces d'inclusions sur la base desdites combinaisons des fonctions de distance et de leurs modifications. Ces surfaces peuvent être réunies pour obtenir la géométrie finale des morphologies de mousse ouverte. Les attributs physiques des géométries extraites sont comparés aux données expérimentales. Une comparaison statistique est présentée décrivant les différentes caractéristiques. L'étude est étendue aux morphologies qui ont été extraites à l'aide d'images tomographiques.À l'aide d'outils d'optimisation de maillage, les triangulations des surfaces peuvent être obtenues, fusionnées et développées sous forme de modèles d'éléments finis (FE). Les modèles sont prêts à être utilisés dans une étude multi-échelle pour obtenir le comportement homogénéisé du matériau. La mise à l'échelle peut aider à évaluer les applications pratiques de ces modèles en les comparant aux données expérimentales d'échantillons physiques. Le comportement des matériaux des VERs est également comparé aux observations expérimentales.Pour augmenter l'efficacité de calcul de l'étude, un modèle de substitution basé sur un réseau neuronal est présenté. Ce modèle peut remplacer le problème aux valeurs limites à l'échelle micro dans une analyse multi-échelle. Les réseaux de neurones sont construits à l'aide de modules spécialement conçus pour prédire le comportement dépendant de l'histoire et sont appelés réseaux de neurones récurrents (RNN). Les modèles de substitution sont entrainés pour prendre en compte le caractère aléatoire du chargement que subit un matériau complexe lors d'une analyse de comportement d'un matériau. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

Under tidsperioden 1965-1974 byggdes i Sverige omkring en miljon nya bostäder, även kallat för Miljonprogrammet. Idag utgörs närmare en tredjedel av det svenska bostadsbeståndet av bostäder från denna period och många byggnader börjar uppnå sin tekniska livslängd. Sverige har efter EU-direktiv tagit fram nationella mål om en effektivare energianvändning. För att snabbare nå dessa mål kan renovering och upprustning av miljonprogrammet kombineras med våningspåbyggnad.   Sverige står också inför växande bostadsbrist, likt under miljonprogrammet, samtidigt som samhället har begränsade ytor såväl i stadskärnor som i tätorter. Genom att rusta upp bostäder från miljonprogrammet i samband med en våningspåbyggnad kan nya bostäder skapas på ett resurseffektivt sätt och energiprestandan för den befintliga byggnaden förbättras.   I det här projektet har energiprestandan för ett tidstypiskt flerbostadshus utvärderats och därefter jämförts mot då flerbostadshuset utrustats med en våningspåbyggnad. Projektet tilldelades ett referenshus i Nacka som efter uppbyggnad och simulering i programvaran IDA ICE resulterade i en årlig energianvändning på 197,1 kWh/m2. En våningspåbyggnad lades till på referenshuset och visade efter simulering i programvaran IDA ICE en ny årlig energianvändning på bland annat 169,7 kWh/m2.   Efter projektet stod det klart att med en våningspåbyggnad kan energiprestanda för ett miljonprogramshus förbättras och i bästa fall kan en byggnad likt referenshuset gå från en energiklass G till E. Bostadsförtätning med hjälp av våningspåbyggnad är gynnsam ur många aspekter. Förutom att det sänker den totala byggnadens energianvändning skapar det också nya bostäder på ett resurseffektivt sätt. Samhället måste försöka skapa incitament för fastighetsägare till att renovera och hitta energieffektiva åtgärder för sina fastigheter. Ett sådant exempel skulle kunna vara tredimensionell fastighetsbildning vilket även är en alternativ form till att finansiera investeringar som exempelvis renoveringar. / During the years 1965-1974 around one million new housing were built in Sweden, this was also known as the “miljonprogrammet”. Today, nearly a third of the Swedish housing stock is from this particular period, and many buildings are reaching the end of their technical lifetime. After the new EU directives Sweden have decided on developing it's on national goals to achieve smart energy consumption. To speed up this development can the renovations of the existing "miljonprogrammet" executed in combination with storey extension.   Sweden is also facing growing housing shortage, much like during construction of the “miljonprogrammet” as well as limited areas both in urban and densely populated areas. By refurbishing buildings from the “miljonprogrammet” in conjunction with a storey extension, new housing can be built in a resource and energy efficient way. This should also improve the energy performance of the existing building.   In this project, the energy performance of an apartment building, typical from this time, was evaluated and then compared to a modified building with a storey extension. A reference house located in Nacka, Sweden was used to simulate the annual energy usage in the software IDA ICE. The simulation yielded an energy usage of 197.1 kWh/m2 for the reference building and 167.1 kWh/m2 for the building with a storey extension.   After the project it became clear that a storey extension on a building from the “miljonprogrammet” improved the existing building's energy consumption. At best, a building like the reference house can improve the energy classification from energy class G to E. Residential densification using storey extension is beneficial in many aspects. In addition to lowering the total energy consumption of the building it also creates new homes in a resource efficient manner. Society must seek to create enticements for property owners to renovate and execute energy efficient measures on their properties. One such example would be three-dimensional property formation which is also an alternative form of financing investment such as a renovation. / <p>Denna studentuppsats, som inte är ett examensarbete, är genomförd i projektkursen 5EN040 under hösten 2015. Studentarbetet har bedrivits i sammarbete med Tyréns Umeå.</p> / Uppsatsen ingår som ett kursmoment i projektkursen 5EN040 i energiteknik

I takt med att äldre byggnader i vårt bostadsbestånd blir i allt större behov av omfattande renoveringar, skärps även våra samhällskrav ytterligare. Då gäller det i samband med renovering att finna hela åtgärdspaket som både ger energibesparing men samtidigt är ekonomiskt lönsam.   I den här rapporten undersöks möjlig energibesparing men också lönsamheten av energisparåtgärder i samband med påbyggnad av nya bostäder i ett redan befintligt flerbostadshus. Byggnadens befintliga värmesystem byts ut mot bergvärme, som också verkar genom ventilationssystemet, och därefter förlängs byggnaden med tre nya våningsplan. Rapporten utvärderar även om påbyggnad av nya bostäder i det enskilda fallet ska betraktas som tillbyggnad eller ombyggnad, samt vilka krav som därefter ställs vid ändring av byggnad enligt PBL och BBR.   Med hjälp av energiberäkningsprogrammet IDA ICE, kunde effekten från de olika energisparåtgärderna studeras. Värdet för den årliga energibesparingen jämfördes därefter med åtgärdernas investeringskostnad. Åtgärder ansågs lönsamma om värdet av den årliga besparingen var tillräckligt stor i förhållande till investeringskostnaden.   För det enskilda fallet ger energibesparande åtgärder i samband med påbyggnad en avsevärd förbättring både ur energisynpunkt men också ekonomiskt perspektiv. Påbyggnaden beräknas initialt återbetalda i och med försäljning av bostadsrätter samtidigt som återbetalningstiden för ingreppen i den befintliga byggnaden troligen betalar sig inom 10-15 år. För det enskilda fallet var möjlig energibesparing efter genomförda åtgärder 74 procent, vilket motsvarar är en minskning med närmare 130 kWh/m2 och år jämfört med referensfallet. Rapporten fastslår att påbyggnaden ska betraktas som tillbyggnad och att fyra bergvärmepumpar är fullt tillräckliga för att både uppnå energibesparing samt uppfylla ekonomisk lönsamhet. / As older buildings in our housing stock are in increasing need of extensive renovations, it further enhances our social requirements. It is then needed alongside with renovations to find whole measures that yields energy savings which also is financially profitable.   In this report, we examine the possible energy savings alongside with the profitability of the energy measures connected with extensions of new housing on top of an existing housing. The current heating system of the building is replaced with geothermal heating, which is also working through to the ventilation system. Thereafter the building is extended with three new floors. The report also evaluates if an extension of new housing in the individual case is to be seen as an extension or a reconstruction, together with the demands of which are put on an altered building in accordance to PBL and BBR.   With the help of the computational energy software IDA ICE, the affect from the different energy measures could be studied. The yearly economical savings was then compared to the cost of the different measures. The measures were deemed profitable if the value of the yearly savings exceeded the initial cost.   For the specific case, the measures of energy savings gave an considerable improvement for the extension, both in energy but also in the economical sense. The investment of the extensions is to be seen payed via sales of apartments, and the payback on the actions taken on the existing building is estimated to within 10 to 15 years. for the individual case the possible yearly energy savings, after completed measures, is upwards of 74 percent, which translates to 130 kWh/m2 per year. This report also states that, in specific case, extensions of new housing is to be seen as an extensions and that four geothermal heating pumps are enough to reach sufficient energy savings together with economical profitability.

Mechanics of structure genome (MSG) is a unified homogenization theory that provides constitutive modeling of three-dimensional (3D) continua, beams and plates. In present work, the author extends the MSG to study the buckling of structures such as stiffened and sandwich panels. Such structures are usually slender or flat and easily buckle under compressive loads or bending moments which may result in catastrophic failure.<div><br><div>Buckling studies of stiffened and sandwich panels are found to be scattered. Most of the existed theories employ unnecessary assumptions or only apply to certain types of structures. There are few unified approaches that are capable of studying the buckling of different kinds of structures altogether. The main improvements of current approach compared with other methods in the literature are avoiding unnecessary assumptions, the capability of predicting all possible buckling modes including the global and local buckling modes, and the potential in studying the buckling of various types of structures.<br></div><div><br></div><div>For global buckling that features small local rotations, MSG mathematically decouples the 3D geometrical nonlinear problem into a linear constitutive modeling using structure genome (SG) and a geometrical nonlinear problem defined in a macroscopic structure. As a result, the original structures are simplified as macroscopic structures such as beams, plates or continua with effective properties, and the global buckling modes are predicted on macroscopic structures. For local buckling that features finite local rotations, Green strain is introduced into the MSG theory to achieve geometrically nonlinear constitutive modeling. Newton’s method is used to solve the nonlinear equilibrium equations for fluctuating functions. To find the bifurcated fluctuating functions, the fluctuating functions are then perturbed under the Bloch-periodic boundary conditions. The bifurcation is found when the tangent stiffness associated with the perturbed fluctuating functions becomes singular. Moreover, the arc-length method is introduced to solve the nonlinear equilibrium equations for post-local-buckling predictions because of its robustness. The imperfection is included in the form of geometrical imperfection by superimposing the scaled buckling modes in linear perturbation analysis on mesh.<br></div><div><br></div><div>Extensive validation case studies are carried out to assess the accuracy of the MSG theory in global buckling analysis and post-global-buckling analysis, and assess the accuracy of the extended MSG theory in local buckling and post-local-buckling analysis. Results using MSG theory and extended MSG theory in buckling analysis are compared with direct numerical solutions such as 3D FEA results and results in literature. Parametric studies are performed to reveal the relative influence of selective geometric parameters on buckling behaviors. The extended MSG theory is also compared with representative volume element (RVE) analysis with Bloch-periodic boundary conditions using commercial finite element packages such as Abaqus to assess the efficiency and accuracy of the present approach.<br></div></div>

Zur Analyse der Beanspruchungen in textilverstärkten Elastomerbauteilen wie Luftfedern, Reifen, Riemen und Schläuchen sind Berechnungsmodelle mit einer feinen Balance zwischen Genauigkeit und Effizienz erforderlich. Die großen Deformationen, stark anisotropen Struktureigenschaften und kleinen Abmessungen der Festigkeitsträger gegenüber denen des Bauteils bedürfen einerseits einer detaillierten Modellierung, andererseits sind die kritischen Bereiche in diesen Bauteilen räumlich stark begrenzt, sodass eine Reduktion des Berechnungsaufwands erstrebenswert ist. Diese Modellreduktion führt zu Simulationen mit geringer Rechenzeit, die für eine praxistaugliche Optimierung von Hybridcord-Elastomer-Verbunden unerlässlich sind. Die beiden Hauptschwerpunkte der vorliegenden Arbeit bilden die kontinuumsmechanische Modellierung von Hybridcorden und die Erstellung repräsentativer Volumenelemente hochbeanspruchter Hybridcord-Elastomer-Verbunde. Aufbauend auf einem anisotropen Plastizitätsmodell zur Erfassung der Reibung in Multifilamentgarnen stellt ein Finite-Elemente-Modell zur Simulation der Verzwirnung von Hybridcorden das Fundament der Arbeit dar. Anhand experimenteller Ergebnisse aus Zug- und Torsionsversuchen sowie einem Vergleich mit Querschnittsaufnahmen wird gezeigt, dass das Modell die komplexen Eigenschaften eines Hybridcords abbilden kann. Die Grundlage der repräsentativen Volumenelemente stellt eine Erweiterung der klassischen periodischen Randbedingungen dar, die eine Berücksichtigung von Krümmungen und Drucklasten ermöglicht. Das Modell eignet sich daher, die Beanspruchungen in den hochbelasteten Bereichen textilverstärkter Elastomerbauteile wie der Rollfalte einer Luftfeder effizient zu analysieren. Mittels Parameterstudien werden abschließend Hybridcorde und Hybridcord-Elastomer-Verbunde untersucht und einige Hinweise für eine optimale Gestaltung hinsichtlich minimaler Beanspruchungen des Elastomers, des Hybridcords sowie der Grenzfläche gegeben. / The analysis of stresses and strains within textile-reinforced rubber components like air springs, tyres, driving belts, and tubes requires accurate as well as efficient computational models. On the one hand, the large deformations, the composite's strongly anisotropic properties, and the large ratio between the size of the cords and the composite necessitate a precise modeling. On the other hand, the highly loaded parts of the components are spatially confined and thus a reduction of the computational effort is desirable. These reduced models are efficient enough for performing engineering-oriented optimizations. The two main priorities of this work are the continuum mechanical modeling of hybrid cords and the development of representative volume elements of highly loaded hybrid cord-rubber composites. Based on an anisotropic plasticity model, which takes the frictional sliding between the filaments within multifilament yarns into account, a finite element model for the simulation of the twisting process of a hybrid cord is the fundament of this work. A comparison with experimental results from tensile and torsional tests as well as images of cross sections validate the proposed hybrid cord model. The basis of the representative volume element is the extension of the classical periodic boundary conditions, which now enable to take the curvature and pressure load into account. Thus, the model is suitable to analyze the highly loaded parts of hybrid cord-rubber composites like the rolling lobe of an air spring. Finally, the set-ups of hybrid cords and hybrid cord-rubber composites are analyzed by means of parameter studies to obtain a minimized loading of the rubber, yarns, and their interface.

Zur Analyse der Beanspruchungen in textilverstärkten Elastomerbauteilen wie Luftfedern, Reifen, Riemen und Schläuchen sind Berechnungsmodelle mit einer feinen Balance zwischen Genauigkeit und Effizienz erforderlich. Die großen Deformationen, stark anisotropen Struktureigenschaften und kleinen Abmessungen der Festigkeitsträger gegenüber denen des Bauteils bedürfen einerseits einer detaillierten Modellierung, andererseits sind die kritischen Bereiche in diesen Bauteilen räumlich stark begrenzt, sodass eine Reduktion des Berechnungsaufwands erstrebenswert ist. Diese Modellreduktion führt zu Simulationen mit geringer Rechenzeit, die für eine praxistaugliche Optimierung von Hybridcord-Elastomer-Verbunden unerlässlich sind. Die beiden Hauptschwerpunkte der vorliegenden Arbeit bilden die kontinuumsmechanische Modellierung von Hybridcorden und die Erstellung repräsentativer Volumenelemente hochbeanspruchter Hybridcord-Elastomer-Verbunde. Aufbauend auf einem anisotropen Plastizitätsmodell zur Erfassung der Reibung in Multifilamentgarnen stellt ein Finite-Elemente-Modell zur Simulation der Verzwirnung von Hybridcorden das Fundament der Arbeit dar. Anhand experimenteller Ergebnisse aus Zug- und Torsionsversuchen sowie einem Vergleich mit Querschnittsaufnahmen wird gezeigt, dass das Modell die komplexen Eigenschaften eines Hybridcords abbilden kann. Die Grundlage der repräsentativen Volumenelemente stellt eine Erweiterung der klassischen periodischen Randbedingungen dar, die eine Berücksichtigung von Krümmungen und Drucklasten ermöglicht. Das Modell eignet sich daher, die Beanspruchungen in den hochbelasteten Bereichen textilverstärkter Elastomerbauteile wie der Rollfalte einer Luftfeder effizient zu analysieren. Mittels Parameterstudien werden abschließend Hybridcorde und Hybridcord-Elastomer-Verbunde untersucht und einige Hinweise für eine optimale Gestaltung hinsichtlich minimaler Beanspruchungen des Elastomers, des Hybridcords sowie der Grenzfläche gegeben.:Inhaltsverzeichnis Abkürzungs- und Symbolverzeichnis VIII 1 Einleitung 1 2 Grundlagen der Mathematik und der Mechanik 6 2.1 Tensoralgebra und -analysis 6 2.2 Nichtlineare Kontinuumsmechanik 11 2.3 Nichtlineare Finite-Elemente-Methode 16 3 Einordnung in den Stand der Forschung 22 4 Experimentelle Untersuchungen 26 4.1 Charakterisierung der Standardcorde 26 4.2 Charakterisierung der Hybridcorde 33 5 Materialmodelle für Multi lamentgarne 38 5.1 Anisotropes Plastizitätsmodell der Filamentreibung 38 5.2 Numerische Lösung der Materialgleichungen 43 5.3 Analytische Lösung für reibungsfreies Gleiten 48 5.4 Modellierung des thermischen Schrumpfens 50 6 FEM-basierte Modellierung von Hybridcorden 53 6.1 Simulation der Verzwirnung eines Standardcords 53 6.2 Erweiterung des Berechnungsmodells auf Hybridcorde 60 6.3 Analytisches Modell der Geometrie eines Hybridcords 65 6.4 Qualitative Charakterisierung des Hybridcordmodells 74 6.5 Parameteridenti kation und Validierung 83 6.6 Optimierungsbeispiele 92 7 Schalenartige RVEs für Cord-Elastomer-Verbunde 96 7.1 Geometrie der Axial- und der Kreuzlage 96 7.2 Erweiterte periodische Randbedingungen 98 7.3 E ektive Schaleneigenschaften 111 7.4 Berücksichtigung der Drucklast 118 7.5 Diskretisierung der RVEs 122 7.6 Submodelltechnik 128 7.7 Parameterstudien an Hybridcord-Elastomer-Verbunden 135 8 Zusammenfassung und Ausblick 146 Literaturverzeichnis 151 / The analysis of stresses and strains within textile-reinforced rubber components like air springs, tyres, driving belts, and tubes requires accurate as well as efficient computational models. On the one hand, the large deformations, the composite's strongly anisotropic properties, and the large ratio between the size of the cords and the composite necessitate a precise modeling. On the other hand, the highly loaded parts of the components are spatially confined and thus a reduction of the computational effort is desirable. These reduced models are efficient enough for performing engineering-oriented optimizations. The two main priorities of this work are the continuum mechanical modeling of hybrid cords and the development of representative volume elements of highly loaded hybrid cord-rubber composites. Based on an anisotropic plasticity model, which takes the frictional sliding between the filaments within multifilament yarns into account, a finite element model for the simulation of the twisting process of a hybrid cord is the fundament of this work. A comparison with experimental results from tensile and torsional tests as well as images of cross sections validate the proposed hybrid cord model. The basis of the representative volume element is the extension of the classical periodic boundary conditions, which now enable to take the curvature and pressure load into account. Thus, the model is suitable to analyze the highly loaded parts of hybrid cord-rubber composites like the rolling lobe of an air spring. Finally, the set-ups of hybrid cords and hybrid cord-rubber composites are analyzed by means of parameter studies to obtain a minimized loading of the rubber, yarns, and their interface.:Inhaltsverzeichnis Abkürzungs- und Symbolverzeichnis VIII 1 Einleitung 1 2 Grundlagen der Mathematik und der Mechanik 6 2.1 Tensoralgebra und -analysis 6 2.2 Nichtlineare Kontinuumsmechanik 11 2.3 Nichtlineare Finite-Elemente-Methode 16 3 Einordnung in den Stand der Forschung 22 4 Experimentelle Untersuchungen 26 4.1 Charakterisierung der Standardcorde 26 4.2 Charakterisierung der Hybridcorde 33 5 Materialmodelle für Multi lamentgarne 38 5.1 Anisotropes Plastizitätsmodell der Filamentreibung 38 5.2 Numerische Lösung der Materialgleichungen 43 5.3 Analytische Lösung für reibungsfreies Gleiten 48 5.4 Modellierung des thermischen Schrumpfens 50 6 FEM-basierte Modellierung von Hybridcorden 53 6.1 Simulation der Verzwirnung eines Standardcords 53 6.2 Erweiterung des Berechnungsmodells auf Hybridcorde 60 6.3 Analytisches Modell der Geometrie eines Hybridcords 65 6.4 Qualitative Charakterisierung des Hybridcordmodells 74 6.5 Parameteridenti kation und Validierung 83 6.6 Optimierungsbeispiele 92 7 Schalenartige RVEs für Cord-Elastomer-Verbunde 96 7.1 Geometrie der Axial- und der Kreuzlage 96 7.2 Erweiterte periodische Randbedingungen 98 7.3 E ektive Schaleneigenschaften 111 7.4 Berücksichtigung der Drucklast 118 7.5 Diskretisierung der RVEs 122 7.6 Submodelltechnik 128 7.7 Parameterstudien an Hybridcord-Elastomer-Verbunden 135 8 Zusammenfassung und Ausblick 146 Literaturverzeichnis 151

Den bostadspolitik som förts de senaste två decennierna har gett oss en alltmer segregerad stadskärna i Stockholm. Byggsubventionernas avveckling på 90-talet har lett till en historiskt låg byggtakt och ett byggande som ensidigt riktat sig till resursstarka grupper i samhället. Parallellt med detta har stora delar av hyresbeståndet ombildats till bostadsrätter vilket medfört att många relativt billiga hyreslägenheter i äldre fastigheter har försvunnit ur beståndet. Dessa är svåra att ersätta med nyproduktion, då dessa är dyrare. Kärnproblemet är förstås att det är dyrt att bygga hus och om man antar att den nuvarande bostadspolitiken består är det ytterst angeläget att utveckla kostnadseffektiva byggmetoder för att möjliggöra lägenheter med överkomliga hyror som kan bidra till att motverka boendesegregationen på sikt. Vårt förslag består av ett bostadshus i Stadshagen. Fastigheten är indelad i två byggnadskroppar som länkas samman via ett system av loftgångar kopplade till ett trapphus. Husen är uppbyggda av volymelement som staplats på en platsgjuten sockel. Elementens konstruktion baseras på transportcontainrar vilket ger en rationell byggprocess och hög grad av prefabrikation. I socklarna ryms en tunnelbanenedgång och en uthyrbar lokal samt gemensamma lokaler för de boende. Lägenheterna finns i tre storlekar: 1:or, 1,5:or och 4:or.  De större lägenheterna är i två plan. / The housing policy conducted over the past two decades has resulted in an increasingly segregated city center in Stockholm. The abolishment of housing subsidies in the 90s led to a historic low rate of construction and an urban development unilaterally directed towards the wealthy. Parallel to this, much of the housing stock has been converted to condominiums which caused many relatively cheap rental apartments in older buildings to disappear from the stock. These are difficult to replace with new housing, as they are more expensive. The core issue is of course that it is expensive to build houses and assuming that the current housing policy will last, ​​it is highly relevant to develop cost-effective construction methods in order to make possible apartments with affordable rents that can help to combat segregation over time. Our proposal consists of a residential building in Stadshagen. The property is divided into two buildings that are linked together by a system of access balconies connected to a stairwell. The houses are constructed with volume elements stacked on a concrete base. The design of the elements is based on shipping containers which provides a rational construction process and a high degree of prefabrication. The base contains an underground entrance, a business premise and common areas for the residents. The apartments are available in three sizes whereof the larger apartments have two floors.