Search results for: finite ring

Authors: Yeonjune Kang

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A triangulation of a planar region is a partition of that region into triangles. In the finite element method, triangulations are often used as the grid underlying a computation. In order to be suitable as a finite element mesh, a triangulation must have well-shaped triangles, according to criteria that depend on the details of the particular problem. For instance, most methods require that all triangles be small and as close to the equilateral shape as possible. Stated differently, one wants to avoid having either thin or flat triangles in the triangulation. There are many triangulation procedures, a particular one being the one known as the longest edge bisection algorithm described below. Starting with a given triangle, locate the midpoint of the longest edge and join it to the opposite vertex of the triangle. Two smaller triangles are formed; apply the same bisection procedure to each of these triangles. Continuing in this manner after n steps one obtains a triangulation of the initial triangle into 2n smaller triangles. The longest edge algorithm was first considered in the late 70’s. It was shown by various authors that this triangulation has the desirable properties for the finite element method: independently of the number of iterations the angles of these triangles cannot get too small; moreover, the size of the triangles decays exponentially. In the present paper we consider a related triangulation algorithm we refer to as the largest angle bisection procedure. As the name suggests, rather than bisecting the longest edge, at each step we bisect the largest angle. We study the properties of the resulting triangulation and prove that, while the general behavior resembles the one in the longest edge bisection algorithm, there are several notable differences as well.

Keywords: angle bisectors, geometry, triangulation, applied mathematics

Procedia PDF Downloads 385

Authors: Sh. Mirhosseini, Y. Haghighatfar, M. Sedighi

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Forced vibration problem of a delaminated beam made of fiber metal laminates is studied in this paper. Firstly, a delamination is considered to divide the beam into four sections. The classic beam theory is assumed to dominate each section. The layers on two sides of the delamination are constrained to have the same deflection. This hypothesis approves the conditions of compatibility as well. Consequently, dynamic response of the beam is obtained by the means of differential transform method (DTM). In order to verify the correctness of the results, a model is constructed using commercial software ABAQUS 6.14. A linear spring with constant stiffness takes the effect of contact between delaminated layers into account. The attained semi-analytical outcomes are in great agreement with finite element analysis.

Keywords: delamination, forced vibration, finite element modelling, natural frequency

Procedia PDF Downloads 287

Authors: Abed Ahmed, Mehrdad Asadi, Jennifer Martay

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Stainless steel pipelines are crucial components to transportation and storage in the oil and gas industry. However, the rise of random attacks and vandalism on these pipes for their valuable transport has led to more security and protection for incoming surface impacts. These surface impacts can lead to large global deformations of the pipe and place the pipe under strain, causing the eventual failure of the pipeline. Therefore, understanding how these surface impact loads affect the pipes is vital to improving the pipes’ security and protection. In this study, experimental test and finite element analysis (FEA) have been carried out on EN3B stainless steel specimens to study the impact behaviour. Low velocity impact tests at 9 m/s with 16 kg dome impactor was used to simulate for high momentum impact for localised failure. FEA models of clamped and deformable boundaries were modelled to study the effect of the boundaries on the pipes impact behaviour on its impact resistance, using experimental and FEA approach. Comparison of experimental and FE simulation shows good correlation to the deformable boundaries in order to validate the robustness of the FE model to be implemented in pipe models with complex anisotropic structure.

Keywords: dynamic impact, deformable boundary conditions, finite element modelling, LS-DYNA, stainless steel pipe

Procedia PDF Downloads 139

Authors: Jeron Maheswaran, Sudath C. Siriwardane

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In fatigue analysis, the structural detail of tubular joint has taken great attention among engineers. The DNV-RP-C203 is covering this topic quite well for simple and clear joint cases. For complex joint and geometry, where joint classification isn’t available and limitation on validity range of non-dimensional geometric parameters, the challenges become a fact among engineers. The classification of joint is important to carry out through the fatigue analysis. These joint configurations are identified by the connectivity and the load distribution of tubular joints. To overcome these problems to some extent, this paper compare the fatigue life of tubular joints in offshore jacket according to the stress concentration factors (SCF) in DNV-RP-C203 and finite element method employed Abaqus/CAE. The paper presents the geometric details, material properties and considered load history of the jacket structure. Describe the global structural analysis and identification of critical tubular joints for fatigue life estimation. Hence fatigue life is determined based on the guidelines provided by design codes. Fatigue analysis of tubular joints is conducted using finite element employed Abaqus/CAE [4] as next major step. Finally, obtained SCFs and fatigue lives are compared and their significances are discussed.

Keywords: fatigue life, stress-concentration factor, finite element analysis, offshore jacket structure

Procedia PDF Downloads 435

Authors: Gozel Judakova, Markus Bause

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We present and analyze reliable numerical techniques for simulating complex flow and transport phenomena related to natural gas transportation in pipelines. Such kind of problems are of high interest in the field of petroleum and environmental engineering. Modeling and understanding natural gas flow and transformation processes during transportation is important for the sake of physical realism and the design and operation of pipeline systems. In our approach a two fluid flow model based on a system of coupled hyperbolic conservation laws is considered for describing natural gas flow undergoing hydratization. The accurate numerical approximation of two-phase gas flow remains subject of strong interest in the scientific community. Such hyperbolic problems are characterized by solutions with steep gradients or discontinuities, and their approximation by standard finite element techniques typically gives rise to spurious oscillations and numerical artefacts. Recently, stabilized and discontinuous Galerkin finite element techniques have attracted researchers’ interest. They are highly adapted to the hyperbolic nature of our two-phase flow model. In the presentation a streamline upwind Petrov-Galerkin approach and a discontinuous Galerkin finite element method for the numerical approximation of our flow model of two coupled systems of Euler equations are presented. Then the efficiency and reliability of stabilized continuous and discontinous finite element methods for the approximation is carefully analyzed and the potential of the either classes of numerical schemes is investigated. In particular, standard benchmark problems of two-phase flow like the shock tube problem are used for the comparative numerical study.

Keywords: discontinuous Galerkin method, Euler system, inviscid two-fluid model, streamline upwind Petrov-Galerkin method, twophase flow

Procedia PDF Downloads 316

Authors: Tamas Mankovits

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Lightweight cellular-type structures like metal foams have excellent mechanical properties, therefore the interest in these materials is widely spreading as load-bearing structural elements, e.g. as implants. Numerous technologies are available to produce metal foams. In this paper the material response of closed cell foam structures produced by direct foaming and additive technology is compared. The production technology circumstances are also investigated. Geometrical variations are developed for foam structures produced by additive manufacturing and simulated by finite element method to be able to predict the mechanical behavior.

Keywords: additive manufacturing, direct foaming, finite element method, metal foam

Procedia PDF Downloads 187

Authors: D. B. Gohil

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Closed die forging is a very complex process, and measurement of actual forces for real material is difficult and time consuming. Hence, the modelling technique has taken the advantage of carrying out the experimentation with the proper model material which needs lesser forces and relatively low temperature. The results of experiments on the model material then may be correlated with the actual material by using the theory of similarity. There are several methods available to resolve the complexity involved in the closed die forging process. Finite Element Method (FEM) and Finite Difference Method (FDM) are relatively difficult as compared to the slab method. The slab method is very popular and very widely used by the people working on shop floor because it is relatively easy to apply and reasonably accurate for most of the common forging load requirement computations.

Keywords: experimentation, forging, process modeling, strain distribution

Procedia PDF Downloads 190

Authors: Dong Wook Lee, Adrian Mistreanu

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The authors have studied a method for analyzing containment and penetration using an explicit nonlinear Finite Element Analysis. This method may be used in the stage of concept design for the protection of external configurations or components of aircraft engines and nuclear power plant structures. This paper consists of the modeling method, the results obtained from the method and the comparison of the results with those calculated from simple analytical method. It shows that the containment capability obtained by proposed method matches well with analytically calculated containment capability.

Keywords: computer aided engineering, containment analysis, finite element analysis, impact analysis, penetration analysis

Procedia PDF Downloads 124

Authors: S. Houcine Habib, B. Elkhalil Hachi, Mohamed Guesmi, Mohamed Haboussi

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In this paper, dynamic fracture behaviors of cracked orthotropic structure are modeled using extended finite element method (X-FEM). In this approach, the finite element method model is first created and then enriched by special orthotropic crack tip enrichments and Heaviside functions in the framework of partition of unity. The mixed mode stress intensity factor (SIF) is computed using the interaction integral technique based on J-integral in order to predict cracking behavior of the structure. The developments of these procedures are programmed and introduced in a self-software platform code. To assess the accuracy of the developed code, results obtained by the proposed method are compared with those of literature.

Keywords: X-FEM, composites, stress intensity factor, crack, dynamic orthotropic behavior

Procedia PDF Downloads 559

Authors: Merve Ermis, Murat Yılmaz, Nihal Eratlı, Mehmet H. Omurtag

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The static and dynamic analyses of hyperboloidal helix having the closed and the open square box sections are investigated via the mixed finite element formulation based on Timoshenko beam theory. Frenet triad is considered as local coordinate systems for helix geometry. Helix domain is discretized with a two-noded curved element and linear shape functions are used. Each node of the curved element has 12 degrees of freedom, namely, three translations, three rotations, two shear forces, one axial force, two bending moments and one torque. Finite element matrices are derived by using exact nodal values of curvatures and arc length and it is interpolated linearly throughout the element axial length. The torsional moments of inertia for close and open square box sections are obtained by finite element solution of St. Venant torsion formulation. With the proposed method, the torsional rigidity of simply and multiply connected cross-sections can be also calculated in same manner. The influence of the close and the open square box cross-sections on the static and dynamic analyses of hyperboloidal helix is investigated. The benchmark problems are represented for the literature.

Keywords: hyperboloidal helix, squared cross section, thin walled cross section, torsional rigidity

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Authors: Amal Ait El Djoudi

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A thermodynamical model of coexisting hadronic and quark–gluon plasma (QGP) phases is used to study the thermally driven deconfining phase transition occurring between the two phases. A color singlet partition function is calculated for the QGP phase with two massless quarks, as in our previous work, but now the finite extensions of the hadrons are taken into account in the equation of state of the hadronic phase. In the present work, the finite-size effects on the system are examined by probing the behavior of some thermodynamic quantities, called response functions, as order parameter, energy density and their derivatives, on a range of temperature around the transition at different volumes. It turns out that the finiteness of the system size has as effects the rounding of the transition and the smearing of all the singularities occurring in the thermodynamic limit, and the additional finite-size effect introduced by the requirement of exact color-singletness involves a shift of the transition point. This shift as well as the smearing of the transition region and the maxima of both susceptibility and specific heat show a scaling behavior with the volume characterized by scaling exponents. Another striking result is the large similarity noted between the behavior of these response functions and that of the cumulants of the probability density. This similarity is worked to try to extract information concerning the occurring phase transition.

Keywords: equation of state, thermodynamics, deconfining phase transition, quark–gluon plasma (QGP)

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Authors: M. R. Daneshgar, S. E. Habibi, E. Daneshgar, A. Daneshgar

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In this paper, a two-dimensional method is developed to simulate the fillet welds in a stiffened cylindrical shell, using finite element method. The stiffener material is aluminum 2519. The thermo-elasto-plastic analysis is used to analyze the thermo-mechanical behavior. Due to the high heat flux rate of the welding process, two uncouple thermal and mechanical analysis are carried out instead of performing a single couple thermo-mechanical simulation. In order to investigate the effects of the welding procedures, two different welding techniques are examined. The resulted residual stresses and distortions due to different welding procedures are obtained. Furthermore, this study employed the technique of element birth and death to simulate the weld filler variation with time in fillet welds. The obtained results are in good agreement with the published experimental and three-dimensional numerical simulation results. Therefore, the proposed 2D modeling technique can effectively give the corresponding results of 3D models. Furthermore, by inspection of the obtained residual hoop and transverse stresses and angular distortions, proper welding procedure is suggested.

Keywords: stiffened cylindrical shell, fillet welds, residual stress, angular distortion, finite element method

Procedia PDF Downloads 342

Authors: K. Djellabi, M. E. H. Latreche

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Induction heating computer simulation is a powerful tool for process design and optimization, induction coil design, equipment selection, as well as education and business presentations. The authors share their vast experience in the practical use of computer simulation for different induction heating and heat treating processes. In this paper deals with mathematical modeling and numerical simulation of induction heating furnaces with axisymmetric geometries. For the numerical solution, we propose finite element methods combined with boundary (FEM) for the electromagnetic model using COMSOL® Multiphysics Software. Some numerical results for an industrial furnace are shown with high frequency.

Keywords: numerical methods, induction furnaces, induction heating, finite element method, Comsol multiphysics software

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Authors: Pedram Khazaie, Sajjad Moein

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In the conventional hot forging of Tongue, which is a fitting for polymer insulator, the material wasted to flash accounts for 20-30% of workpiece. In order to reduce the cost of forged products, this waste material must be minimized. In this study, a flashless forging die is designed and simulated using the finite element method (FEM). A solution to avoid overloading the die with a simple preform is also presented. Moreover, since in flashless forging, burr is formed on the edge of workpiece, a controlled flash forging method is proposed to solve this problem. The simulation results have been validated by experiments; achieving close agreement between simulated and experimental data. It was shown that numerical modeling is helpful in reducing cost and time in the manufacturing process.

Keywords: burr formation, die design, finite element method, flashless forging

Procedia PDF Downloads 148

Authors: M. T. Alodat

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In this paper, we propose a mechanism for skewing any symmetric distribution. The new distribution is called the deflation-inflation distribution (DID). We discuss some statistical properties of the DID such moments, stochastic representation, log-concavity. Also we fit the distribution to real data and we compare it to normal distribution and Azzlaini's skew normal distribution. Numerical results show that the DID fits the the tree ring data better than the other two distributions.

Keywords: normal distribution, moments, Fisher information, symmetric distributions

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Authors: Shun-Qi Zhang, Shu-Yang Zhang, Min Chen, , Jing Bai

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Piezoelectric laminated smart structures can be subjected to the strong driving electric field, which may result in large displacements and rotations. In one hand, piezoelectric materials usually behave very significant material nonlinear effects under strong electric fields. On the other hand, thin-walled structures undergoing large displacements and rotations exist nonnegligible geometric nonlinearity. In order to give a precise prediction of piezo laminated smart structures under the large electric field, this paper develops a finite element (FE) model accounting for material nonlinearity (piezoelectric part) and geometric nonlinearity based on the first order shear deformation (FSOD) hypothesis. The proposed FE model is first validated by both experimental and numerical examples from the literature. Afterwards, it is applied to simulate for plate and shell structures with multiple piezoelectric patches under the strong applied electric field. From the simulation results, it shows that large discrepancies occur between linear and nonlinear predictions for piezoelectric laminated structures driving at the strong electric field. Therefore, both material and geometric nonlinearities should be taken into account for piezoelectric structures under strong electric.

Keywords: piezoelectric smart structures, finite element analysis, geometric nonlinearity, electroelastic material nonlinearities

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Authors: Azad Mohammed Ali Saber, Lanja Saeed Omer

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The present study deals with numerical method (FE) and experimental investigations on the vibration behavior of carbon fiber-polyester laminated plates. Finite element simulation is done using APDL (Ansys Parametric Design Language) macro codes software version 19. Solid185 layered structural element, including eight nodes, is adopted in this analysis. The experimental work is carried out using (Hand Layup method) to fabricate different layers and orientation angles of composite laminate plates. Symmetric samples include four layers (00/900)s and six layers (00/900/00)s, (00/00/900)s. Antisymmetric samples include one layer (00), (450), two layers (00/900), (-450/450), three layers (00/900/00), four layers (00/900)2, (-450/450)2, five layers (00/900)2.5, and six layers (00/900)3, (-450/450)3. An experimental investigation is carried out using a modal analysis technique with a Fast Fourier Transform Analyzer (FFT), Pulse platform, impact hammer, and accelerometer to obtain the frequency response functions. The influences of different parameters such as the number of layers, aspect ratio, modulus ratio, ply orientation, and different boundary conditions on the dynamic behavior of the CFRPs are studied, where the 1st, 2nd, and 3rd natural frequencies are observed to be the minimum for cantilever boundary condition (CFFF) and the maximum for full clamped boundary condition (CCCC). Experimental results show that the natural frequencies of laminated plates are significantly reliant on the type of boundary conditions due to the restraint effect at the edges. Good agreement is achieved among the finite element and experimental results. All results indicate that any increase in aspect ratio causes a decrease in the natural frequency of the CFRPs plate, while any increase in the modulus ratio or number of layers causes an increase in the fundamental natural frequency of vibration.

Keywords: vibration, composite materials, finite element, APDL ANSYS

Procedia PDF Downloads 28

Authors: S. J. Shahidzadeh Tabatabaei, A. M. Fattahi

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Modal analysis of an FGM plate containing the ceramic phase of Al2O3 and metal phase of stainless steel 304 was performed using ABAQUS, with the assumptions that the material has an elastic mechanical behavior and its Young modulus and density are varying in thickness direction. For this purpose, a subroutine was written in FORTRAN and linked with ABAQUS. First, a simulation was performed in accordance to other researcher’s model, and then after comparing the obtained results, the accuracy of the present study was verified. The obtained results for natural frequency and mode shapes indicate good performance of user-written subroutine as well as FEM model used in present study. After verification of obtained results, the effect of clamping condition and the material type (i.e. the parameter n) was investigated. In this respect, finite element analysis was carried out in fully clamped condition for different values of n. The results indicate that the natural frequency decreases with increase of n, since with increase of n, the amount of ceramic phase in FGM plate decreases, while the amount of metal phase increases, leading to decrease of the plate stiffness and hence, natural frequency, as the Young modulus of Al2O3 is equal to 380 GPa and the Young modulus of stainless steel 304 is equal to 207 GPa.

Keywords: FGM plates, modal analysis, natural frequency, finite element method

Procedia PDF Downloads 334

Authors: Jorge A. Cruz-Morales, Joel Vargas, Arlette A. Santiago, Mikhail A. Tlenkopatchev

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In industrial processes such as oil extraction and refining, products are handled or generated in the gas phase, which represents a challenge in terms of treatment and purification. During the past three decades, new scientific findings and technological advances in separation based on the use of membranes have led to simpler and more efficient gas separation processes, optimizing the use of energy and generating less pollution. This work reports the synthesis and ring-opening metathesis polymerization (ROMP) of new structural isomers based on norbornene dicarboximides bearing trifluoromethyl moieties, specifically N-2-trifluoromethylphenyl-exo,endo-norbornene-5,6-dicarboximide (2a) and N-3-trifluoromethylphenyl-exo,endo-norbornene-5,6-dicarboximide (2b), using tricyclohexylphosphine [1,3-bis(2,4,6-trimethylphenyl)-4,5-dihydroimidazol-2-ylidene][benzylidene] ruthenium dichloride (I), bis(tricyclohexylphosphine) benzylidene ruthenium (IV) dichloride (II), and bis(tricyclohexylphosphine) p-fluorophenylvinylidene ruthenium (II) dichloride (III). It was observed that the -CF3 moiety attached at the ortho position of the aromatic ring increases thermal and mechanical properties of the polymer, whereas meta substitution has the opposite effect. A comparative study of gas transportation in membranes, based on these fluorinated polynorbornenes, showed that -CF3 ortho substitution increases permeability of the polymer membrane as a consequence of the increase in both gas solubility and gas diffusion. In contrast, gas permeability coefficients of the meta-substituted polymer membrane are rather similar to those of that which is non-fluorinated; this can be attributed to a lower fractional free volume. The meta-substituted polymer membrane, besides showing the largest permselectivity coefficients of all the isomers studied here, was also found to have one of the largest permselectivity coefficients for separating H2/C3H6 into glassy polynorbornene dicarboximides.

Keywords: gas transport membranes, polynorbornene dicarboximide, ROMP, structural isomers

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Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping

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In this paper, we present a high order group explicit method in solving the two dimensional Helmholtz equation. The presented method is derived from a nine-point fourth order finite difference approximation formula obtained from a 45-degree rotation of the standard grid which makes it possible for the construction of iterative procedure with reduced complexity. The developed method will be compared with the existing group iterative schemes available in literature in terms of computational time, iteration counts, and computational complexity. The comparative performances of the methods will be discussed and reported.

Keywords: explicit group method, finite difference, helmholtz equation, rotated grid, standard grid

Procedia PDF Downloads 444

Authors: M. A. Wijewardane, S. A. N. C. Sudasinghe, H. K. G. Punchihewa, W. K. D. L. Wickramasinghe, S. A. Philip, M. R. S. U. Kumara

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Visual comfort is one of the major parameters that can be taken to measure the human comfort in any environment. If the provided illuminance level in a working environment does not meet the workers visual comfort, it will lead to eye-strain, fatigue, headache, stress, accidents and finally, poor productivity. However, improvements in lighting do not necessarily mean that the workplace requires more light. Unnecessarily higher illuminance levels will also cause poor visual comfort and health risks. In addition, more power consumption on lighting will also result in higher energy costs. So, during this study, visual comfort and the illuminance requirement for the workers in textile/apparel industry were studied to perform different tasks (i.e. cutting, sewing and knitting) at their workplace. Experimental studies were designed to identify the optimum illuminance requirement depending upon the varied fabric colour and type and finally, energy saving potentials due to controlled illuminance level depending on the workforce requirement were analysed. Visual performance of workers during the sewing operation was studied using the ‘landolt ring experiment’. It was revealed that around 36.3% of the workers would like to work if the illuminance level varies from 601 lux to 850 lux illuminance level and 45.9% of the workers are not happy to work if the illuminance level reduces less than 600 lux and greater than 850 lux. Moreover, more than 65% of the workers who do not satisfy with the existing illuminance levels of the production floors suggested that they have headache, eye diseases, or both diseases due to poor visual comfort. In addition, findings of the energy analysis revealed that the energy-saving potential of 5%, 10%, 24%, 8% and 16% can be anticipated for fabric colours, red, blue, yellow, black and white respectively, when the 800 lux is the prevailing illuminance level for sewing operation.

Keywords: Landolt Ring experiment, lighting energy consumption, illuminance, textile and apparel industry, visual comfort

Procedia PDF Downloads 196

Authors: Lounes Aouane, Omar Bouledroua

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Sonatrach uses 24,000 kilometers of pipelines to transport gas and oil. Over time, these pipes run the risk of bursting due to corrosion inside and/or outside the pipeline. For this reason, a check must be made with the help of an equipped scraper. This intelligent tool provides a detailed picture of all errors in the pipeline. Based on the ERF values, these wear defects are divided into two parts: acceptable defect and unacceptable defect. The objective of this work is to conduct a comparative study of the different methods of calculating the marginal pressure found in the literature (DNV RP F-101, SHELL, P-CORRC, NETTO and CSA Z662). This comparison will be made from a database of 329 burst tests published in the literature. Finally, we will propose a new approach based on the finite element method using the commercial software ANSYS.

Keywords: hydrogen embrittlement, pipelines, hydrogen, transient flow, cyclic pressure, fatigue crack growth

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Authors: F. Al-Mufadi, F. Djavanroodi

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During the last decade ultrafine grained (UFG) and nano-structured (NS) materials have experienced a rapid development. In this research work finite element analysis has been carried out to investigate the plastic strain distribution in equal channel angular process (ECAP). The magnitudes of standard deviation (S. D.) and inhomogeneity index (Ci) were compared for different ECAP passes. Verification of a three-dimensional finite element model was performed with experimental tests. Finally the mechanical property including impact energy of ultrafine grained pure commercially pure Aluminum produced by severe plastic deformation method has been examined. For this aim, equal channel angular pressing die with the channel angle, outer corner angle and channel diameter of 90°, 20° and 20 mm had been designed and manufactured. Commercial pure Aluminum billets were ECAPed up to four passes by route BC at the ambient temperature. The results indicated that there is a great improvement at the hardness measurement, yield strength and ultimate tensile strength after ECAP process. It is found that the magnitudes of HV reach 67 HV from 21 HV after the final stage of process. Also, about 330% and 285% enhancement at the YS and UTS values have been obtained after the fourth pass as compared to the as-received conditions, respectively. On the other hand, the elongation to failure and impact energy have been reduced by 23% and 50% after imposing four passes of ECAP process, respectively.

Keywords: SPD, ECAP, FEM, pure Al, mechanical properties

Procedia PDF Downloads 171

Authors: Richard Lewis

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The following assumptions of the Big Bang theory are challenged and found to be false: the cosmological principle, the assumption that all matter formed at the same time and the assumption regarding the cause of the cosmic microwave background radiation. The evolution of the universe is described based on the conclusion that the universe is finite with a space boundary. This conclusion is reached by ruling out the possibility of an infinite universe or a universe which is finite with no boundary. In a finite universe, the centre of the universe can be located with reference to our home galaxy (The Milky Way) using the speed relative to the Cosmic Microwave Background (CMB) rest frame and Hubble's law. This places our home galaxy at a distance of approximately 26 million light years from the centre of the universe. Because we are making observations from a point relatively close to the centre of the universe, the universe appears to be isotropic and homogeneous but this is not the case. The CMB is coming from a source located within the event horizon of the universe. There is sufficient mass in the universe to create an event horizon at the Schwarzschild radius. Galaxies form over time due to the energy released by the expansion of space. Conservation of energy must consider total energy which is mass (+ve) plus energy (+ve) plus spacetime curvature (-ve) so that the total energy of the universe is always zero. The predominant position of galaxy formation moves over time from the centre of the universe towards the boundary so that today the majority of new galaxy formation is taking place beyond our horizon of observation at 14 billion light years.

Keywords: cosmology, dark energy, dark matter, evolution of the universe

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Authors: Himanshu Singh, Rishi Kant, Shantanu Bhattacharya

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This paper adopts a top-down approach for mathematical modeling to predict the size reduction from micro to nano-scale through persistent etching. The process is simulated using a finite difference approach. Previously, various researchers have simulated the etching process for 1-D and 2-D substrates. It consists of two processes: 1) Convection-Diffusion in the etchant domain; 2) Chemical reaction at the surface of the particle. Since the process requires analysis along moving boundary, partial differential equations involved cannot be solved using conventional methods. In 1-D, this problem is very similar to Stefan's problem of moving ice-water boundary. A fixed grid method using finite volume method is very popular for modelling of etching on a one and two dimensional substrate. Other popular approaches include moving grid method and level set method. In this method, finite difference method was used to discretize the spherical diffusion equation. Due to symmetrical distribution of etchant, the angular terms in the equation can be neglected. Concentration is assumed to be constant at the outer boundary. At the particle boundary, the concentration of the etchant is assumed to be zero since the rate of reaction is much faster than rate of diffusion. The rate of reaction is proportional to the velocity of the moving boundary of the particle. Modelling of the above reaction was carried out using Matlab. The initial particle size was taken to be 50 microns. The density, molecular weight and diffusion coefficient of the substrate were taken as 2.1 gm/cm3, 60 and 10-5 cm2/s respectively. The etch-rate was found to decline initially and it gradually became constant at 0.02µ/s (1.2µ/min). The concentration profile was plotted along with space at different time intervals. Initially, a sudden drop is observed at the particle boundary due to high-etch rate. This change becomes more gradual with time due to declination of etch rate.

Keywords: particle size reduction, micromixer, FDM modelling, wet etching

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Authors: Jin-Uk Park

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Recently, the semiconductor industry is rapidly demanding complicated structures and mass production. From the point of view of mass production, the ETCH industry is concentrating on maintaining the ER (Etch rate) of the wafer edge constant regardless of changes over time. In this study, two major thermal factors affecting process were identified and controlled. First, the filler of the thermal pad was studied. Second, the significant difference of handling the thermal pad during PM was studied.

Keywords: etcher, thermal pad, wet cleaning, thermal conductivity

Procedia PDF Downloads 181

Authors: N. K. Mohd Affendi, T. A. R. Tuan Abdullah, S. A. Syed Mustaffa

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In power industry transformer is an important component and most of us familiar by the functioning principle of a transformer electrically. There are many losses occur during the operation of a transformer that causes heat generation. This heat, if not dissipated properly will reduce the lifetime and effectiveness of the transformer. Transformer cooling helps in maintaining the temperature rise of various paths. This paper proposed to minimize the ambient temperature of the transformer room in order to lower down the temperature of the transformer. A simulation has been made using finite element methods programs called FEMM (Finite Elements Method Magnetics) to create a virtual model based on actual measurement of a transformer. The generalization of the two-dimensional (2D) FEMM results proves that by minimizing the ambient temperature, the heat of the transformer is decreased. The modeling process and of the transformer heat flow has been presented.

Keywords: heat generation, temperature rise, ambient temperature, FEMM

Procedia PDF Downloads 379

Authors: Rishabh Shukla, Achin Agrawal, Anupam Saxena, S. Mandal

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The existence of a crack, affects the mechanical behaviour and various properties of a structure to a great degree. This paper focuses on recognizing the parameters that gets changed due to the formation of cracks and have a great impact on the performance of the structure. Spalling is a major concern as it leaves the reinforcement bars more susceptible to environmental attacks. Beams of cross section 300 mm × 500 mm are designed and for a calculated area of steel, two different arrangements of reinforced bars are analysed. Results are prepared for different stages of cracking for each arrangement of rebars. The parameters for both arrangements are then compared. The Finite Element Analysis (FEA) is carried out and changes in the properties like flexural strength, Elasticity and modal frequency are reported. The conclusions have been drawn by comparing the results.

Keywords: cracks, elasticity, spalling, FEA

Procedia PDF Downloads 263

Authors: Xu Runzhang, Yang Yanbing, Niu Yi, Zhang Mingyou, Liu Yu

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For a class of semilinear parabolic equations with linear dynamical boundary conditions in a bounded domain, we obtain both global solutions and finite time blow-up solutions when the initial data varies in the phase space H1(Ω). Our main tools are the comparison principle, the potential well method and the concavity method. In particular, we discuss the behavior of the solutions with the initial data at critical and high energy level.

Keywords: high energy level, critical energy level, linear dynamical boundary condition, semilinear parabolic equation

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Authors: N. Guo, C. Xu, Z. C. Yang

Abstract:

In order to ensure the high reliability of an aircraft, the accurate structural dynamics analysis has become an indispensable part in the design of an aircraft structure. Therefore, the structural finite element model which can be used to accurately calculate the structural dynamics and their transfer relations is the prerequisite in structural dynamic design. A dynamic finite element model updating method is presented to correct the uncertain parameters of the finite element model of a structure using measured modal parameters. The coordinate modal assurance criterion is used to evaluate the correlation level at each coordinate over the experimental and the analytical mode shapes. Then, the weighted summation of the natural frequency residual and the coordinate modal assurance criterion residual is used as the objective function. Moreover, the hybrid pattern search (HPS) optimization technique, which synthesizes the advantages of pattern search (PS) optimization technique and genetic algorithm (GA), is introduced to solve the dynamic FE model updating problem. A numerical simulation and a model updating experiment for GARTEUR aircraft model are performed to validate the feasibility and effectiveness of the present dynamic model updating method, respectively. The updated results show that the proposed method can be successfully used to modify the incorrect parameters with good robustness.

Keywords: model updating, modal parameter, coordinate modal assurance criterion, hybrid genetic/pattern search

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