Cette thèse est focalisée sur la conception et la réalisation d'un filtre CEM hybride intégré pour une application aéronautique. Les travaux effectués durant cette thèse sont réalisés dans le cadre d’un projet FRAE (Fondation de Recherche pour l’Aéronautique et l’Espace) intitulé FEMINA (Filtrage Electromagnétiques et Matériaux pour l’INtégration en Aéronautique). Afin de protéger le réseau de bord des perturbations électromagnétiques conduites et rayonnées et répondre aux normes concernant la compatibilité électromagnétique (CEM) et plus particulièrement la norme aéronautique "DO160F [150KHz, 30MHz]», un filtre CEM est absolument nécessaire pour les cartes d’alimentations des dispositifs électroniques d’un avion. Les niveaux des perturbations générées par ce type d’équipement exigent une conception soignée pour assurer le filtrage des courants parasites qui se propagent en mode commun (MC) et en mode différentiel (MD). C’est pourquoi, la première partie du travail réalisé est consacrée à la modélisation électromagnétique de la carte d’alimentation utilisée comme support à cette étude. Cette modélisation est basée sur une représentation de type «boîte noire». Le modèle identifié est composé de sources de perturbations et d’impédances de MC et de MD équivalentes. Cette première étape permet de définir la structure électrique du filtre et les valeurs des composants à mettre en œuvre. Pour atteindre les performances requises, nous proposons dans ce travail un filtre CEM hybride optimisé, hybride signifiant qu’il est réalisé par association d’une partie purement passive et d’un filtre actif. Cette association permet de tirer le meilleur parti de chaque technologie de filtrage. Le filtre actif permet de traiter les perturbations à basses fréquences et la partie passive est dimensionnée pour les perturbations à hautes fréquences. Une intégration complète dans le circuit imprimé (PCB) des parties passives, capacitives et inductives, est proposée dans la deuxième partie de ce travail. Après avoir choisi les matériaux magnétique et diélectrique qui répondent au mieux au cahier de charge défini dans la première partie, plusieurs tests d’intégration dans le PCB ont été effectués. En prenant en compte la fragilité des matériaux magnétiques (ferrites), une géométrie plane qui répond aux spécifications a été proposée. Les principaux avantages de l'intégration proposée sont la réduction des effets inductifs et capacitifs parasites conduisant, de fait, à une augmentation des atténuations à hautes fréquences et l’augmentation de la compacité du filtre CEM. Nous démontrons que le filtre passif intégré réalisé réduit les interférences en MC et en MD dans la gamme de fréquences qui s'étend de 2,5MHz à 30MHz. Afin de compenser les tensions perturbatrices de mode différentiel jusqu’à 2,5MHz, une nouvelle topologie de filtre actif est proposée. Dans cette structure, l’injection des tensions de compensation des perturbations est effectuée à l’aide d’un enroulement auxiliaire ajouté aux enroulements couplés du filtre passif intégré. Les composants du filtre actif sont montés sur la face supérieure du PCB (composants CMS) dans lequel le filtre passif est intégré. L'assemblage du filtre hybride intégré (4 x 5 x 0,4 cm3) réduit les perturbations en MC et en MD dans la gamme de fréquence [150 kHz, 30 MHz]. Grâce à l'intégration et à l'optimisation de la topologie du filtre actif, le volume du filtre hybride est 75% plus faible que celui de l’ancien filtre CEM utilisé à l’entrée du convertisseur (4 x 5 x 1,6 cm3) tout en conservant un rendement élevé. / This thesis is focused on the design and implementation of a hybrid integrated EMC filter for aerospace application. The work performed in this thesis is carried out in the framework of FRAE project (Research Foundation for Aviation and Space) titled FEMINA (Electromagnetic Filtering and Materials for the INtegration in Aerospace). To protect the network board from both conducted and radiated electromagnetic interferences and to meet the standards for electromagnetic compatibility (EMC) and especially the aviation standard "DO160F [150 KHz, 30 MHz]," an EMC filter is absolutely necessary to the aircraft's electronic power supply board. The disturbance levels generated by this type of equipment require careful design to ensure the filtering of parasitic currents that propagate in common mode (CM) and differential mode (DM). Therefore, the first part of the work is devoted to the electromagnetic modeling of the power supply board used as support for this study. This modeling is based on a "black box" representation. The identified model is composed of equivalent disturbance sources and impedances in CM and DM. This first step leads to define the electrical structure of the filter and the component values. To achieve the required performances, an optimized hybrid EMC filter is proposed in this work- hybrid means an association of a purely passive part and active filter. This association will make the most advantage of each filtering technology. The active filter can handle disturbances at low frequencies and the passive part is designed to the high frequencies. Full integration within the printed circuit board (PCB) of passive parts, capacitive and inductive, is proposed in the second part of this work. After choosing the magnetic and dielectric materials that best meet the defined specifications in the first part, several integration tests on the PCB have been made. Considering the fragility of magnetic materials (ferrites), a planar geometry that meets the specifications has been proposed. The main advantages of the proposed integration are the reduction of inductive and capacitive parasitic effects lead to an increase the attenuation at high frequencies and to increase the compactness of the EMC filter. We demonstrate that the realizing of integrated passive filter reduces the CM and DM interference in the frequency range extending from 2.5 MHz to 30MHz. To compensate the differential mode interference voltages up to 2.5 MHz, a new topology of an active filter is proposed. In this structure, the injection of disturbances compensation voltage is performed using an auxiliary winding added to the coupled windings of integrated passive filter. The active filter components are mounted on the upper side of PCB (SMD components) in which the passive filter is integrated. The assembly of the integrated hybrid filter (4 x 5 x 0.4 cm3) reduces the CM and DM disturbances in the frequency range [150 kHz, 30 MHz]. Thanks to the integration and optimization of the active filter topology, the hybrid filter volume is 75% lower than that of the former EMC filter used at the input of the converter (4 x 5 x 1.6 cm3) while maintaining a high efficiency.

Une nouvelle approche appelée “Approche Pseudo Inverse” (API) est développée pour la modélisation du procédé de forgeage à froid des pièces axisymétriques. L'API est basée sur la connaissance de la forme de la pièce finale. Certaines configurations intermédiaires « réalistes » ont été introduites dans l'API pour considérer le chemin de déformations. Elles sont créées géométriquement sans traitement de contact et ensuite corrigées par la méthode de surface libre afin de respecter l'équilibre, les conditions aux limites et la condition d'incompressibilité. Un nouvel algorithme direct de plasticité est développé, conduisant à une méthode d'intégration plastique très rapide, précise et robuste même dans le cas de très grands incréments de déformations. Un modèle d'endommagement en déformation, est couplé à la plasticité et implémenté dans l'API. Les validations numériques montrent que l'API donne des résultats très proches des résultats de l'approche incrémentale mais en utilisant beaucoup moins de temps de calcul.L'API est adoptée comme solveur du forgeage pour la conception et l'optimisation des préformes du forgeage multi-passes. La rapidité et la robustesse de l'API rendent la procédure d'optimisation très performante. Une nouvelle technique est développée pour générer automatiquement le contour initial d'un outil de préforme pour la procédure d'optimisation. Les variables de conception sont les positions verticales des points de contrôle des courbes B-spline définissant les formes des outils de préforme. Notre optimisation multi-objectif consiste à minimiser la variation de la déformation plastique équivalente dans la pièce finale et la force du poinçon au cours du forgeage. Un algorithme génétique et un algorithme de recuit simulé sont utilisés pour trouver les points d'optimum de Pareto. Pour réduire le nombre de simulations de forgeage, un méta-modèle de substitution basé sur la méthode de krigeage est adopté pour établir une surface de réponse approximative. Les résultats obtenus par l'API en utilisant les outils de préforme optimaux issues de l'optimisation sont comparés à ceux obtenus par les approches incrémentales classiques pour montrer l'efficacité et les limites de l'API. La procédure d'optimisation combinée avec l'API peut être un outil numérique rapide et performant pour la conception et l'optimisation des outillages de préforme. / A new method called “Pseudo Inverse Approach” (PIA) is developed for the axi-symmetrical cold forging modelling. The PIA is based on the knowledge of the final part shape. Some « realistic » intermediate configurations are introduced in the PIA to consider the deformation path. They are created geometrically without contact treatment, and then corrected by using a free surface method in order to satisfy the equilibrium, the boundary conditions and the metal incompressibility. A new direct algorithm of plasticity is proposed, leading to a very fast, accurate and robust plastic integration method even in the case of very large strain increments. An isotropic damage model in deformation is coupled with the plasticity and implemented in the PIA. Numerical tests have shown that the Pseudo Inverse Approach gives very close results to those obtained by the incremental approach, but using much less calculation time.The PIA is adopted as forging solver for the design and optimization of preform tools in the multi-stage forging process. The rapidity and robustness of the PIA make the optimization procedure very powerful. A new method is developed to automatically generate the initial preform tool shape for the optimization procedure. The design variables are the vertical positions of the control points of B-spline curves describing the preform tool shape. Our multi-objective optimization is to minimize the equivalent plastic strain in the final part and the punch force during the forging process. The Genetic algorithm and Simulated Annealing algorithm are used to find optimal Pareto points. To reduce the number of forging simulations, a surrogate meta-model based on the kriging method is adopted to build an approximate response surface. The results obtained by the PIA using the optimal preform tools issued from the optimization procedure are compared to those obtained by using the classical incremental approaches to show the effectiveness and limitations of the PIA. The optimization procedure combined with the PIA can be a rapid and powerful tool for the design and optimization of the preform tools.

A gas turbine engine design process was developed for the design of a common core engine family. The process considers initial and projected variant engine applications, likely technology maturation, and various sources of uncertainty when making initial core design considerations. A physics based modeling and simulation environment was developed to enforce geometric core commonality between the core defining design engine and a common core variant engine. The environment also allows for upgrade options and technology to be infused into the variant engine design. The relationships established in the model enable commonality to be implicitly enforced when performing simultaneous design space explorations of the common core design and all corresponding variant engine designs. A robust design simulation process was also developed, enabling probabilistic surrogate model representations of the common core engine family design space to be produced. The probabilistic models provide confidence interval performance estimates with a single function call for an inputted set of core and variant design settings and the uncertainty distribution shape parameter settings representative of an uncertainty scenario of interest. The unique form of the probabilistic surrogate models enables large numbers of common core engine family applications to be considered simultaneously, each being simulated under a unique uncertainty scenario. Implications of core design options can be instantaneously predicted for all engine applications considered, allowing for favorable common core design regions to be identified in a highly efficient manner.

Made available in DSpace on 2015-05-14T13:21:37Z (GMT). No. of bitstreams: 1 parte1.pdf: 2426440 bytes, checksum: ed3c18b465357e2c561cffbd380b983f (MD5) Previous issue date: 2008-07-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The chemiluminescence (CL) of luminol-cobalt(II) reaction has been used in analytical systems for capillary electrophoresis, chromatography, -TAS (microTotal Analysis System), etc. Even with the diversity of applications, the steps of this reaction have not been completely elucidated and have been still a subject of research and controversy. Many works reported only to the isolated studies of the influence of each variable in the luminol-cobalt(II) reaction and, as such studies do not consider the interactions among variables, they do not exploit the total performance of this reaction in order to increase the chemiluminescent intensity (ICL). In this context, the use of an experimental design and a ChemiLumimetric Flow-Batch System (CLFBS) is proposed in this work in order to study and to optimize this reaction, aiming at to develop an automatic method to determine vitamin B12 (VB12) in drugs. For optimization purpose, a 24 factorial design was carried out fixing the cobalt concentration at 3.0 g L-1 and varying the concentration of luminol, hydrogen peroxide, sodium hydroxide and the order of mixture of these reagents. Sixteen assays were performed in five replicates, generating a total of eighty experiments. The analysis using normal plot of the experimental design revealed that the luminol concentration and the order of mixture of the reagents are variables more important than the NaOH or H2O2 concentrations to luminol-cobalt(II) reaction. These two parameters were responsible to enhance the chemiluminescent signal in about 80%. Another study was carried out in order to evaluate the CLFBS performance by using the optimized variables which were suggested by the factorial design study. Calibration curves were built by using standard solution of Co(II) and VB12 and the analytical parameters for Co(II) curve were: ΔICL = -21.39 +1771.37[Co2+] (r2 = 0.9996), LD and LQ = 12.0 ng L-1, RSD = 1.8% (n = 5), analytical sensitivity = 1947.29 W/g L-1; and VB12 curve were: ΔICL = -186.71 + 12.90 [VB12] (r2 = 0.9999), LD = 14.53 mg L-1 and LQ = 14.70 mg L-1, RSD = 2.1% (n = 4) and analytical sensitivity = 10.76 W/μg L-1. The results of the vitamin B12 analysis in drug samples employing the luminol-cobalt(II) reaction and CLFBS were enough satisfactory. Relative errors smaller than 4% were obtained by using curve calibration or standard addition method. The recovery studies yield very good values, which were of 97 to 103%. In addition, a good agreement was obtained when a drug sample was analyzed by the proposed and the reference (HPLC) method. Thus, the automatic chemilumimetric method, which was here developed and optimized, can be considered a promising alternative to quality control of vitamin B12 in drugs. / A quimiluminescência (QL) da reação luminol-cobalto(II) vem sendo empregada em sistemas analíticos de eletroforese capilar, cromatografia, -TAS (microTotal Analysis System), etc. Mesmo com a diversidade de aplicações, essa reação possui etapas pouco elucidadas que continuam sendo alvo de pesquisas e polêmicas. Muitos trabalhos relatam apenas estudos isolados da influência de cada variável na reação luminol-cobalto(II) e, por não considerar as interações entre as variáveis, estes estudos não exploram ao máximo a performance analítica desta reação. Neste contexto, foi proposto neste trabalho o uso de um planejamento experimental e de um Sistema Quimilumimétrico Fluxo-Batelada (SQLFB) para o estudo e a otimização desta reação com vista a desenvolver um método automático para a determinação de vitamina B12 (VB12) em medicamentos. Na otimização, foi utilizado um planejamento fatorial 24 em que foi mantido constante a concentração de cobalto(II) em 3,0 g L-1 enquanto variou-se as concentrações de luminol, peróxido de hidrogênio, hidróxido de sódio e a ordem de mistura destes constituintes. Foram efetuados dezesseis ensaios em quintuplicata, perfazendo um total de 80 experimentos realizados. A análise usando o gráfico normal do planejamento experimental revelou que a concentração de luminol ([Lu]) e a ordem da mistura (OM) dos reagentes são variáveis mais importante do que a concentração de NaOH e H2O2 para a reação luminol-cobalto(II). Ambas variáveis [Lu] e OM foram responsáveis por aumentar o sinal quimiluminescente em cerca de 80%. Um outro estudo foi realizado para avaliar a performance do SQLFB, empregando as variáveis otimizadas que foram sugeridas pelo estudo do planejamento fatorial. Curvas de calibração foram construídas utilizando soluções padrão de Co(II) e de VB12 e os parâmetros analíticos para a curva Co(II) foram: ΔIQL=-21,39+1771,37[Co2+](r2 = 0,9996), LD=1,54 ng L-1 e LQ=5,13 ng L-1, DPR=1,8% (n=5) e sensibilidade analítica=1947,29 Watts/μg L-1; e para a curva VB12 foram: ΔIQL= -186,71 + 12,90[VB12] (r2 = 0,9999), LD=0,89 μg L-1 e LQ = 2,98 μg L-1, DPR=2,1% (n=4) e sensibilidade analítica=10,76 Watts/μg L-1. Os resultados obtidos nas análises de vitamina B12 em medicamentos empregando a reação luminol-cobalto(II) e o SQLFB foram bastante satisfatórios. Erros relativos menores do que 4% foram obtidos empregando as técnicas de curva de calibração e de adição de padrão. Em estudos de recuperação, os valores foram também muito bons, ficando entre 97 e 103%. Além disso, uma boa concordância entre os resultados foi obtida quando uma amostra foi analisada empregando o método aqui proposto e o método de referência (HPLC). Portanto, o método quimilumimétrico automático aqui desenvolvido e otimizado pode ser considerado uma alternativa promissora para o controle de qualidade de vitamina B12 em medicamentos.

Le contrôle thermique des réactions dans les réacteurs à lits fixes nécessite la maîtrise du transfert thermique en proche paroi. Afin d’optimiser leur conception et en particulier de maintenir un chemin réactionnel le plus proche possible de l’isothermicité, un modèle de transfert thermique pertinent dans un tel milieu est indispensable. Deux premières thèses au Laboratoire d'Energétique et de Mécanique Théorique et Appliquée ont permis de mettre au point un modèle dispersif utilisable à cœur de réacteur. La présente thèse met en évidence un effet de paroi non négligeable causé par la variation de porosité du lit à l’approche de la paroi. Ce travail propose un raccordement du cœur, où le modèle thermique précédent est légitime, à la paroi, par une couche homogénéisée. Cette approche est validée par une caractérisation expérimentale des paramètres du modèle sur un dispositif de laboratoire en utilisant une méthode d’inversion originale reposant sur une approche Bayesienne. Une validation de cette caractérisation dans une géométrie plus proche d’un réacteur industriel est également effectuée / Thermal control for chemical reactions conducted in fixed-bed reactors requires a fine knowledge about heat transfer in the near-wall region of the bed. In order to optimize the process design, to minimize the mass of catalyst that is needed, one must attempt to maintain the operational path of the reactor the closest of the isotherm functioning. A pertinent and reliable heat transfer model is then required. Two thesis were realized in the Laboratoire d'Energétique et de Mécanique Théorique et Appliquée in order to construct a corresponding dispersive model. This model can be used at the core of the reactor, where the porous medium can be homogenized. This thesis shows a wall effect that cannot be neglected. This wall effect is directly caused by the important variation of the porosity distribution near the wall of the bed. This work proposes a junction between a core layer, where the previous model is still valid, and the wall through an homogenized near-wall layer. This approach is validated by the mean of an experimental characterization of the model parameters, using an original inversion technique based on a Bayesian approach. A validation of this characterization in another geometry is also done. This geometry is closer to an industrial reactor

This thesis addresses issues related to the simulation and optimization of the injection molding of short fiber-reinforced plastics (SFRPs). The injection molding process is modeled by a two phase flow problem. The simulation of the two phase flow is accompanied by the solution of the Folgar-Tucker equation (FTE) for the simulation of the moments of fiber orientation densities. The FTE requires the solution of the so called 'closure problem'', i.e. the representation of the 4th order moments in terms of the 2nd order moments. In the absence of fiber-fiber interactions and isotropic initial fiber density, the FTE admits an analytical solution in terms of elliptic integrals. From these elliptic integrals, the closure problem can be solved by a simple numerical inversion. Part of this work derives approximate inverses and analytical inverses for special cases of fiber orientation densities. Furthermore a method is presented to generate rational functions for the computation of arbitrary moments in terms of the 2nd order closure parameters. Another part of this work treats the determination of effective material properties for SFRPs by the use of FFT-based homogenization methods. For these methods a novel discretization scheme, the 'staggered grid'' method, was developed and successfully tested. Furthermore the so called 'composite voxel'' approach was extended to nonlinear elasticity, which improves the approximation of material properties at the interfaces and allows the reduction of the model order by several magnitudes compared to classical approaches. Related the homogenization we investigate optimal experimental designs to robustly determine effective elastic properties of SFRPs with the least number of computer simulations. Finally we deal with the topology optimization of injection molded parts, by extending classical SIMP-based topology optimization with an approximate model for the fiber orientations. Along with the compliance minimization by topology optimization we also present a simple shape optimization method for compensation of part warpage for an black-box production process.:Acknowledgments v Abstract vii Chapter 1. Introduction 1 1.1 Motivation 1 1.2 Nomenclature 3 Chapter 2. Numerical simulation of SFRP injection molding 5 2.1 Introduction 5 2.2 Injection molding technology 5 2.3 Process simulation 6 2.4 Governing equations 8 2.5 Numerical implementation 18 2.6 Numerical examples 25 2.7 Conclusions and outlook 27 Chapter 3. Numerical and analytical methods for the exact closure of the Folgar-Tucker equation 35 3.1 Introduction 35 3.2 The ACG as solution of Jeffery's equation 35 3.3 The exact closure 36 3.4 Carlson-type elliptic integrals 37 3.5 Inversion of R_D-system 40 3.6 Moment tensors of the angular central Gaussian distribution on the n-sphere 49 3.7 Experimental evidence for ACG distribution hypothesis 54 3.8 Conclusions and outlook 60 Chapter 4. Homogenization of SFRP materials 63 4.1 Introduction 63 4.2 Microscopic and macroscopic model of SFRP materials 63 4.3 Effective linear elastic properties 65 4.4 The staggered grid method 68 4.5 Model order reduction by composite voxels 80 4.6 Optimal experimental design for parameter identification 93 Chapter 5. Optimization of parts produced by SFRP injection molding 103 5.1 Topology optimization 103 5.2 Warpage compensation 110 Chapter 6. Conclusions and perspectives 115 Appendix A. Appendix 117 A.1 Evaluation of R_D in Python 117 A.2 Approximate inverse for R_D in Python 117 A.3 Inversion of R_D using Newton's/Halley's method in Python 117 A.4 Inversion of R_D using fixed point method in Python 119 A.5 Moment computation using SymPy 120 A.6 Fiber collision test 122 A.7 OED calculation of the weighting matrix 123 A.8 OED Jacobian of objective and constraints 123 Appendix B. Theses 125 Bibliography 127 / Diese Arbeit befasst sich mit Fragen der Simulation und Optimierung des Spritzgießens von kurzfaserverstärkten Kunststoffen (SFRPs). Der Spritzgussprozess wird durch ein Zweiphasen-Fließproblem modelliert. Die Simulation des Zweiphasenflusses wird von der Lösung der Folgar-Tucker-Gleichung (FTE) zur Simulation der Momente der Faserorientierungsdichten begleitet. Die FTE erfordert die Lösung des sogenannten 'Abschlussproblems'', d. h. die Darstellung der Momente 4. Ordnung in Form der Momente 2. Ordnung. In Abwesenheit von Faser-Faser-Wechselwirkungen und anfänglich isotroper Faserdichte lässt die FTE eine analytische Lösung durch elliptische Integrale zu. Aus diesen elliptischen Integralen kann das Abschlussproblem durch eine einfache numerische Inversion gelöst werden. Ein Teil dieser Arbeit leitet approximative Inverse und analytische Inverse für spezielle Fälle von Faserorientierungsdichten her. Weiterhin wird eine Methode vorgestellt, um rationale Funktionen für die Berechnung beliebiger Momente in Bezug auf die Abschlussparameter 2. Ordnung zu generieren. Ein weiterer Teil dieser Arbeit befasst sich mit der Bestimmung effektiver Materialeigenschaften für SFRPs durch FFT-basierte Homogenisierungsmethoden. Für diese Methoden wurde ein neuartiges Diskretisierungsschema 'staggerd grid'' entwickelt und erfolgreich getestet. Darüber hinaus wurde der sogenannte 'composite voxel''-Ansatz auf die nichtlineare Elastizität ausgedehnt, was die Approximation der Materialeigenschaften an den Grenzflächen verbessert und die Reduzierung der Modellordnung um mehrere Größenordnungen im Vergleich zu klassischen Ansätzen ermöglicht. Im Zusammenhang mit der Homogenisierung untersuchen wir optimale experimentelle Designs, um die effektiven elastischen Eigenschaften von SFRPs mit der geringsten Anzahl von Computersimulationen zuverlässig zu bestimmen. Schließlich beschäftigen wir uns mit der Topologieoptimierung von Spritzgussteilen, indem wir die klassische SIMP-basierte Topologieoptimierung um ein Näherungsmodell für die Faserorientierungen erweitern. Neben der Compliance-Minimierung durch Topologieoptimierung stellen wir eine einfache Formoptimierungsmethode zur Kompensation von Teileverzug für einen Black-Box-Produktionsprozess vor.:Acknowledgments v Abstract vii Chapter 1. Introduction 1 1.1 Motivation 1 1.2 Nomenclature 3 Chapter 2. Numerical simulation of SFRP injection molding 5 2.1 Introduction 5 2.2 Injection molding technology 5 2.3 Process simulation 6 2.4 Governing equations 8 2.5 Numerical implementation 18 2.6 Numerical examples 25 2.7 Conclusions and outlook 27 Chapter 3. Numerical and analytical methods for the exact closure of the Folgar-Tucker equation 35 3.1 Introduction 35 3.2 The ACG as solution of Jeffery's equation 35 3.3 The exact closure 36 3.4 Carlson-type elliptic integrals 37 3.5 Inversion of R_D-system 40 3.6 Moment tensors of the angular central Gaussian distribution on the n-sphere 49 3.7 Experimental evidence for ACG distribution hypothesis 54 3.8 Conclusions and outlook 60 Chapter 4. Homogenization of SFRP materials 63 4.1 Introduction 63 4.2 Microscopic and macroscopic model of SFRP materials 63 4.3 Effective linear elastic properties 65 4.4 The staggered grid method 68 4.5 Model order reduction by composite voxels 80 4.6 Optimal experimental design for parameter identification 93 Chapter 5. Optimization of parts produced by SFRP injection molding 103 5.1 Topology optimization 103 5.2 Warpage compensation 110 Chapter 6. Conclusions and perspectives 115 Appendix A. Appendix 117 A.1 Evaluation of R_D in Python 117 A.2 Approximate inverse for R_D in Python 117 A.3 Inversion of R_D using Newton's/Halley's method in Python 117 A.4 Inversion of R_D using fixed point method in Python 119 A.5 Moment computation using SymPy 120 A.6 Fiber collision test 122 A.7 OED calculation of the weighting matrix 123 A.8 OED Jacobian of objective and constraints 123 Appendix B. Theses 125 Bibliography 127