Search results for: numerical homogenization

Authors: Hassan Samadi, Mustapha El Jarroudi

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In this work, we consider the homogenization of a non-linear problem in periodic medium with two periodic connected media exchanging a heat flux throughout their common interface. The interfacial exchange coefficient λ is assumed to tend to zero or to infinity following a rate λ=λ(ε) when the size ε of the basic cell tends to zero. Three homogenized problems are determined according to some critical value depending of λ and ε. Our method is based on Γ-Convergence techniques.

Keywords: variational methods, epiconvergence, homogenization, convergence technique

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Authors: M. Arunachalam, M. Pandey

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Nacre, a biological material that forms the inner-layer of sea shells can achieve high toughness and strength by way of staggered arrangement of strong tablets with soft and weak organic interface. Under applied loads the tablets slide over the adjacent tablets, thus generating inelastic deformation and toughness on macroscopic scale. A two dimensional finite element based homogenization methodology is adopted for obtaining the effective material properties of Nacre using a representative volume element (RVE) at finite deformations. In this work, the material behaviour for tablet and interface are assumed to be Isotropic elastic and Isotropic elastic-perfectly plastic with strain softening respectively. Numerical experiments such as uniaxial tension test along X, Y directions and simple shear test are performed on the RVE with uniform displacement and periodic constraints applied at the RVE boundaries to obtain the anisotropic homogenized response and maximum local stresses within each constituents of Nacre. Homogenized material model is then tested for macroscopic structure under three point bending condition and the results obtained are comparable with the results obtained for detailed microstructure based structure, thus homogenization provides a bridge between macroscopic scale and microscopic scale and homogenized material properties obtained from microstructural (RVE) analysis could be used in large scale structural analysis.

Keywords: finite element, homogenization, inelastic deformation, staggered arrangement

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Authors: M. Chen, S-Q. Zhang, X. Wang, D. Tate

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This paper presents a numerical solution, namely limit and shakedown analysis, to predict the safety state of smart structures made of heterogeneous materials under unknown cyclic loadings, for instance, the flexure hinge in the micro-positioning stage driven by piezoelectric actuator. In combination of homogenization theory and finite-element method (FEM), the safety evaluation problem is converted to a large-scale nonlinear optimization programming for an acceptable bounded loading as the design reference. Furthermore, a general numerical scheme integrated with the FEM and interior-point-algorithm based optimization tool is developed, which makes the practical application possible.

Keywords: limit state, shakedown analysis, homogenization, heterogeneous structure

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Authors: Hamed Khezrzadeh

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Many investigations on the micromechanical structure of materials indicate that there exist fractal patterns at the micro scale in some of the main construction and industrial materials. A recently presented micro-fractal theory brings together the well-known periodic homogenization and the fractal geometry to construct an appropriate model for determination of the mechanical properties of particle reinforced composite materials. The proposed multi-step homogenization scheme considers the mechanical properties of different constituent phases in the composite together with the interaction between these phases throughout a step-by-step homogenization technique. In the proposed model the interaction of different phases is also investigated. By using this method the effect of fibers grading on the mechanical properties also could be studied. The theory outcomes are compared to the experimental data for different types of particle-reinforced composites which very good agreement with the experimental data is observed.

Keywords: fractal geometry, homogenization, micromehcanics, particulate composites

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Authors: Sarra Haouala, Issam Doghri

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In this work, a multiscale computational strategy is proposed for the analysis of structures, which are described at a refined level both in space and in time. The proposal is applied to two-phase viscoelastic-viscoplastic (VE-VP) reinforced thermoplastics subjected to large numbers of cycles. The main aim is to predict the effective long time response while reducing the computational cost considerably. The proposed computational framework is a combination of the mean-field space homogenization based on the generalized incrementally affine formulation for VE-VP composites, and the asymptotic time homogenization approach for coupled isotropic VE-VP homogeneous solids under large numbers of cycles. The time homogenization method is based on the definition of micro and macro-chronological time scales, and on asymptotic expansions of the unknown variables. First, the original anisotropic VE-VP initial-boundary value problem of the composite material is decomposed into coupled micro-chronological (fast time scale) and macro-chronological (slow time-scale) problems. The former is purely VE, and solved once for each macro time step, whereas the latter problem is nonlinear and solved iteratively using fully implicit time integration. Second, mean-field space homogenization is used for both micro and macro-chronological problems to determine the micro and macro-chronological effective behavior of the composite material. The response of the matrix material is VE-VP with J2 flow theory assuming small strains. The formulation exploits the return-mapping algorithm for the J2 model, with its two steps: viscoelastic predictor and plastic corrections. The proposal is implemented for an extended Mori-Tanaka scheme, and verified against finite element simulations of representative volume elements, for a number of polymer composite materials subjected to large numbers of cycles.

Keywords: asymptotic expansions, cyclic loadings, inclusion-reinforced thermoplastics, mean-field homogenization, time homogenization

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Authors: M. Palizvan, M. T. Abadi, M. H. Sadr

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Due to variations in damage mechanisms in the microscale, the behavior of fiber-reinforced composites is nonlinear and difficult to model. To make use of computational advantages, homogenization method is applied to the micro-scale model in order to minimize the cost at the expense of detail of local microscale phenomena. In this paper, the effective stiffness is calculated using the homogenization of nonlinear behavior of a composite representative volume element (RVE) containing fiber-matrix debonding. The damage modes for the RVE are considered by using cohesive elements and contacts for the cohesive behavior of the interface between fiber and matrix. To predict more realistic responses of composite materials, different random distributions of fibers are proposed besides square and hexagonal arrays. It was shown that in some cases, there is quite different damage behavior in different fiber distributions. A comprehensive comparison has been made between different graphs.

Keywords: homogenization, cohesive zone model, fiber-matrix debonding, RVE

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Authors: I. Ioannou, I. M. Gitman

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This study focused on the contribution of micro-mechanical parameters on the macro-mechanical response of short fiber composites, namely polypropylene matrix reinforced by glass fibers. In the framework of this paper, an attention has been given to the glass fibers length, as micromechanical parameter influences the overall macroscopic material’s behavior. Three dimensional numerical models were developed and analyzed through the concept of a Representative Volume Element (RVE). Results of the RVE-based approach were compared with analytical Halpin-Tsai’s model.

Keywords: effective properties, homogenization, representative volume element, short fiber reinforced composites

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Authors: M. Palizvan, M. H. Sadr, M. T. Abadi

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The representative volume element (RVE) plays a central role in the mechanics of random heterogeneous materials with a view to predicting their effective properties. In this paper, a computational homogenization methodology, developed to determine effective linear elastic properties of composite materials, is extended to predict the effective nonlinear elastoplastic response of long fiber reinforced composite. Finite element simulations of volumes of different sizes and fiber volume fractures are performed for calculation of the overall response RVE. The dependencies of the overall stress-strain curves on the number of fibers inside the RVE are studied in the 2D cases. Volume averaged stress-strain responses are generated from RVEs and compared with the finite element calculations available in the literature at moderate and high fiber volume fractions. For these materials, the existence of an RVE is demonstrated for the sizes of RVE corresponding to 10–100 times the diameter of the fibers. In addition, the response of small size RVE is found anisotropic, whereas the average of all large ones leads to recover the isotropic material properties.

Keywords: homogenization, periodic boundary condition, elastoplastic properties, RVE

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Authors: Felix Givois, Nicolas R. Gauger, Matthias Kabel

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The efficient digital material characterization is of great interest to many fields of application. It consists of the following three steps. First, a 3D reconstruction of 2D scans must be performed. Then, the resulting gray-value image of the material sample is enhanced by image processing methods. Finally, partial differential equations (PDE) are solved on the segmented image, and by averaging the resulting solutions fields, effective properties like stiffness or conductivity can be computed. Due to the high resolution of current CT images, the latter is typically performed with matrix-free solvers. Among them, a solver that uses the explicit formula of the Green-Eshelby operator in Fourier space has been proposed by Moulinec and Suquet. Its algorithmic, most complex part is the Fast Fourier Transformation (FFT). In our talk, we will discuss the potential quantum advantage that can be obtained by replacing the FFT with the Quantum Fourier Transformation (QFT). We will especially show that the data transfer for noisy intermediate-scale quantum (NISQ) devices can be improved by using appropriate boundary conditions for the PDE, which also allows using semi-classical versions of the QFT. In the end, we will compare the results of the QFT-based algorithm for simple geometries with the results of the FFT-based homogenization method.

Keywords: most likelihood amplitude estimation (MLQAE), numerical homogenization, quantum Fourier transformation (QFT), NISQ devises

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Authors: M. Beusink, E. W. C. Coenen

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The increased application of novel structural materials, such as high grade asphalt, concrete and laminated composites, has sparked the need for a better understanding of the often complex, non-linear mechanical behavior of such materials. The effective macroscopic mechanical response is generally dependent on the applied load path. Moreover, it is also significantly influenced by the microstructure of the material, e.g. embedded fibers, voids and/or grain morphology. At present, multiscale techniques are widely adopted to assess micro-macro interactions in a numerically efficient way. Computational homogenization techniques have been successfully applied over a wide range of engineering cases, e.g. cases involving first order and second order continua, thin shells and cohesive zone models. Most of these homogenization methods rely on Representative Volume Elements (RVE), which model the relevant microstructural details in a confined volume. Imposed through kinematical constraints or boundary conditions, a RVE can be subjected to a microscopic load sequence. This provides the RVE's effective stress-strain response, which can serve as constitutive input for macroscale analyses. Simultaneously, such a study of a RVE gives insight into fine scale phenomena such as microstructural damage and its evolution. It has been reported by several authors that the type of boundary conditions applied to the RVE affect the resulting homogenized stress-strain response. As a consequence, dedicated boundary conditions have been proposed to appropriately deal with this concern. For the specific case of a planar assumption for the analyzed structure, e.g. plane strain, axisymmetric or plane stress, this assumption needs to be addressed consistently in all considered scales. Although in many multiscale studies a planar condition has been employed, the related impact on the multiscale solution has not been explicitly investigated. This work therefore focuses on the influence of the planar assumption for multiscale modeling. In particular the plane stress case is highlighted, by proposing three different implementation strategies which are compatible with a first-order computational homogenization framework. The first method consists of applying classical plane stress theory at the microscale, whereas with the second method a generalized plane stress condition is assumed at the RVE level. For the third method, the plane stress condition is applied at the macroscale by requiring that the resulting macroscopic out-of-plane forces are equal to zero. These strategies are assessed through a numerical study of a thin walled structure and the resulting effective macroscale stress-strain response is compared. It is shown that there is a clear influence of the length scale at which the planar condition is applied.

Keywords: first-order computational homogenization, planar analysis, multiscale, microstrucutures

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Authors: Temitope Olumide Olugbade

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Low resistance and delayed fracture to corrosion, especially in harsh environmental conditions, often limit the wide application of high-manganese (high-Mn) steels. To address this issue, the present work investigates the influence of microalloying on the corrosion properties of high-Mn steels. Microalloyed and base high-Mn steels were synthesized through an arc melting process under an argon atmosphere. To generate different microstructures, the temperature and duration were varied via thermal homogenization treatments. The electrochemical impedance spectroscopy (EIS) and potentiodynamic polarization techniques were used to determine the corrosion properties in 0.6 M NaCl aqueous solution at room temperature. The relationship between the microstructures and corrosion properties was investigated via Scanning Kelvin Probe Microscopy (SKPFM), energy dispersive X-ray spectroscopy (EDX), and Scanning electron microscopy (SEM) techniques. The local corrosion properties were investigated via in situ atomic force spectroscopy (AFM), considering the homogenization treatments. The results indicate that microalloying is a successful technique for enhancing the corrosion behavior of high-Mn steels. Compared to other alloying elements, Vanadium has shown improvement in corrosion properties for both general and local corrosion in chloride environments.

Keywords: corrosion, high-manganese steel, homogenization, microalloying, vanadium

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Authors: Morteza Hadi

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This research investigates the potential enhancement of the rollability of Cu-Ge-Ni alloy through the mitigation of microstructural and compositional inhomogeneities via two distinct heat treatment methods: homogenization and solution treatment. To achieve this objective, the alloy with the desired composition was fabricated using a vacuum arc remelting furnace (VAR), followed by sample preparation for microstructural, compositional, and heat treatment analyses at varying temperatures and durations. Characterization was conducted employing optical and scanning electron microscopy (SEM), X-ray diffraction (XRD), and Vickers hardness testing. The results obtained indicate that a minimum duration of 10 hours is necessary for adequate homogenization of the alloy at 750°C. This heat treatment effectively removes coarse dendrites from the casting microstructure and significantly reduces elemental separations. However, despite these improvements, the presence of a second phase with markedly different hardness from the matrix results in poor rolling ability for the alloy. The optimal time for solution treatment at various temperatures was determined, with the most effective cycle identified as 750°C for 2 hours, followed by rapid quenching in water. This process induces the formation of a single-phase microstructure and complete elimination of the second  phase, as confirmed by X-ray diffraction analysis. Results demonstrate a reduction in hardness by 30 Vickers, and the elimination of microstructural unevenness enables successful thickness reduction by up to 50% through rolling without encountering cracking.

Keywords: Cu-Ge-Ni alloy, homogenization. solution treatment, rollability

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Authors: H. Hentati, R. Abdelmoula, Li Jia, A. Maalej

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In this work, we present numerical simulations of the quasi-static crack propagation based on the variation approach. We perform numerical simulations of a piece of brittle material without initial crack. An alternate minimization algorithm is used. Based on these numerical results, we determine the influence of numerical parameters on the location of crack. We show the importance of trying to optimize the time of numerical computation and we present the first attempt to develop a simple numerical method to optimize this time.

Keywords: fracture mechanics, optimization, variation approach, mechanic

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Authors: E. M. Hassan, A. L. Kalamkarov

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Two micromechanical models for 3D smart composite with embedded periodic or nearly periodic network of generally orthotropic reinforcements and actuators are developed and applied to cubic structures with unidirectional orientation of constituents. Analytical formulas for the effective piezothermoelastic coefficients are derived using the Asymptotic Homogenization Method (AHM). Finite Element Analysis (FEA) is subsequently developed and used to examine the aforementioned periodic 3D network reinforced smart structures. The deformation responses from the FE simulations are used to extract effective coefficients. The results from both techniques are compared. This work considers piezoelectric materials that respond linearly to changes in electric field, electric displacement, mechanical stress and strain and thermal effects. This combination of electric fields and thermo-mechanical response in smart composite structures is characterized by piezoelectric and thermal expansion coefficients. The problem is represented by unit-cell and the models are developed using the AHM and the FEA to determine the effective piezoelectric and thermal expansion coefficients. Each unit cell contains a number of orthotropic inclusions in the form of structural reinforcements and actuators. Using matrix representation of the coupled response of the unit cell, the effective piezoelectric and thermal expansion coefficients are calculated and compared with results of the asymptotic homogenization method. A very good agreement is shown between these two approaches.

Keywords: asymptotic homogenization method, finite element analysis, effective piezothermoelastic coefficients, 3D smart network composite structures

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Authors: Serpa A. M., Gómez Hoyos C., Velásquez-Cock J. A., Ruiz L. F., Vélez Acosta L. M., Gañan P., Zuluaga R.

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Turmeric (Curcuma Longa L) is an Indian rhizome known for its biological properties, derived from its active compounds such as curcuminoids. Curcumin, the main polyphenol in turmeric, only represents around 3.5% of the dehydrated rhizome and extraction yields between 41 and 90% have been reported. Therefore, for every 1000 tons of turmeric powder used for the extraction of curcumin, around 970 tons of residues are generated. The present study evaluates the effect of different mechanical treatments (waring blender, grinder and high-pressure homogenization) on the physical and chemical properties of turmeric, as an alternative for the transformation of the entire rhizome. Suspensions of turmeric (10, 20 y 30%) were processed by waring blender during 3 min at 12000 rpm, while the samples treated by grinder were processed evaluating two different Gaps (-1 and -1,5). Finally, the process by high-pressure homogenization, was carried out at 500 bar. According to the results, the luminosity of the samples increases with the severity of the mechanical treatment, due to the stabilization of the color associated with the inactivation of the oxidative enzymes. Additionally, according to the microstructure of the samples, the process by grinder (Gap -1,5) and by high-pressure homogenization allowed the largest size reduction, reaching sizes up to 3 m (measured by optical microscopy). This processes disrupts the cells and breaks their fragments into small suspended particles. The infrared spectra obtained from the samples using an attenuated total reflectance accessory indicates changes in the 800-1200 cm⁻¹ region, related mainly to changes in the starch structure. Finally, the thermogravimetric analysis shows the presence of starch, curcumin and some minerals in the suspensions.

Keywords: characterization, mechanical treatments, suspensions, turmeric rhizome

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Authors: Gautier Girard, Marion Martiny, Sebastien Mercier, Mohamad Jrad, Mohamed-Slim Bahi, Laurent Bodin, Francois Lechleiter, David Nevo, Sophie Dareys

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Reliability of electronic devices has always been of highest interest for Aero-MIL and space applications. In any electronic device, Printed Circuit Board (PCB), providing interconnection between components, is a key for reliability. During the last decades, PCB technologies evolved to sustain and/or fulfill increased original equipment manufacturers requirements and specifications, higher densities and better performances, faster time to market and longer lifetime, newer material and mixed buildups. From the very beginning of the PCB industry up to recently, qualification, experiments and trials, and errors were the most popular methods to assess system (PCB) reliability. Nowadays OEM, PCB manufacturers and scientists are working together in a close relationship in order to develop predictive models for PCB reliability and lifetime. To achieve that goal, it is fundamental to characterize precisely base materials (laminates, electrolytic copper, …), in order to understand failure mechanisms and simulate PCB aging under environmental constraints by means of finite element method for example. The laminates are woven composites and have thus an orthotropic behaviour. The in-plane properties can be measured by combining classical uniaxial testing and digital image correlation. Nevertheless, the out-of-plane properties cannot be evaluated due to the thickness of the laminate (a few hundred of microns). It has to be noted that the knowledge of the out-of-plane properties is fundamental to investigate the lifetime of high density printed circuit boards. A homogenization method combining analytical and numerical approaches has been developed in order to obtain the complete elastic orthotropic behaviour of a woven composite from its precise 3D internal structure and its experimentally measured in-plane elastic properties. Since the mechanical properties of the resin surrounding the fibres are unknown, an inverse method is proposed to estimate it. The methodology has been applied to one laminate used in hyperfrequency spatial applications in order to get its elastic orthotropic behaviour at different temperatures in the range [-55°C; +125°C]. Next; numerical simulations of a plated through hole in a double sided PCB are performed. Results show the major importance of the out-of-plane properties and the temperature dependency of these properties on the lifetime of a printed circuit board. Acknowledgements—The support of the French ANR agency through the Labcom program ANR-14-LAB7-0003-01, support of CNES, Thales Alenia Space and Cimulec is acknowledged.

Keywords: homogenization, orthotropic behaviour, printed circuit board, woven composites

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Authors: Mohsen Zahraei

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‎In this paper, ‎the notion of ‎rank-k numerical range of rectangular complex matrix polynomials‎ ‎are introduced. ‎Some algebraic and geometrical properties are investigated. ‎Moreover, ‎for ε>0 the notion of Birkhoff-James approximate orthogonality sets for ε-higher ‎rank numerical ranges of rectangular matrix polynomials is also introduced and studied. ‎The proposed definitions yield a natural generalization of the standard higher rank numerical ranges.

Keywords: ‎‎Rank-k numerical range‎, ‎isometry‎, ‎numerical range‎, ‎rectangular matrix polynomials

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Authors: Chin-Yun Chen

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Numerical integration is an essential tool for deriving different physical quantities in engineering and science. The effectiveness of a numerical integrator depends on different factors, where the crucial one is the error estimation. This work presents an error estimator that combines a derivative free method to improve the performance of verified numerical quadrature.

Keywords: numerical quadrature, error estimation, derivative free method, interval computation

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Authors: Mounir Baccar, Amel Gammoudi, Abdelhak Ayadi

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The efficient mixing of highly viscous fluids is required for many industries such as food, polymers or paints production. The homogeneity is a challenging operation for this fluids type since they operate at low Reynolds number to reduce the required power of the used impellers. Particularly, close-clearance impellers, mainly helical ribbons, are chosen for highly viscous fluids agitated in laminar regime which is currently heated through vessel wall. Indeed, they are characterized by high shear strains closer to the vessel wall, which causes a disturbing thermal boundary layer and ensures the homogenization of the bulk volume by axial and radial vortices. The hydrodynamic and thermal behaviors of Newtonian fluids in vessels agitated by helical ribbon impellers, has been mostly studied by many researchers. However, rarely researchers investigated numerically the agitation of yield stress fluid by means of helical ribbon impellers. This paper aims to study the effect of the Double Helical Ribbon (DHR) stirrers on both the hydrodynamic and the thermal behaviors of yield stress fluids treated in a cylindrical vessel by means of numerical simulation approach. For this purpose, continuity, momentum, and thermal equations were solved by means of 3D finite volume technique. The effect of Oldroyd (Od) and Reynolds (Re) numbers on the power (Po) and Nusselt (Nu) numbers for the mentioned stirrer type have been studied. Also, the velocity and thermal fields, the dissipation function and the apparent viscosity have been presented in different (r-z) and (r-θ) planes.

Keywords: Bingham fluid, Hydrodynamic and thermal behavior, helical ribbon, mixing, numerical modelling

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Authors: Jaime Muñoz, José Arcos, Oscar Bautista Federico Méndez

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The influence of a pulsatile electroosmotic flow (PEOF) at the rate of spread, or dispersivity, for a non-reactive solute released in a microcapillary with slippage at the boundary wall (modeled by the Navier-slip condition) is theoretically analyzed. Based on the flow velocity field developed under such conditions, the present study implements an analytical scheme of scaling known as the Theory of Homogenization, in order to obtain a mathematical expression for the dispersivity, valid at a large time scale where the initial transients have vanished and the solute spreads under the Taylor dispersion influence. Our results show the dispersivity is a function of a slip coefficient, the amplitude of the imposed electric field, the Debye length and the angular Reynolds number, highlighting the importance of the latter as an enhancement/detrimental factor on the dispersivity, which allows to promote the PEOF as a strong candidate for chemical species separation at lab-on-a-chip devices.

Keywords: dispersivity, microcapillary, Navier-slip condition, pulsatile electroosmotic flow, Taylor dispersion, Theory of Homogenization

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Authors: Aka S. Koffi, N’Goran Yao, Philippe Bastide, Denis Bruneau, Diby Kadjo

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Cocoa beans (Theobroma cocoa L.) are the main components for chocolate manufacturing. The beans must be correctly fermented at first. Traditional process to perform the first fermentation (lactic fermentation) often consists in confining cacao beans using banana leaves or a fermentation basket, both of them leading to a poor product thermal insulation and to an inability to mix the product. Box fermenter reduces this loss by using a wood with large thickness (e>3cm), but mixing to homogenize the product is still hard to perform. Automatic fermenters are not rentable for most of producers. Heat (T>45°C) and acidity produced during the fermentation by microbiology activity of yeasts and bacteria are enabling the emergence of potential flavor and taste of future chocolate. In this study, a cylindro-rotative fermenter (FCR-V1) has been built and coconut fibers were used in its structure to confine heat. An axis of rotation (360°) has been integrated to facilitate the turning and homogenization of beans in the fermenter. This axis permits to put fermenter in a vertical position during the anaerobic alcoholic phase of fermentation, and horizontally during acetic phase to take advantage of the mid height filling. For circulation of air flow during turning in acetic phase, two woven rattan with grid have been made, one for the top and second for the bottom of the fermenter. In order to reduce air flow during acetic phase, two airtight covers are put on each grid cover. The efficiency of the turning by this kind of rotation, coupled with homogenization of the temperature, caused by the horizontal position in the acetic phase of the fermenter, contribute to having a good proportion of well-fermented beans (83.23%). In addition, beans’pH values ranged between 4.5 and 5.5. These values are ideal for enzymatic activity in the production of the aromatic compounds inside beans. The regularity of mass loss during all fermentation makes it possible to predict the drying surface corresponding to the amount being fermented.

Keywords: cocoa fermentation, fermenter, microbial activity, temperature, turning

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Authors: Camila Lozano-Vivas, Camila Quevedo-Villamil, Ingrid Munoz-Quijano, Diego Loaiza

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Colombia's limited oil reserves make the finding of new fields of extraction or the potentiate of the existing ones a more important task to do every day; the exploration projects that allow to have a better knowledge of the oil basins are essential. The upper Magdalena Valley basin - VSM, whose reserves are limited, has been one of the first basins for the exploration and production of hydrocarbons in Colombia. The Hondita and Lomagorda formations were deposited in the Late Cretaceous Middle Albian to the Coniacian and are characterized by being the hydrocarbon-generating rocks in the VSM basin oil system along with the Shale de Bambucá; therefore multiple studies have been made. In the oil industry, geochemical properties are used to understand the origin, migration, accumulation, and alteration of hydrocarbons and, in general, the evolution of the basin containing them. One of the most important parameters to understand this evolution is the formation temperature of the oil system. For this reason, a microthermometric study of fluid inclusions was carried out to recognize formation temperatures and to determine certain basic physicochemical variables, homogenization temperature, pressure, density and salinity of the fluid at the time of entrapment, providing evidence on the history of different events in different geological environments in the evolution of a sedimentary basin. Prior to this study, macroscopic and microscopic petrographic analyses of the samples collected in the field were performed. The results of the mentioned properties of the fluid inclusions in the different samples analyzed have salinities ranging from 20.22% to 26.37% eq. by weight NaCl, similar densities found in the ranges of 1.05 to 1.16 g/cc and an average homogenization temperature at 142.92°C, indicating that, at the time of their entanglement, the rock was in the window of generation of medium hydrocarbons –light with fragile characteristics of the rock that would make it useful to treat them as naturally fractured reservoirs.

Keywords: homogenization temperature, fluid inclusions, microthermometry, salinity

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Authors: Ahlem Mougaida, Hedi Bel Hadj Salah

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Several methods are suggested to improve the numerical integration in Galerkin weak form for Meshless methods. In fact, integrating without taking into account the characteristics of the shape functions reproduced by Meshless methods (rational functions, with compact support etc.), causes a large integration error that influences the PDE’s approximate solution. Comparisons between different methods of numerical integration for rational functions are discussed and compared. The algorithms are implemented in Matlab. Finally, numerical results were presented to prove the efficiency of our algorithms in improving results.

Keywords: adaptive methods, meshless, numerical integration, rational quadrature

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Authors: Oktavia Eka Puspita

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The possibility of using Solid Lipid Nanoparticles (SLN) for topical use is an interesting feature concerning this system has occlusive properties on the skin surface therefore enhance the penetration of drugs through the stratum corneum by increased hydration. This advantage can be used to enhance the drug penetration of topical delivery such as Diclofenac sodium for the relief of signs and symptoms of osteoarthritis, rheumatoid arthritis and ankylosing spondylitis. The purpose of this study was focused on the preparation and physical characterization of Diclofenac sodium loaded SLN (D-SLN). D loaded SLN were prepared by hot homogenization followed by ultrasonication technique. Since the occlusion factor of SLN is related to its particle size the formulation of D-SLN in present study two formulations different in its surfactant contents were prepared to investigate the difference of the particle size resulted. Surfactants selected for preparation of formulation A (FA) were lecithin soya and Tween 80 whereas formulation B (FB) were lecithin soya, Tween 80, and Sodium Lauryl Sulphate. D-SLN were characterized for particle size and distribution, polydispersity index (PI), zeta potential using Beckman-Coulter Delsa™ Nano. Overall, the particle size obtained from FA was larger than FB. FA has 90% of the particles were above 1000 nm, while FB has 90% were below 100 nm.

Keywords: solid lipid nanoparticles, hot homogenization technique, particle size analysis, topical administration

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Authors: Merrimi El Bekkaye, El Bikri Khalid, Benamar Rhali

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In the present paper, the problem of geometrically non-linear free vibration of symmetrically and asymmetrically laminated composite beams (LCB) resting on nonlinear Pasternak elastic Foundation with immovable ends is studied. A homogenization procedure has been performed to reduce the problem under consideration to that of the isotropic homogeneous beams with effective bending stiffness and axial stiffness parameters. This simple formulation is developed using the governing axial equation of the beam in which the axial inertia and damping are ignored. The theoretical model is based on Hamilton’s principle and spectral analysis. Iterative form solutions are presented to calculate the fundamental nonlinear frequency parameters which are found to be in a good agreement with the published results. On the other hand, the influence of the foundation parameters on the nonlinear frequency to the linear frequency ratio of the LCB has been studied. The non-dimensional curvatures associated to the fundamental mode are also given in the case of clamped-clamped symmetrically and asymmetrically laminated composite beams.

Keywords: large vibration amplitudes, laminated composite beam, Pasternak foundation, composite beams

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Authors: Carla E. O. de Moraes, Gladson O. Antunes, Mauro A. Rincon

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The aim of this paper is to study the internal stabilization of the Bernoulli-Euler equation numerically. For this, we consider a square plate subjected to a feedback/damping force distributed only in a subdomain. An algorithm for obtaining an approximate solution to this problem was proposed and implemented. The numerical method used was the Finite Difference Method. Numerical simulations were performed and showed the behavior of the solution, confirming the theoretical results that have already been proved in the literature. In addition, we studied the validation of the numerical scheme proposed, followed by an analysis of the numerical error; and we conducted a study on the decay of the energy associated.

Keywords: Bernoulli-Euler plate equation, numerical simulations, stability, energy decay, finite difference method

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Authors: Marasovic Branka, Aljinovic Zdravka, Poklepovic Tea

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Numerical methods like binomial and trinomial trees and finite difference methods can be used to price a wide range of options contracts for which there are no known analytical solutions. American options are the most famous of that kind of options. Besides numerical methods, American options can be valued with the approximation formulas, like Bjerksund-Stensland formulas from 1993 and 2002. When the value of American option is approximated by Bjerksund-Stensland formulas, the computer time spent to carry out that calculation is very short. The computer time spent using numerical methods can vary from less than one second to several minutes or even hours. However to be able to conduct a comparative analysis of numerical methods and Bjerksund-Stensland formulas, we will limit computer calculation time of numerical method to less than one second. Therefore, we ask the question: Which method will be most accurate at nearly the same computer calculation time?

Keywords: Bjerksund and Stensland approximations, computational analysis, finance, options pricing, numerical methods

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Authors: Pawel Flaszynski, Piotr Doerffer, Jan Holnicki-Szulc, Grzegorz Mikulowski

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Results of numerical simulations for transonic flow in a piezoelectric valve are presented. The valve is the main part of an adaptive pneumatic shock absorber. Flow structure in the valve domain and the influence of the flow non-uniformity in the valve on a mass flow rate is investigated. Numerical simulation results are compared with experimental data.

Keywords: pneumatic valve, transonic flow, numerical simulations, piezoelectric valve

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

Abstract:

Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations

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Authors: Zuodong Liang, Dong-Sheng Jeng

Abstract:

Seabed instability around an offshore pipeline is one of key factors that need to be considered in the design of offshore infrastructures. Unlike previous investigations, a three-dimensional numerical model for the wave-induced soil response around an offshore pipeline is proposed in this paper. The numerical model was first validated with 2-D experimental data available in the literature. Then, a parametric study will be carried out to examine the effects of wave, seabed characteristics and confirmation of pipeline. Numerical examples demonstrate significant influence of wave obliquity on the wave-induced pore pressures and the resultant seabed liquefaction around the pipeline, which cannot be observed in 2-D numerical simulation.

Keywords: pore pressure, 3D wave model, seabed liquefaction, pipeline

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