Academic literature on the topic 'Homogenization structure'
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Journal articles on the topic "Homogenization structure"
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Krejčí, Tomáš, Aleš Jíra, Luboš Řehounek, Michal Šejnoha, Jaroslav Kruis, and Tomáš Koudelka. "Homogenization of trabecular structures." MATEC Web of Conferences 310 (2020): 00041. http://dx.doi.org/10.1051/matecconf/202031000041.
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Numerical modeling of implants and specimens made from trabecular structures can be difficult and time-consuming. Trabecular structures are characterized as spatial truss structures composed of beams. A detailed discretization using the finite element method usually leads to a large number of degrees of freedom. It is attributed to the effort of creating a very fine mesh to capture the geometry of beams of the structure as accurately as possible. This contribution presents a numerical homogenization as one of the possible methods of trabecular structures modeling. The proposed approach is based on a multi-scale analysis, where the whole specimen is assumed to be homogeneous at a macro-level with assigned effective properties derived from an independent homogenization problem at a meso-level. Therein, the trabecular structure is seen as a porous or two-component medium with the metal structure and voids filled with the air or bone tissue at the meso-level. This corresponds to a two-level finite element homogenization scheme. The specimen is discretized by a reasonable coarse mesh at the macro-level, called the macro-scale problem, while the actual microstructure represented by a periodic unit cell is discretized with sufficient accuracy, called the meso-scale problem. Such a procedure was already applied to modeling of composite materials or masonry structures. The application of this multi-scale analysis is illustrated by a numerical simulation of laboratory compression tests of trabecular specimens.
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Chen, Wei, Pi Zhi Zhao, Yu Li Zhou, and Yan Feng Pan. "Effects of Homogenization Conditions on the Microstructures of Twin-Roll Cast Foil Stock of AA8021 Aluminum Alloy." Materials Science Forum 877 (November 2016): 296–302. http://dx.doi.org/10.4028/www.scientific.net/msf.877.296.
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AA8021 aluminum alloy twin-roll cast strips with 7mm gauge were rolled to 3.8mm gauge sheets and given homogenization, further rolled into 0.55mm gauge foil stocks with intermediate annealing. This paper investigated the influence of homogenization conditions on microstructures of foil stocks in detail. The results show that, for the foil stock made from the sheet without homogenization, the grain structure is partially recrystallized. While the grain structure of foil stock made from the sheet with medium temperature homogenization is fully recrystallized, but it is coarse near sheet surface. However, foil stock made from the sheet with high temperature homogenization has fine and uniform recrystallized grain structures. The differences of grain structures among these three kinds of foil stocks can be understood by the variation in solid solution content of Fe, Si, Mn and distribution of intermetallic compounds. The optimized homogenization condition was adopted by our plant to produce foil stock, and its grain structure was fine and uniform. The surface quality of final aluminum foil rolled from the foil stock could meet high grade requirements of customers.
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BRAIDES, ANDREA, and DAG LUKKASSEN. "REITERATED HOMOGENIZATION OF INTEGRAL FUNCTIONALS." Mathematical Models and Methods in Applied Sciences 10, no. 01 (February 2000): 47–71. http://dx.doi.org/10.1142/s0218202500000057.
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We consider the homogenization of sequences of integral functionals defined on media with several length-scales. Our general results connected to the corresponding homogenized functional are used to analyze new types of structures and to illustrate the wide range of effective properties achievable through reiteration. In particular, we consider a two-phase structure which is optimal when the integrand is a quadratic form and point out examples where the macroscopic behavior of this structure underlines an effective energy density which is lower than that of the best possible multirank laminate. We also present some results connected to a reiterated structure where the effective property is extremely sensitive of the growth of the integrand.
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Aftandiliants, Ye G. "Modelling of structure forming in structural steels." Naukovij žurnal «Tehnìka ta energetika» 11, no. 4 (September 10, 2020): 13–22. http://dx.doi.org/10.31548/machenergy2020.04.013.
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The study showed that the influence of alloying elements on the secondary structure formation of the steels containing from 0.19 to 0.37 wt. % carbon; 0.82-1.82 silicon; 0.63-3.03 manganese; 1.01-3.09 chromium; 0.005-0.031 nitrogen; up to 0.25 wt.% vanadium and austenite grain size is determined by their change in the content of vanadium nitride phase in austenite, its alloying and overheating above tac3, and the dispersion of ferrite-pearlite, martensitic and bainitic structures is determined by austenite grain size and thermal kinetic parameters of phase transformations. Analytical dependencies are defined that describe the experimental data with a probability of 95% and an error of 10% to 18%. An analysis results of studying the structure formation of structural steel during tempering after quenching show that the dispersion and uniformity of the distribution of carbide and nitride phases in ferrite is controlled at complete austenite homogenization by diffusion mobility and the solubility limit of carbon and nitrogen in ferrite, and secondary phase quantity in case of the secondary phase presence in austenite more than 0.04 wt. %. Equations was obtained which, with a probability of 95% and an error of 0.7 to 2.6%, describe the real process.
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Griso, Georges, Larysa Khilkova, Julia Orlik, and Olena Sivak. "Homogenization of Perforated Elastic Structures." Journal of Elasticity 141, no. 2 (June 5, 2020): 181–225. http://dx.doi.org/10.1007/s10659-020-09781-w.
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Abstract The paper is dedicated to the asymptotic behavior of $\varepsilon$ ε -periodically perforated elastic (3-dimensional, plate-like or beam-like) structures as $\varepsilon \to 0$ ε → 0 . In case of plate-like or beam-like structures the asymptotic reduction of dimension from $3D$ 3 D to $2D$ 2 D or $1D$ 1 D respectively takes place. An example of the structure under consideration can be obtained by a periodic repetition of an elementary “flattened” ball or cylinder for plate-like or beam-like structures in such a way that the contact surface between two neighboring balls/cylinders has a non-zero measure. Since the domain occupied by the structure might have a non-Lipschitz boundary, the classical homogenization approach based on the extension cannot be used. Therefore, for obtaining Korn’s inequalities, which are used for the derivation of a priori estimates, we use the approach based on interpolation. In case of plate-like and beam-like structures the proof of Korn’s inequalities is based on the displacement decomposition for a plate or a beam, respectively. In order to pass to the limit as $\varepsilon \to 0$ ε → 0 we use the periodic unfolding method.
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Marsan, A. L., and D. Dutta. "Construction of a Surface Model and Layered Manufacturing Data From 3D Homogenization Output." Journal of Mechanical Design 118, no. 3 (September 1, 1996): 412–18. http://dx.doi.org/10.1115/1.2826901.
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A homogenization method has been recently developed to optimize the topology of a structure. This method will suggest a structural topology, but the results will be in finite element form. Most engineering applications, however, require smooth structures, whether the faces of the structures be planar or curved. Given the topology of a three-dimensional structure as suggested by the homogenization method, an algorithm is developed to interpret the structure and generate a smooth, manufacturable surface representation of the structure. Structures designed by the homogenization method can be quite complex and traditional manufacturing technique may not be well suited for constructing them. Layered manufacturing is adopted for producing such structures and it is shown how to generate the necessary data for this novel manufacturing technique from the surface model of the structure. Some steps of the algorithm require designer inputs. Examples are given which demonstrates this algorithm.
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Armstrong, Scott, Tuomo Kuusi, and Jean-Christophe Mourrat. "The additive structure of elliptic homogenization." Inventiones mathematicae 208, no. 3 (November 17, 2016): 999–1154. http://dx.doi.org/10.1007/s00222-016-0702-4.
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Tsalis, Dimitrios, Nicolas Charalambakis, Kevin Bonnay, and George Chatzigeorgiou. "Effective properties of multiphase composites made of elastic materials with hierarchical structure." Mathematics and Mechanics of Solids 22, no. 4 (December 7, 2015): 751–70. http://dx.doi.org/10.1177/1081286515612142.
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In this paper, the analytical solution of the multi-step homogenization problem for multi-rank composites with generalized periodicity made of elastic materials is presented. The proposed homogenization scheme may be combined with computational homogenization for solving more complex microstructures. Three numerical examples are presented, concerning locally periodic stratified materials, matrices with wavy layers and wavy fiber-reinforced composites.
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Jin, Ji-Won, Byung-Wook Jeon, Chan-Woong Choi, and Ki-Weon Kang. "Multi-Scale Probabilistic Analysis for the Mechanical Properties of Plain Weave Carbon/Epoxy Composites Using the Homogenization Technique." Applied Sciences 10, no. 18 (September 18, 2020): 6542. http://dx.doi.org/10.3390/app10186542.
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Probabilistic analyses of carbon fabric composites were conducted using the Monte Carlo simulation based on a homogenization technique to evaluate the mechanical properties of composites and their stochastic nature. First, the homogenization analysis was performed for a micro-level structure, which fiber and matrix are combined. The effective properties obtained from this analysis were compared with the results from the rule of mixture theory to verify the homogenization analysis. And, tensile tests were conducted to clearly evaluate the result and the reliability was verified by comparing the results of the tensile tests and homogenization analysis. In addition, the Monte Carlo simulation was performed based on homogenization analyses to consider the uncertainties of the micro-level structure combined of fiber and matrix. Next, the results of this simulation were applied to the macro-level structure combined of the tow and matrix to perform the Monte Carlo simulation based on the homogenization technique. Finally, the sensitivity analysis was conducted to identify the effect of constituents of the carbon plain weave composite and the linear correlation of the micro- and macro-level structures combined of the fiber/matrix and tow/matrix, respectively. The findings of this study verified that the effective properties of the plain weave carbon/epoxy composite and their uncertainties depended on the properties of the carbon fiber and epoxy, which are the basic constituents of plain weave carbon/epoxy composites.
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Sherniyozov, A., and Sh Payziyev. "FOCAL SPOT STRUCTURE OF FRESNEL LENS AND ITS HOMOGENIZATION." «Узбекский физический журнал» 21, no. 4 (August 21, 2019): 245–49. http://dx.doi.org/10.52304/.v21i4.113.
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Using statistical Monte-Carlo photon-tracing method, we numerically studied focal spot structure of flat Fresnel lens. It has been shown that due to dispersion effect, focal spot structure changes considerably. In addition, we demonstrated homogenization of strongly focused photons. Rectangular prism can be applied to achieve the homogenization.
Dissertations / Theses on the topic "Homogenization structure"
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Sun, Xiangkun. "Elastic wave propagation in periodic structures through numerical and analytical homogenization techniques." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEC041/document.
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Dans ce travail, la méthode homogénéisation de multi-échelle, ainsi que diverses méthodes non homogénéisation, seront présentés pour étudier le comportement dynamique des structures périodiques. La méthode de multi-échelle commence par la séparation d'échelles. Dans ce cas, une échelle microscopique pour décrire le comportement local et une échelle macroscopique pour décrire le comportement global sont introduites. D'après la théorie de l'homogénéisation, la longueur d'onde est supposée grande, et la longueur de la cellule doit être beaucoup plus petite que la longueur caractéristique de la structure. Ainsi, le domaine d'homogénéisation est limité à la première zone de propagation. Le modèle d'homogénéisation traditionnel utilise des valeurs moyennes des éléments, mais le domaine de validité pratique est beaucoup plus petit que la première bande interdite. Alors, le développement de nouveaux modèles homogénéisés est beaucoup motivé par cet inconvénient. Par rapport au modèle d'homogénéisation traditionnel, équations d'ordre supérieur sont proposées pour fournir des modèles homogénéisation plus précises. Deux méthodes multi-échelles sont introduites: la méthode de développement asymptotique, et la méthode de l'homogénéisation des milieux périodiques discrètes (HMPD). Ces méthodes seront appliquées de façon séquentielle dans le cas d'onde longitudinale et le cas d'onde transversale. Les mêmes modèles d'ordre supérieur sont obtenus par les deux méthodes dans les deux cas. Ensuite, les modèles proposés sont validés en examinant la relation de dispersion et de la fonction de réponse fréquentielle. Des solutions analytiques et la méthode des ondes éléments finis(WFEM) sont utilisés pour donner les références. Des études paramétriques sont effectuées dans le cas infini, et deux différentes conditions aux limites sont prises en compte dans le cas fini. Ensuite, le HMPD et CWFEM sont utilisés pour étudier les vibrations longitudinales et transversales des structures réticulées dans le cas 1D et 2D. Le domaine de validité du HPDM est réévalué à l'aide de la fonction de propagation identifiée par le CWFEM. L'erreur relative au nombre d'onde obtenue par HPDM est illustré sur la fonction de la fréquence et le rapport d'échelle. Des études paramétriques sur l'épaisseur de la structure sont réalisées par la relation de dispersion. La dynamique des structures finies sont également étudiés en utilisant la HPDM et CWFEMIn this work, the multi-scale homogenization method, as well as various non homogenization methods, will be presented to study the dynamic behaviour of periodic structures. The multi-scale method starts with the scale-separation, which indicates a micro-scale to describe the local behaviour and a macro-scale to describe the global behaviour. According to the homogenization theory, the long-wave assumption is used, and the unit cell length should be much smaller than the characteristic length of the structure. Thus, the valid frequency range of homogenization is limited to the first propagating zone. The traditional homogenization model makes use of material properties mean values, but the practical validity range is far less than the first Bragg band gap. This deficiency motivated the development of new enriched homogenized models. Compared to traditional homogenization model, higher order homogenized wave equations are proposed to provide more accuracy homogenized models. Two multi-scale methods are introduced: the asymptotic expansion method, and the homogenization of periodic discrete media method (HPDM). These methods will be applied sequentially in longitudinal wave cases in bi-periodic rods and flexural wave cases in bi-periodic beams. Same higher order models are obtained by the two methods in both cases. Then, the proposed models are validated by investigating the dispersion relation and the frequency response function. Analytical solutions and wave finite element method (WFEM) are used as references. Parametric studies are carried out in the infinite case while two different boundary conditions are considered in the finite case. Afterwards, the HPDM and the CWFEM are employed to study the longitudinal and transverse vibrations of framed structures in 1D case and 2D case. The valid frequency range of the HPDM is re-evaluated using the wave propagation feature identified by the CWFEM. The relative error of the wavenumber by HPDM compared to CWFEM is illustrated in the function of frequency and scale ratio. Parametric studies on the thickness of the structure is carried out through the dispersion relation. The dynamics of finite structures are also investigated using the HPDM and CWFEM
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Machovičová, Tatiana. "Banachovy algebry." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-445456.
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By Banach algebra we mean Banach space enriched with a multiplication operation. It is a mathematical structure that is used in the non-periodic homogenization of composite materials. The theory of classical homogenization studies materials assuming the periodicity of the structure. For real materials, the assumption of a periodicity is not enough and is replaced by the so-called an abstract hypothesis based on a concept composed mainly of the spectrum of Banach algebra and Sigma convergence. This theory was introduced in 2004.
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Russell, Brandon C. "HOMOGENIZATION IN PERFORATED DOMAINS AND WITH SOFT INCLUSIONS." UKnowledge, 2018. https://uknowledge.uky.edu/math_etds/55.
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In this dissertation, we first provide a short introduction to qualitative homogenization of elliptic equations and systems. We collect relevant and known results regarding elliptic equations and systems with rapidly oscillating, periodic coefficients, which is the classical setting in homogenization of elliptic equations and systems. We extend several classical results to the so called case of perforated domains and consider materials reinforced with soft inclusions. We establish quantitative H1-convergence rates in both settings, and as a result deduce large-scale Lipschitz estimates and Liouville-type estimates for solutions to elliptic systems with rapidly oscillating periodic bounded and measurable coefficients. Finally, we connect these large-scale estimates with local regulartity results at the microscopic-level to achieve interior Lipschitz regularity at every scale.
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Zafra-Camón, Guillermo. "Calculation of global properties of a multi-layered solid wood structure using Finite Element Analysis." Thesis, Uppsala universitet, Tillämpad mekanik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-298677.
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Finite Element Method (FEM) is a powerful numerical tool which, combined with the fast development of Computer Science in the lastdecades, had made possible to perform mechanical analysis of a widerange of bodies and boundary conditions. However, the complexity of some cases may turn the calculationprocess too slow and sometimes even unaffordable for most computers. This work aims to simplify an intricate system of layers withdifferent geometries and material properties by approximating itthrough a homogeneous material, with unique mechanical parameters.Besides the Finite Element analysis, a theoretical model is created, in order to understand the basis of the problem, and, as a firstapproach, check whether the assumptions made in the FEM model areacceptable or not. This work intends to make a small contribution to the understandingof the mechanical behaviour of the Vasa vessel, which will eventuallylead to the design of a new support structure for the ship. The preservation of the Vasa is a priority for the Swedish Property Board, as it is one of the main monuments of Sweden.
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Xavier, Rodrigo Yokoyama [UNESP]. "Influência da deformação plástica no tratamento térmico de homogeneização de um aço ferramenta para trabalho a frio." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/148843.
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O nível de qualidade de peças produzidas a partir de grandes lingotes está intimamente relacionado à qualidade dos lingotes em si. Dentre os diversos defeitos inerentes ao processo de solidificação, destacam-se as microssegregações de elementos de liga, que causam uma deterioração nas propriedades do produto final. Uma maneira de reduzir o dano causado pela microssegregação é através do Tratamento Térmico de Homogeneização, este por sua vez demanda elevados tempos de processo, elevando custos e tempos de fabricação. Uma das formas de reduzir os tempos de homogeneização, uma vez que este apresenta caráter difusional, é através da redução do espaçamento interdendrítico. Neste trabalho foi analisada a influência da deformação plástica como forma de reduzir o espaçamento entre dendritas no tratamento térmico de homogeneização. Para tal fim, utilizou-se um lingote fundido em aço ferramenta de composição química similar ao AISI A2. As amostras foram retiradas do núcleo do lingote no estado bruto de solidificação e sofreram deformações de 0,6 e 1,3 através do processo de laminação a quente, sendo temperadas em água na sequência. Após laminadas as amostras passaram por um tratamento térmico de homogeneização na temperatura de 1200°C por 8h ou 16h e foram novamente temperadas em água. As análises foram feitas através de Microscopia Óptica, Dureza Vickers, Difratometria de Raios-X e Microscopia Eletrônica de Varredura. Foi observado em todas as amostras a presença de microrechupes, e uma microestrutura composta predominantemente por dendritas oriundas da solidificação, identificadas pela fase martensítica, envoltas por uma matriz formada de austenita retida, contendo carbonetos e sulfetos. Com a deformação plástica foi possível quebrar a estrutura dendrítica a aproximar as regiões segregadas das não segregadas. O tratamento térmico por um tempo de 8h não foi suficiente para homogeneizar a microestrutura e reduzir as microssegregações, independentemente do estado de deformação das amostras. O tratamento térmico por 16h apresentou os melhores resultados em relação à homogeneidade química, sendo tanto melhor o resultado quanto maior a deformação imposta às amostras.
The quality of pieces produced from large ingots is closely related to the quality of ingots itself. Among the various defects inherent to the solidification process, there is the microsegregation of alloying elements, causing a deterioration in the properties of the final product. One way to reduce the damage caused by microsegregation is through the homogenization heat treatment, this in turn demands long time of process, increasing costs and lead-times for manufacture. One way to reduce the homogenization time, since it has a diffusive character, is by reducing the interdendritic spacing. In this study was analyzed the influence of plastic deformation as a mean to reduce the spacing between dendrites in the homogenization heat treatment. For this purpose it was used a cast ingot of chemical composition similar to the AISI A2 tool steel. Samples were cut from the ingot center in the as-cast state and suffered deformations of 0.6 and 1.3 through the hot rolling process and quenched in water in the sequence. After rolling the samples passed through a homogenization heat treatment at a temperature of 1200°C for 8h and 16h and again were quenched in water. Analyses were performed by Optical Microscopy, Vickers Hardness, X-Ray Diffractometry and Scanning Electron Microscopy. It was observed in all samples the presence of microcavities, and a microstructure consisting predominantly by solidifications dendrites identified by a martensitic phase, involved by a retained austenite matrix containing carbides and sulfides. The plastic deformation broke the dendritic structure, and approached the segregated regions to the non-segregated regions. The heat treatment for 8h was not sufficient to homogenize the microstructure and reduce the microsegregation, independently of the deformation state of the samples. The heat treatment for 16h presented the best results in relation to the chemical homogeneity, and the better the result as the greater the deformation imposed on the samples.
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Nguyen, Tracey Mai T. "The Effects of Microfluidization and Homogenization on the Composition and Structure of Liposomal Aggregates from Whey Buttermilk and Commercial Buttermilk." DigitalCommons@CalPoly, 2013. https://digitalcommons.calpoly.edu/theses/1075.
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Milk derived ingredients from the production of cheese and butter can be used as vehicles for nutrients. Buttermilk is a nutritious product of milk that comes from the churning of cream into butter. One of the advantages of buttermilk is that it is enriched in milk fat globule components, such as phospholipids and forms emulsions with fat when treated with high shear. The objective of this work was to explore the effects of shear on regular buttermilk and whey buttermilk in terms of liposomal aggregate size and chemical composition. The effects of microfluidization at 2000 psi and homogenization at 2000 psi/500 psi on the particle size distribution of liposomal aggregates between whey buttermilk (WBM) at pH 4.6 and 6.8 and commercial sweet buttermilk (SBM) at pH 4.60 were compared with whey protein isolate (WPI) at pH 4.6. At pH 6.80, WPI and SBM are too soluble in water to measure particle size but WBM is not as soluble. From this investigation, the mean particle diameter of the SBM aggregates at pH 4.6 decreased after the first pass through the microfluidizer and the same is true, after homogenization. SBM aggregates at pH 4.6 had a significantly larger mean particle diameter before treatments in both shear processes compared to WPI at pH 4.6 and WBM at pH 4.6 and WBM at pH 6.8 (p < 0.0001). WPI at pH 4.6 and WBM at both pH showed no significant differences in their mean particle size in both homogenized and microfluidized treatments. WPI and SBM samples resulted in significant particle diameter differences vi from before to after homogenizing at pH 4.6. SBM at pH 4.6 had significantly larger average particle diameter than WBM at pH 4.6 (p < 0.0002), WPI at pH 4.6 (p < 0.0002) and WBM at pH 6.8 (p < 0.0045) before microfluidization at pass 0.
WBM and WPI across all treatments showed very similar tendencies in small particle size attributes and some similarities in protein composition. In addition, the small aggregate size of WBM is suggested to be influenced by the presence of phospholipids and thus, creating significantly smaller mean particles compared to SBM even before inducing high shear. In contrast, treated and untreated SBM differed from WBM in phospholipid composition in both homogenization and microfluidization techniques. WBM samples contained more phospholipids than SBM, whereas WPI samples contained very low concentrations of phospholipids. Through HPLC analysis, WPI, SBM, and WBM showed different profiling of the phospholipid classes. These differences may be due structural changes of the aggregates from shearing, initial thermal treatments or hydrophobic and/or protein-phospholipid interactions between the aggregates. SBM samples also exhibited different protein profiling than WBM and WPI samples. This study suggests that high shear and presence of phospholipids impact the size distribution of liposomal aggregates through structural alterations. The aggregates can be utilized as a novel ingredient and in the processing of dairy foods to deliver nutrition.
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Gazzo, Salvatore. "Characterisation of the mechanical behaviour of networks and woven fabrics with a discrete homogenization model." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSET006/document.
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Au cours des dernières décennies, le développement de nouveaux matériaux a progressé pour les applications liées à la mécanique. De nouvelles générations de composites ont été développées, qui peut offrir des avantages par rapport aux tapis unidirectionnels renforcés de fibres couramment utilisés les matériaux prennent alors le nom de woven fabrics. Le comportement de ce matériau est fortement influencé par la micro-structure du matériau. Dans la thèse, les modèles mécaniques et les schémas numériques capables de modéliser les comportement des tissus et des matériaux de réseau généraux ont été développés. Le modèle prend en compte la micro-structure au moyen d'une technique d'homogénéisation. Les fibres dans le réseau ont été traités comme des micro-poutres, ayant une rigidité à la fois en extension et en flexion, avec différents types de connexions. La procédure développée a été appliquée pour obtenir les modèles mécaniques homogénéisés pour certains types de réseaux de fibres biaxiaux et quadriaxiaux, simulant soit des réseaux de fibres (en ce cas a été supposé parmi les fibres) ou des tissus avec une interaction négligeable entre les faisceaux de fibres et en empêchant tout glissement relatif (dans ce cas, les connexions ont été simulés au moyen de pivots). Différentes géométries ont été analysées, y compris la cas dans lesquels les fibres ne sont pas orthogonales. On obtient généralement un premier milieu à gradient mais, dans certains cas, la procédure d'homogénéisation lui-même indique qu'un continuum d'ordre supérieur est mieux adapté pour représenter la déformation de la micro-structure. Des résultats spéciaux ont été obtenus dans le cas de fibres reliées par pivots. Dans ce cas, un matériau orthotrope à module de cisaillement nul a été obtenu. Un tel matériau a un tenseur constitutif elliptique, il peut donc conduire à des concentrations de contrainte. Cependant, il a été montré que certaines considérations sur le comportement physique de tels réseaux indiqué que les termes d'ordre supérieur inclus dans l'expansion des forces internes et des déformations, de sorte qu'un matériau de gradient de déformation a été obtenu. Les résultats obtenus peuvent être utilisés pour la conception de matériaux spécifiques nécessitant des propriétés. Bien que le modèle de référence soit un matériau de réseau, les résultats obtenus peuvent être appliqué à d'autres types similaires de microstructures, comme des matériaux pantographiques, des micro-dispositifs composé de micro-poutres, etc. Ils étaient limités à la gamme d'élasticité linéaire, qui est petite déformation et comportement élastique linéaire. Ensuite, les simulations numériques ont été axées sur les tests d'extension et les tests de biais. Le obtenu configurations déformées sont conformes aux tests expérimentaux de la littérature, tant pour tissus équilibrés et non équilibrés. De plus, une comparaison entre les premier et deuxième gradients des prédictions numériques ont été effectuées. Il a été observé que les prédictions de deuxième gradient mieux simuler les preuves expérimentalesIn the past decades there has been an impressive progress in the development of new materials for mechanical related applications. New generations of composites have been developed, that can offer advantages over the unidirectional fibre-reinforced mats commonly used then materials take the name of woven fabrics. The behaviour of this material is strongly influenced by the micro-structure of the material. In the thesis mechanical models and a numerical scheme able to model the mechanical behaviour of woven fabrics and general network materials have been developed. The model takes in to account the micro-structure by means of a homogenization technique. The fibres in the network have been treated like microbeams, having both extensional and bending stiffness, with different types of connection, according to the pattern and detail of the network. The developed procedure was applied for obtaining the homogenized mechanical models for some types of biaxial and quadriaxial networks of fibres, simulating either fibre nets (in this case rigid connection were assumed among the fibres) or tissues with negligible interaction between the fibre bundles, and with relative sliding prevented (in this case the connections were simulated by means of pivots). Different geometries were analysed, including the cases in which the fibres are not orthogonal. A first gradient medium is usually obtained but, in some cases, the homogenization procedure itself indicates that a higher order continuum is better fit to represent the deformation of the micro-structure. Special results were obtained for the case of fibres connected by pivots. In this cases an orthotropic material with zero shear modulus was obtained. Such a material has a not elliptic constitutive tensor, thus it can lead to strain concentrations. However, it was shown that some considerations about the physical behaviour of such networks indicated that higher order terms had to be included in the expansion of the internal forces and deformations, so that a strain gradient material was obtained. The results obtained can be used for the design of specific materials requiring ad-hoc properties. Although the reference model is a network material, the results obtained can be applied to other similar kinds of microstructures, like pantographic materials, micro devices composed by microbeams etc. They have been limited at the range of linear elasticity, that is small deformation and linear elastic behaviour. Then, numerical simulations were focused on extension tests and bias tests. The obtained deformed configurations are consistent with the literature experimental tests, both for balanced and unbalanced tissues. Moreover, a comparison between first and second gradient numerical predictions was performed. It was observed that second gradient predictions better simulate the experimental evidences
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Silva, Uziel Paulo da. "Um estudo do método de homogeneização assimptótica visando aplicações em estruturas ósseas." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/82/82131/tde-02092010-094935/.
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O osso é um sólido heterogêneo com estrutura bastante complexa que geralmente exige o emprego de múltiplas escalas em sua análise. A análise do comportamento eletromecânico da estrutura óssea tem sido realizada por meio de métodos da mecânica clássica, métodos de elementos finitos e métodos de homogeneização. Procura-se descrever matematicamente a relação entre o comportamento eletromecânico da estrutura óssea e as propriedades efetivas, ou, globais. Assim, muitos esforços têm sido despendidos para desenvolver modelos analíticos rigorosos capazes de predizer as propriedades globais e locais das estruturas ósseas. O propósito deste trabalho é estudar o método de Homogeneização Assimptótica (MHA) com a finalidade de determinar as propriedades eletromecânicas efetivas de estruturas heterogêneas, tais como a estrutura óssea. Inicialmente, são analisados o problema de condução de calor e o problema elástico e demonstra-se que estes problemas estão relacionados entre si. Para o problema de condução de calor, dois métodos para obter as constantes efetivas são apresentados. Além disso, uma aplicação do MHA em osso cortical é apresentada e os resultados estão de muito bom acordo com resultados encontrados na literatura. Em vista disto, verifica-se a possibilidade da aplicação do MHA para determinar as propriedades efetivas da estrutura óssea com estrutura cristalina na classe 622.The bone is a heterogeneous solid with a highly complex structure that requires a multiple scale type of analysis. To analyze the electromechanical behavior of the bone structure, methods of classical mechanics, finite element methods, and methods of homogenization are being used. This analysis describes mathematically the relationship between the electromechanical behavior of the bone structure and its effective, or, global, properties. Thus, many efforts have been spent to develop rigorous analytical models capable of predicting the global and local effective properties of bone structures. The purpose of this work is to study the Asymptotic Homogenization Method (AHM) in order to determine the electromechanical effective properties of heterogeneous structures, such as the bone structure. The analysis of heat conduction and elastic problem using AHM shows that these problems are related to each other. Furthermore, an application of the AHM in cortical bone is presented and the results are shown to be in very good agreement with results found in the literature. Finally, this work shows great promise in the application of the AHM to determine the effective properties of a bone structure whose constituent material belongs to the crystal class 622.
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Rastkar, Siavash. "Characterization of Homogenized Mechanical Properties of Porous Ceramic Materials Based on Their Realistic Microstructure." FIU Digital Commons, 2016. http://digitalcommons.fiu.edu/etd/2478.
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The recent advances in the Materials Engineering have led to the development of new materials with customized microstructure in which the properties of its constituents and their geometric distribution have a considerable effect on determination of the macroscopic properties of the substance. Direct inclusion of the material microstructure in the analysis on a macro level is challenging since spatial meshes created for the analysis should have enough resolution to be able to accurately capture the geometry of the microstructure. In most cases this leads to a huge finite element model which requires a substantial amount of computational resources.
To circumvent this limitation a number of homogenization techniques were developed. By considering a small element of the material, referred to as Representative Volume Element (RVE), homogenization methods make it possible to include the effects of a material’s microstructure on the overall properties at the macro level. However, complexity of the microstructure geometry and the necessity of satisfying periodic boundary conditions introduce additional difficulties into the analysis procedure.
In this dissertation we propose a hybrid homogenization method that combines Asymptotic homogenization with MeshFree Solution Structures Method (SSM). Our approach allows realistic inclusion of complex geometry of the microstructure that can be captured from micrographs or micro CT scans. In addition to unprecedented flexibility in handling complex geometries, this method also provides a completely automatic analysis procedure. Using meshfree solution structures simplifies meshing to creating a simple cartesian grid which only needs to contain the domain. This also eliminates manual modifications which usually needs to be performed on meshes created from image data.
A computational platform is developed in C++ based on meshfree/asymptotic method. In this platform also a novel meshfree solution structure is designed to provide exact satisfaction of periodic boundary conditions for boundary value problems such as homogenization. Performance of the developed platform is tested over 2D and 3D domains against previously published data and/or conventional finite element methods. After getting satisfactory results, homogenized properties are used to compute localized stress and strain distributions over inhomogeneous structures.
Furthermore, effects of geometric features of pores/inclusions on homogenized mechanical properties is investigated and it is demonstrated that the developed platform could provide an automated quantitative analysis tool for studying effects of different design parameters on homogenized properties.
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Griso, Georges. "Etudes asymptotiques de structures réticulées minces." Paris 6, 1995. http://www.theses.fr/1995PA066338.
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La premiere partie de cette these est consacree a l'etude asymptotique de problemes elliptiques du second ordre, dans une structure reticulee periodique dependant de deux parametres, avec differentes conditions sur la frontiere des trous de la structure. La deuxieme partie de cette these a pour objet l'obtention d'un modele de jonction des poutres et l'application de ce modele a l'etude d'une grue
Books on the topic "Homogenization structure"
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Bensoussan, Alain. Asymptotic analysis for periodic structures. Providence, R.I: American Mathematical Society, 2011.
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Cioranescu, D. Homogenization of reticulated structures. New York: Springer, 1999.
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Cioranescu, Doina, and Jeannine Saint Jean Paulin. Homogenization of Reticulated Structures. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-2158-6.
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Hassani, Behrooz, and Ernest Hinton. Homogenization and Structural Topology Optimization. London: Springer London, 1999. http://dx.doi.org/10.1007/978-1-4471-0891-7.
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Shape optimization by the homogenization method. New York: Springer, 2002.
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E, Hinton, ed. Homogenization and structural topology optimization: Theory, practice, and software. London: Springer, 1999.
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Hassani, Behrooz. Homogenization and structural topology optimization: Theory, practice and software. Berlin [u.a.]: Springer, 2012.
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Urbański, Aleksander. The unified finite element formulation of homogenization of structural members with a periodic microstructure. Kraków: Wydawn. PK., 2005.
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Manevich, L. I. Mechanics of periodically heterogeneous structures. Berlin: Springer, 2002.
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United States. National Aeronautics and Space Administration., ed. Materials with periodic internal structure: Computation based on homogenization and comparison with experiment. [Washington, D.C.]: National Aeronautics and Space Administration, 1990.
Find full textBook chapters on the topic "Homogenization structure"
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Kikuchi, Noboru, and Katsuyuki Suzuki. "Structural Optimization of a Linearly Elastic Structure using the Homogenization Method." In Composite Media and Homogenization Theory, 183–203. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4684-6787-1_11.
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Hassani, Behrooz, and Ernest Hinton. "Homogenization Theory for Media with Periodic Structure." In Homogenization and Structural Topology Optimization, 11–30. London: Springer London, 1999. http://dx.doi.org/10.1007/978-1-4471-0891-7_2.
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Jeulin, D. "Random Structure Models for Homogenization and Fracture Statistics." In Mechanics of Random and Multiscale Microstructures, 33–91. Vienna: Springer Vienna, 2001. http://dx.doi.org/10.1007/978-3-7091-2780-3_2.
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Millet, Olivier, Khaled Bourbatache, and Abdelkarim Aït-Mokhtar. "Homogenization Methods for Ionic Transfers in Saturated Heterogeneous Materials." In Structure Design and Degradation Mechanisms in Coastal Environments, 117–60. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2015. http://dx.doi.org/10.1002/9781119006046.ch3.
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Caffarelli, Luis, and Luis Silvestre. "Issues in Homogenization for Problems with Non Divergence Structure." In Calculus of Variations and Nonlinear Partial Differential Equations, 43–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-75914-0_2.
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Panasenko, G., I. Pankratova, and A. Piatnitski. "Homogenization of a Convection–Diffusion Equation in a Thin Rod Structure." In Integral Methods in Science and Engineering, Volume 1, 279–90. Boston: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4899-2_26.
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Gerasimenko, T. E., N. V. Kurbatova, D. K. Nadolin, A. V. Nasedkin, A. A. Nasedkina, P. A. Oganesyan, A. S. Skaliukh, and A. N. Soloviev. "Homogenization of Piezoelectric Composites with Internal Structure and Inhomogeneous Polarization in ACELAN-COMPOS Finite Element Package." In Advanced Structured Materials, 113–31. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-17470-5_8.
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Goda, Ibrahim, Mohamed Assidi, and Jean-Francois Ganghoffer. "Cosserat Anisotropic Models of Trabecular Bone from the Homogenization of the Trabecular Structure: 2D and 3D Frameworks." In Advanced Structured Materials, 111–41. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36394-8_7.
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Pettersen, Tanja, Yan Jun Li, Trond Furu, and Knut Marthinsen. "Effect of Changing Homogenization Treatment on the Particle Structure in Mn-Containing Aluminium Alloys." In Materials Science Forum, 301–6. Stafa: Trans Tech Publications Ltd., 2007. http://dx.doi.org/10.4028/0-87849-443-x.301.
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Cioranescu, Doina, and Jeannine Saint Jean Paulin. "Lattice-Type Structures." In Homogenization of Reticulated Structures, 71–142. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-2158-6_2.
Full textConference papers on the topic "Homogenization structure"
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Broc, Daniel, and Jean-Franc¸ois Sigrist. "Fluid-Structure Interaction: Numerical Validation of an Homogenization Method." In ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/pvp2006-icpvt-11-93156.
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The considered structure is a nuclear reactor vessel, composed of two concentric inner and outer structures, with water in the annular space between. Previous dynamic analysis showed that this water lead to strong fluid structure interaction coupling the structures. The annular space is filled by regularly spaced cylinders, which are linked to the inner structure. Their influence was neglected in the first studies. Recent analyses, using homogenization methods, show that these cylinders increase the FSI coupling in the vessel. The homogenization methods is based on general principles developed in the study of tube bundles, and very well established, from a physical and numerical point of view. Even if it seems reasonable to have a high degree of confidence in the results obtained with this homogenization methods, it is still interesting to validate the results of the “homogenization analysis” with a comparison with “direct calculations”, taking into account the real geometry of the system. The paper presents the main results of the validation. The main limitation of the “direct calculations” is the size of the mesh and the computer time. The main limitation for the “homogenization analysis” is that the actual modeling does not take into account the anisotropy in the Fluid Structure Interaction in the annular space.
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Buryachenko, Valeriy A. "Computational Homogenization in Peristatics of Periodic Structure Composites." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-86517.
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A composite material (CM) of periodic structure with the peristatic properties of constituents (see Silling, J. Mech. Phys. Solids 2000; 48:175–209) is analyzed by a generalization of the classical locally elastic computational homogenization to its peristatic counterpart. One introduces new volumetric periodic boundary conditions (PBC) at the interaction boundary of a representative unit cell (UC). A generalization of the Hill’s equality to peristatic composites is proved. The general results establishing the links between the effective moduli and the corresponding mechanical influence functions are obtained. The discretization of the equilibrium equation acts as a macro-to-micro transition of the deformation-driven type, where the overall deformation is controlled. Determination of the microstructural displacements allows one to estimate the peristatic traction at the geometrical UC’s boundary which is exploited for estimation of the macroscopic stresses and the effective moduli. One demonstrates computationally, through one-dimensional examples, the approach proposed.
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Marsan, Anne L., and Deba Dutta. "Construction of a CAD Model From 3D Homogenization Output." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0018.
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Abstract A homogenization method has been recently developed to optimize the topology of a structure. This method will suggest a structural topology, but the results will be in a discretized, finite element form. Most engineering applications, however, require smooth structures, whether the faces of the structures be planar or curved. Given the topology of a three-dimensional structure as suggested by the homogenization method, an algorithm is developed to interpret the structure and generate a smooth, manufacturable surface representation of the structure. Some steps of the algorithm require designer inputs. An example is given which demonstrates this algorithm.
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Gonella, Stefano, and Massimo Ruzzene. "Homogenization of Vibrating Periodic Lattice Structures." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84428.
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The paper describes a homogenization technique for periodic lattice structures. The analysis is performed by considering the irreducible unit cell as a building block that defines the periodic pattern. In particular, the continuum equivalent representation for the discrete structure is sought with the objective of retaining information regarding the local properties of the lattice, while condensing its global behavior into a set of differential equations. These equations can then be solved either analytically or numerically, thus providing a model which involves a significantly lower number of variables than those required for the detailed model of the assembly. The methodology is first tested by comparing the dispersion relations obtained through homogenization with those corresponding to the detailed model of the unit cells and then extended to the comparison of exact and approximate harmonic responses. This comparison is carried out for both one-dimensional and two-dimensional assemblies. The application to three-dimensional structures is not attempted in this work and will be approached in the future without the need for substantial conceptual changes in the theoretical procedure. Hence the presented technique is expected to be applicable to a wide range of periodic structures, with applications ranging from the design of structural elements of mechanical and aerospace interest to the optimization of smart materials with attractive mechanical, thermal or electrical properties.
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Broc, Daniel, and Gianluca Artini. "Fluid Structure Interaction for Tubes Bundles: Different Homogenization Methods." In ASME 2017 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/pvp2017-65727.
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ASTRID is a project for an industrial prototype of a 600 MWe sodium cooled Fast Reactor, led by CEA. An important program is in progress for the development and the validation of numerical tools for the simulation of the dynamic mechanical behavior of the Fast Reactor cores, with both experimental and numerical parts. The cores are constituted of Fuel Assemblies (of FA) and Neutronic Shields (or NS) immersed in the primary coolant (sodium), which circulates inside the Fluid Assemblies. The FA and the NS are slender structures, which may be considered as beams, form a mechanical point of view. The dynamic behavior of this system has to be understood, for design and safety studies. Two main movements have to be considered: global horizontal movements under a seismic excitation, and opening of the core. The fluid leads to complex interactions between the structures in the whole core. The dynamic behavior of the core is also strongly influenced by contacts between the beams and by the sodium, which limit the relative displacements. Numerical methods and models are built to describe and simulate this dynamic behavior. The validation of the numerical tools is based on the results of different experimental programs, already performed or in progress. The paper is mainly devoted to the modeling of the Fluid Structure Interaction phenomena in the Fast Reactor cores. Tubes bundles immersed in a dense fluid are very common in the nuclear industry (reactor cores and steam generators). In the case of an external excitation (earthquake or shock) the presence of the fluid leads to “inertial effects” with lower natural frequencies, and “dissipative effects”, with higher damping. The geometry of a tubes bundle is complex, which may lead to very huge sizes for the numerical models. Many works have been made during the last decades to develop homogenization, in order to simplify the problem. Theoretical analyses are presented on different simplifications and assumptions which can be made in the homogenization approach. The accuracy of the different assumptions depends of the conditions of the system: fluid flow or fluid at rest, small or large displacements of the structure. In the general case, it is theoretically necessary to consider the Navier Stokes equations: the fluid flow is fully nonlinear. Models have been developed during the last years, based on the Euler linear equations, corresponding to a fluid at rest, with small displacements of the structure. Only the inertial effects are theoretically described but the dissipative effects may be taken into account by using a Rayleigh damping. Different theoretical analyses show that, even in the case of a nonlinear fluid flow, the linear potential flow models may be used as linear equivalent models. In the cases with an important head loss in the fluid flow through the tubes, the fluid movement is mainly driven by the important forces exchanged with the structure and by the pressure gradient. The global equations of the system are close to the equations used for porous media, like the Darcy equations. An important condition to get a relevant model is to describe globally the energy balance in the system. The energy given to the fluid by the solid correspond to a variation of kinetic energy in the fluid and to energy dissipation in the fluid. Attention will be paid to the cases where the tubes bundle is in interaction with free fluid, without tubes. The global equation of the system has to be accurate for the tubes bundle and for the free fluid also.
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Park, Sang-In, David W. Rosen, Seung-kyum Choi, and Chad E. Duty. "Effective Mechanical Properties of Lattice Material Fabricated by Material Extrusion Additive Manufacturing." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34683.
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In this paper, a two-step homogenization method is proposed and implemented for evaluating effective mechanical properties of lattice structured material fabricated by the material extrusion additive manufacturing process. In order to consider the characteristics of the additive manufacturing process in estimation procedures, the levels of scale for homogenization are divided into three stages — the levels of layer deposition, structural element, and lattice structure. The method consists of two transformations among stages. In the first step, the transformation between layer deposition and structural element levels is proposed to find the geometrical and material effective properties of structural elements in the lattice structure. In the second step, the method to estimate effective mechanical properties of lattice material is presented, which uses a unit cell and is based on the discretized homogenization method for periodic structure. The method is implemented for cubic lattice structure and compared to experimental results for validation purposes.
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Filippov, A. A., and V. M. Fomin. "Determination of nanoparticles elasticity moduli in the epoxy composite using homogenization models." In PROCEEDINGS OF THE ADVANCED MATERIALS WITH HIERARCHICAL STRUCTURE FOR NEW TECHNOLOGIES AND RELIABLE STRUCTURES. Author(s), 2018. http://dx.doi.org/10.1063/1.5083328.
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Artini, Gianluca, and Daniel Broc. "Fluid Structure Interaction Homogenization for Tube Bundles: Significant Dissipative Effects." In ASME 2018 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/pvp2018-84344.
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In the nuclear industry, tube arrays immersed in dense fluid are often encountered. These systems have a large amount of tubes necessary to increase the thermal power exchanged and their dynamical analysis for safety assessment and in life operation is one of the major concern of the nuclear industry. The presence of the fluid creates a strong coupling between tubes which must be taken into account for complete dynamical analysis. However, the description of fluid’s effects on oscillating structures demands great numerical efforts, especially when the tube number increases making any direct numerical simulations impossible to achieve. In this framework, homogenization methods are a possible solution in order to deal with tube bundle Fluid-Structure Interaction (FSI) problems; in fact, it gives the possibility to analyze the dynamics of the global coupled system in large domain with reasonable degree of detail and faster simulations times. At the CEA of Saclay a method based on the linearized Euler equations has been developed. It was presented in a previous PVP conference and its main goal is to assess the effect of spatial deformations of the tube bundle displacement field on the dynamic behavior. In the present paper, after an analysis on the modeling of fluid force where dissipative effects are significant, a homogenized model based on the Navier-Stokes equations is introduced. Simulations in bi-dimensional configurations for different excitations are performed.
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Wang, Jianhua, Wenxiu Tao, Zhifeng Liu, and Congbin Yang. "Topological Optimization of R- Robot Structure Based on Homogenization Method." In 2017 5th International Conference on Frontiers of Manufacturing Science and Measuring Technology (FMSMT 2017). Paris, France: Atlantis Press, 2017. http://dx.doi.org/10.2991/fmsmt-17.2017.226.
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Sigrist, Jean-Franc¸ois, and Daniel Broc. "A Homogenization Method for the Modal Analysis of a Nuclear Reactor With Fluid-Structure Interaction." In ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/pvp2006-icpvt-11-93013.
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The present paper exposes a homogenization method developed in order to perform the modal analysis of a nuclear reactor with fluid-structure interaction effects. The homogenization approach is used in order to take into account the presence of internal structures within the pressure vessel. A homogenization method is proposed in order to perform a numerical calculation of the frequencies and modal masses for the eigenmodes of the coupled fluid-structure problem. The technique allows the use of a simplified fluid-structure model that takes into account the presence of internal structures: the theory bases are first recalled, leading to a new formulation of the fluid-structure coupled problem. The finite element discretization of the coupled formulation leads to the modification of the classical fluid-structure interaction operators. The consistency of the formulation is established from a theoretical point of view by evaluating the total mass of the coupled system with the fluid and structure mass operator, and the modified added mass operator. The method is tested and validated on a 2D case (two concentric cylinders with periodical rigid inclusions within the annular space) and applied on the industrial case. A complete modal analysis (calculation of frequencies and modal masses) is performed on a simplified geometry of a nuclear reactor with and without internal structures. Numerical results are then compared and discussed, and the influence of the internal structures on the fluid-structure coupled phenomenon is highlighted.