Search results for: Homogenization method

Authors: Kannanut Chamsri

Abstract:

Darcy’s Law is a well-known constitutive equation describing the flow of a fluid through a porous medium. The equation shows a relationship between the superficial or Darcy velocity and the pressure gradient which was first experimentally observed by Henry Darcy in 1855-1856. In this study, we apply homogenization method to Stokes equation in order to derive Darcy’s Law. The process of deriving the equation is complicated, especially in multidimensional domain. Thus, for the sake of simplicity, we use the indicial notation as well as the homogenization. This combination provides a smooth, simple and easy technique to derive Darcy’s Law.

Keywords: Darcy’s Law, Homogenization method, Indicial notation

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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: 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 unitcell 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, Effective Piezothermoelastic Coefficients, Finite Element Analysis, 3D Smart Network Composite Structures.

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Authors: Z. Pavlík, M. Čáchová, E. Vejmelková, T. Korecký, J. Fořt, M. Pavlíková, R. Černý

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The effect of waste ceramic powder on the thermal properties of lime-pozzolana composites is investigated. At first, the measurements of effective thermal conductivity of lime-pozzolan composites are performed in dependence on moisture content from the dry state to fully water saturated state using a pulse method. Then, the obtained data are analyzed using two different homogenization techniques, namely the Lichtenecker’s and Dobson’s formulas, taking into account Wiener’s and Hashin/Shtrikman bounds. 

Keywords: Waste ceramic powder, lime-pozzolan plasters, effective thermal conductivity, homogenization techniques.

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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: 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: A. Zerkane, K. El Bikri, R. Benamar

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The purpose of the present paper is to show that the problem of geometrically nonlinear free vibrations of functionally graded beams (FGB) with immovable ends can be reduced to that of isotropic homogeneous beams with effective bending stiffness and axial stiffness parameters by using an homogenization procedure. The material properties of the functionally graded composites examined are assumed to be graded in the thickness direction and estimated through the rule of mixture. The theoretical model is based on the Euler-Bernouilli beam theory and the Von Kármán geometrical nonlinearity assumptions. Hamilton’s principle is applied and a multimode approach is derived to calculate the fundamental nonlinear frequency parameters, which are found to be in a good agreement with the published results. The non-dimensional curvatures associated to the nonlinear fundamental mode are also given for various vibration amplitudes in the case of clamped-clamped FGB.

Keywords: Nonlinear vibrations, functionally graded materials, homogenization procedure.

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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: B. Ramgopal Reddy, K. Ramji, B. Satyanarayana

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In this paper, free vibration analysis of carbon nanotube (CNT) reinforced laminated composite panels is presented. Three types of panels such as flat, concave and convex are considered for study. Numerical simulation is carried out using commercially available finite element analysis software ANSYS. Numerical homogenization is employed to calculate the effective elastic properties of randomly distributed carbon nanotube reinforced composites. To verify the accuracy of the finite element method, comparisons are made with existing results available in the literature for conventional laminated composite panels and good agreements are obtained. The results of the CNT reinforced composite materials are compared with conventional composite materials under different boundary conditions.

Keywords: CNT Reinforced Composite Panels, Effective ElasticProperties, Finite Element Method, Natural Frequency.

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Authors: Rawia M. Khalil, Ahmed A. Abd El Rahman, Mahfouz A. Kassem, Mohamed S. El Ridi, Mona M. Abou Samra, Ghada E. A. Awad, Soheir S. Mansy

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Solid lipid nanoparticles (SLNs) have gained great attention for the topical treatment of skin associated fungal infection as they facilitate the skin penetration of loaded drugs. Our work deals with the preparation of nystatin loaded solid lipid nanoparticles (NystSLNs) using the hot homogenization and ultrasonication method. The prepared NystSLNs were characterized in terms of entrapment efficiency, particle size, zeta potential, transmission electron microscopy, differential scanning calorimetry, rheological behavior and in vitro drug release. A stability study for 6 months was performed. A microbiological study was conducted in male rats infected with Candida albicans, by counting the colonies and examining the histopathological changes induced on the skin of infected rats. The results showed that SLNs dispersions are spherical in shape with particle size ranging from 83.26±11.33 to 955.04±1.09 nm. The entrapment efficiencies are ranging from 19.73±1.21 to 72.46±0.66% with zeta potential ranging from -18.9 to -38.8 mV and shear-thinning rheological Behavior. The stability studies done for 6 months showed that nystatin (Nyst) is a good candidate for topical SLN formulations. A least number of colony forming unit/ ml (cfu/ml) was recorded for the selected NystSLN compared to the drug solution and the commercial Nystatin® cream present in the market. It can be fulfilled from this work that SLNs provide a good skin targeting effect and may represent promising carrier for topical delivery of Nyst offering the sustained release and maintaining the localized effect, resulting in an effective treatment of cutaneous fungal infection.

Keywords: Candida infections, Hot homogenization, Nystatin, Solid lipid nanoparticles, Stability, Topical delivery.

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Authors: Ahmed. S. Alasmari, M. S. Soliman, Magdy M. El-Rayes

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This study focuses on the effect of the addition of magnesium (Mg) and silver (Ag) on the mechanical properties of aluminum based alloys. The alloying elements will be added at different levels using the factorial design of experiments of 2²; the two factors are Mg and Ag at two levels of concentration. The superior mechanical properties of the produced Al-Cu-Mg-Ag alloys after aging will be resulted from a unique type of precipitation named as Ω-phase. The formed precipitate enhanced the tensile strength and thermal stability. This paper further investigated the microstructure and mechanical properties of as cast Al–Cu–Mg–Ag alloys after being complete homogenized treatment at 520 °C for 8 hours followed by isothermally age hardening process at 190 °C for different periods of time. The homogenization at 520 °C for 8 hours was selected based on homogenization study at various temperatures and times. The alloys’ microstructures were studied by using optical microscopy (OM). In addition to that, the fracture surface investigation was performed using a scanning electronic microscope (SEM). Studying the microstructure of aged Al-Cu-Mg-Ag alloys reveal that the grains are equiaxed with an average grain size of about 50 µm. A detailed fractography study for fractured surface of the aged alloys exhibited a mixed fracture whereby the random fracture suggested crack propagation along the grain boundaries while the dimples indicated that the fracture was ductile. The present result has shown that alloy 5 has the highest hardness values and the best mechanical behaviors.

Keywords: Precipitation hardening, aluminum alloys, aging, design of experiments, analysis of variance, heat treatments.

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Authors: B. Cilek Tatar, G. Sumnu, M. Oztop, E. Ayaz

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Encapsulation protects sensitive food ingredients against heat, oxygen, moisture and pH until they are released to the system. It can mask the unwanted taste of nutrients that are added to the foods for fortification purposes. Cherry laurels (Prunus laurocerasus) contain phenolic compounds which decrease the proneness to several chronic diseases such as types of cancer and cardiovascular diseases. The objective of this research was to study the effects of centrifugation, different coating materials and homogenization methods on microencapsulation of powders obtained from cherry laurels. In this study, maltodextrin and mixture of maltodextrin:whey protein with a ratio of 1:3 (w/w) were chosen as coating materials. Total solid content of coating materials was kept constant as 10% (w/w). Capsules were obtained from powders of freeze-dried cherry laurels through encapsulation process by silent crusher homogenizer or microfluidization. Freeze-dried cherry laurels were core materials and core to coating ratio was chosen as 1:10 by weight. To homogenize the mixture, high speed homogenizer was used at 4000 rpm for 5 min. Then, silent crusher or microfluidizer was used to complete encapsulation process. The mixtures were treated either by silent crusher for 1 min at 75000 rpm or microfluidizer at 50 MPa for 3 passes. Freeze drying for 48 hours was applied to emulsions to obtain capsules in powder form. After these steps, dry capsules were grounded manually into a fine powder. The microcapsules were analyzed for total antioxidant activity with DPPH (1,1-diphenyl-2-picrylhydrazyl) radical scavenging method. Prior to high speed homogenization, the samples were centrifuged (4000 rpm, 1 min). Centrifugation was found to have positive effect on total antioxidant activity of capsules. Microcapsules treated by microfluidizer were found to have higher total antioxidant activities than those treated by silent crusher. It was found that increasing whey protein concentration in coating material (using maltodextrin:whey protein 1:3 mixture) had positive effect on total antioxidant activity for both silent crusher and microfluidization methods. Therefore, capsules prepared by microfluidization of centrifuged mixtures can be selected as the best conditions for encapsulation of cherry laurel powder by considering their total antioxidant activity. In this study, it was shown that capsules prepared by these methods can be recommended to be incorporated into foods in order to enhance their functionality by increasing antioxidant activity.

Keywords: Antioxidant activity, cherry laurel, microencapsulation, microfluidization.

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Authors: R. Bures, M. Streckova, M. Faberova, P. Kurek

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Composite material based on Fe3Si micro-particles and Mn-Zn nano-ferrite was prepared using powder metallurgy technology. The sol-gel followed by autocombustion process was used for synthesis of Mn0.8Zn0.2Fe2O4 ferrite. 3 wt.% of mechanically milled ferrite was mixed with Fe3Si powder alloy. Mixed micro-nano powder system was homogenized by the Resonant Acoustic Mixing using ResodynLabRAM Mixer. This non-invasive homogenization technique was used to preserve spherical morphology of Fe3Si powder particles. Uniaxial cold pressing in the closed die at pressure 600 MPa was applied to obtain a compact sample. Microwave sintering of green compact was realized at 800°C, 20 minutes, in air. Density of the powders and composite was measured by Hepycnometry. Impulse excitation method was used to measure elastic properties of sintered composite. Mechanical properties were evaluated by measurement of transverse rupture strength (TRS) and Vickers hardness (HV). Resistivity was measured by 4 point probe method. Ferrite phase distribution in volume of the composite was documented by metallographic analysis. It has been found that nano-ferrite particle distributed among micro- particles of Fe3Si powder alloy led to high relative density (~93%) and suitable mechanical properties (TRS >100 MPa, HV ~1GPa, E-modulus ~140 GPa) of the composite. High electric resistivity (R~6.7 ohm.cm) of prepared composite indicate their potential application as soft magnetic material at medium and high frequencies.

Keywords: Micro- and nano-composite, soft magnetic materials, microwave sintering, mechanical and electric properties.

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Authors: A. M. Hassanain, Nader M. A. Mohamed, M. Naguib Aly, Alya A. Badawi, M. A. Gaheen

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The thermal, epithermal and fast fluxes were calculated for three irradiation channels at Egypt Second Research Reactor (ETRR-2) using CITVAP code. The validity of the calculations was verified by experimental measurements. There are some deviations between measurements and calculations. This is due to approximations in the calculation models used, homogenization of regions, condensation of energy groups and uncertainty in nuclear data used. Neutron flux data for the three irradiation channels are now available. This would enable predicting the irradiation conditions needed for future radioisotope production.

Keywords: ETRR-2, Neutron flux, Radioisotope production, CITVAP

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Authors: T. Kuchukhidze, N. Jalagonia, T. Korkia, V. Gabunia, N. Jalabadze, R. Chedia

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In this work, obtaining methods of ultrafine alumina powdery composites and high temperature pressing technology of matrix ceramic composites with different compositions have been discussed. Alumina was obtained by solution combustion synthesis and sol-gel methods. Metal carbides containing powdery composites were obtained by homogenization of finishing powders in nanomills, as well as by their single-step high temperature synthesis .Different types of matrix ceramics composites (α-Al2O3-ZrO2-Y2O3, α-Al2O3- Y2O3-MgO, α-Al2O3-SiC-Y2O3, α-Al2O3-WC-Co-Y2O3, α-Al2O3- B4C-Y2O3, α-Al2O3- B4C-TiB2 etc.) were obtained by using OXYGON furnace. Consolidation of powders were carried out at 1550- 1750°C (hold time - 1 h, pressure - 50 MPa). Corundum ceramics samples have been obtained and characterized by high hardness and fracture toughness, absence of open porosity, high corrosion resistance. Their density reaches 99.5-99.6% TD. During the work, the following devices have been used: High temperature vacuum furnace OXY-GON Industries Inc (USA), Electronic Scanning Microscopes Nikon Eclipse LV 150, Optical Microscope NMM- 800TRF, Planetary mill Pulverisette 7 premium line, Shimadzu Dynamic Ultra Micro Hardness Tester DUH-211S, Analysette 12 Dynasizer.

Keywords: α-Alumina, Consolidation, Matrix Ceramics, Powdery composites.

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Authors: Zhengsheng Wang, Jing Qi, Chuntao Liu, Yuanjun Li

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The harmonic Arnoldi method can be used to find interior eigenpairs of large matrices. However, it has been shown that this method may converge erratically and even may fail to do so. In this paper, we present a new method for computing interior eigenpairs of large nonsymmetric matrices, which is called weighted harmonic Arnoldi method. The implementation of the method has been tested by numerical examples, the results show that the method converges fast and works with high accuracy.

Keywords: Harmonic Arnoldi method, weighted harmonic Arnoldi method, eigenpair, interior eigenproblem, non symmetric matrix.

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Authors: Jin Sup Kim, Woo Young Jung, Minho Kwon

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In general dynamic analyses, lower mode response is of interest, however the higher modes of spatially discretized equations generally do not represent the real behavior and not affects to global response much. Some implicit algorithms, therefore, are introduced to filter out the high-frequency modes using intended numerical error. The objective of this study is to introduce the P-method and PC α-method to compare that with dissipation method and Newmark method through the stability analysis and numerical example. PC α-method gives more accuracy than other methods because it based on the α-method inherits the superior properties of the implicit α-method. In finite element analysis, the PC α-method is more useful than other methods because it is the explicit scheme and it achieves the second order accuracy and numerical damping simultaneously.

Keywords: Dynamic, α-Method, P-Method, PC α-Method, Newmark method.

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Authors: Arnab Majumdar, Sanjoy Sadhukhan

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Although gun barrel steels are an important variety from defense view point, available literatures are very limited. In the present work, an IF grade Ni-Cr-Mo-V high strength low alloy steel is produced in Electric Earth Furnace-ESR Route. Ingot was hot forged to desired dimension with a reduction ratio of 70-75% followed by homogenization, hardening and tempering treatment. Sample chemistry, NMIR, macro and micro structural analyses were done. Mechanical properties which include tensile, impact, and fracture toughness were studied. Ultrasonic testing was done to identify internal flaws. The existing high strength low alloy Ni-Cr-Mo-V steel shows improved properties in modified processing route and heat treatment schedule in comparison to properties noted earlier for manufacturing of gun barrels. The improvement in properties seems to withstand higher explosive loads with the same amount of steel in gun barrel application.

Keywords: Gun barrel steels, IF grade, physical properties, thermal and mechanical processing, mechanical properties, ultrasonic testing.

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Authors: Pramod Jagtap, Kisan Jadhav, Neha Dand

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Risperidone (RISP) is an antipsychotic agent and has low water solubility and nontargeted delivery results in numerous side effects. Hence, an attempt was made to develop SLNs hydrogel for intranasal delivery of RISP to achieve maximum bioavailability and reduction of side effects. RISP loaded SLNs composed of 1.65% (w/v) lipid mass were produced by high shear homogenization (HSH) coupled ultrasound (US) method using glycerylmonostearate (GMS) or Imwitor 900K (solid lipid). The particles were loaded with 0.2% (w/v) of the RISP & surface-tailored with a 2.02% (w/v) non-ionic surfactant Tween® 80. Optimization was done using 32 factorial design using Design Expert® software. The prepared SLNs dispersion incorporated into Polycarbophil AA1 hydrogel (0.5% w/v). The final gel formulation was evaluated for entrapment efficiency, particle size, rheological properties, X ray diffraction, in vitro diffusion, ex vivo permeation using sheep nasal mucosa and histopathological studies for nasocilliary toxicity. The entrapment efficiency of optimized SLNs was found to be 76 ± 2%, polydispersity index <0.3., particle size 278 ± 5 nm. This optimized batch was incorporated into hydrogel. The pH was found to be 6.4 ± 0.14. The rheological behaviour of hydrogel formulation revealed no thixotropic behaviour. In histopathology study, there was no nasocilliary toxicity observed in nasal mucosa after ex vivo permeation. X-ray diffraction data shows drug was in amorphous form. Ex vivo permeation study shows controlled release profile of drug.

Keywords: Ex vivo, particle size, risperidone, solid lipid nanoparticles.

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Authors: Y. Sangsen, K. Likhitwitayawuid, B. Sritularak, K. Wiwattanawongsa, R. Wiwattanapatapee

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Novel solid lipid nanoparticles (SLNs) were developed to improve oral bioavailability of oxyresveratrol (OXY). The SLNs were prepared by a high speed homogenization technique, at an effective speed and time, using Compritol^® 888 ATO (5% w/w) as the solid lipid. The appropriate weight proportions (0.3% w/w) of OXY affected the physicochemical properties of blank SLNs. The effects of surfactant types on the properties of the formulations such as particle size and entrapment efficacy were also investigated. Conclusively, Tween 80 combined with soy lecithin was the most appropriate surfactant to stabilize OXY-loaded SLNs. The mean particle size of the optimized formulation was 134.40 ± 0.57 nm. In vitro drug release study, the selected S2 formulation showed a retarded release profile for OXY with no initial burst release compared to OXY suspension in the simulated gastrointestinal fluids. Therefore, these SLNs could provide a suitable system to develop for the oral OXY delivery.

Keywords: Solid lipid nanoparticles, Physicochemical properties, in vitro drug release, Oxyresveratrol.

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Authors: J.S.C. Prentice

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The RK1GL2X3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on the RK1GL2 method which, in turn, is a particular case of the general RKrGLm method. The RK1GL2X3 method is a fourth-order method, even though its underlying Runge-Kutta method RK1 is the first-order Euler method, and hence, RK1GL2X3 is considerably more efficient than RK1. This enhancement is achieved through an implementation involving triple-nested two-point Gauss- Legendre quadrature.

Keywords: RK1GL2X3, RK1GL2, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, local error, global error.

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Authors: El Kaak, Rachid, El Bikri, Khalid, Benamar, Rhali

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This paper describes a study of geometrically nonlinear free vibration of thin circular functionally graded (CFGP) plates resting on Winkler elastic foundations. The material properties of the functionally graded composites examined here are assumed to be graded smoothly and continuously through the direction of the plate thickness according to a power law and are estimated using the rule of mixture. The theoretical model is based on the classical Plate theory and the Von-Kármán geometrical nonlinearity assumptions. An homogenization procedure (HP) is developed to reduce the problem considered here to that of isotropic homogeneous circular plates resting on Winkler foundation. Hamilton-s principle is applied and a multimode approach is derived 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 fundamental frequency has also been analysed.

Keywords: Functionally graded materials, nonlinear vibrations, Winkler foundation.

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Authors: Mohammed Salem Alzahrani

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In this paper the optimality of the solution of an existing real word assignment problem known as the seat assignment problem using Seat Assignment Method (SAM) is discussed. SAM is the newly driven method from three existing methods, Hungarian Method, Northwest Corner Method and Least Cost Method in a special way that produces the easiness & fairness among all methods that solve the seat assignment problem.

Keywords: Assignment Problem, Hungarian Method, Least Cost Method, Northwest Corner Method, Seat Assignment Method (SAM), A Real Word Assignment Problem.

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Authors: Seifedine Kadry

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In this article, our objective is the analysis of the resolution of non-linear differential systems by combining Newton and Continuation (N-C) method. The iterative numerical methods converge where the initial condition is chosen close to the exact solution. The question of choosing the initial condition is answered by N-C method.

Keywords: Continuation Method, Newton Method, Finite Difference Method, Numerical Analysis and Non-Linear partial Differential Equation.

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Authors: Ampon Dhamacharoen, Kanittha Chompuvised

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In this work, we solve multipoint boundary value problems where the boundary value conditions are equations using the Newton-Broyden Shooting method (NBSM).The proposed method is tested upon several problems from the literature and the results are compared with the available exact solution. The experiments are given to illustrate the efficiency and implementation of the method.

Keywords: Boundary value problem; Multipoint equation boundary value problems, Shooting Method, Newton-Broyden method.

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Authors: M. F. Patricio, P. M. Rosa

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In this paper a class of numerical methods to solve linear and nonlinear PDEs and also systems of PDEs is developed. The Differential Transform method associated with the Method of Lines (MoL) is used. The theory for linear problems is extended to the nonlinear case, and a recurrence relation is established. This method can achieve an arbitrary high-order accuracy in time. A variable stepsize algorithm and some numerical results are also presented.

Keywords: Method of Lines, Differential Transform Method.

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Authors: Z. Veselý, M. Honner

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High power laser – total emissivity method (HPL-TE method) for determination of coatings relative total emissivity dependent on the temperature is introduced. Method principle, experimental and evaluation parts of the method are described. Computer model of HPL-TE method is employed to perform the sensitivity analysis of the effect of method parameters on the sample surface temperature in the positions where the surface temperature and radiation heat flux are measured.

Keywords: High temperature laser testing, measurement ofthermal properties, emissivity, coatings.

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Authors: Ibrahim Abu-Alshaikh

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In this study, a new root-finding method for solving nonlinear equations is proposed. This method requires two starting values that do not necessarily bracketing a root. However, when the starting values are selected to be close to a root, the proposed method converges to the root quicker than the secant method. Another advantage over all iterative methods is that; the proposed method usually converges to two distinct roots when the given function has more than one root, that is, the odd iterations of this new technique converge to a root and the even iterations converge to another root. Some numerical examples, including a sine-polynomial equation, are solved by using the proposed method and compared with results obtained by the secant method; perfect agreements are found.

Keywords: Iterative method, root-finding method, sine-polynomial equations, nonlinear equations.

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Authors: N. M. Kamoh, M. C. Soomiyol

Abstract:

In this work, a five step continuous method for the solution of third order ordinary differential equations was developed in block form using collocation and interpolation techniques of the shifted Legendre polynomial basis function. The method was found to be zero-stable, consistent and convergent. The application of the method in solving third order initial value problem of ordinary differential equations revealed that the method compared favorably with existing methods.

Keywords: Shifted Legendre polynomials, third order block method, discrete method, convergent.

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