Search results for: finite clauses

Authors: Subhamita Chakraborty, Shubhabrata Datta, Sujay Kumar Mukherjea, Partha Protim Chattopadhyay

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Manufacturing of multiphase high strength steel in hot strip mill have drawn significant attention due to the possibility of forming low temperature transformation product of austenite under continuous cooling condition. In such endeavor, reliable prediction of temperature profile of hot strip coil is essential in order to accesses the evolution of microstructure at different location of hot strip coil, on the basis of corresponding Continuous Cooling Transformation (CCT) diagram. Temperature distribution profile of the hot strip coil has been determined by using finite volume method (FVM) vis-à-vis finite difference method (FDM). It has been demonstrated that FVM offer greater computational reliability in estimation of contact pressure distribution and hence the temperature distribution for curved and irregular profiles, owing to the flexibility in selection of grid geometry and discrete point position, Moreover, use of finite volume concept allows enforcing the conservation of mass, momentum and energy, leading to enhanced accuracy of prediction.

Keywords: simulation, modeling, thermal analysis, coil cooling, contact pressure, finite volume method

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Authors: N. Fusun Oyman Serteller

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In this paper, the techniques to solve time dependent electromagnetic wave propagation equations based on the Finite Difference Method (FDM) are proposed by comparing the results with Finite Element Method (FEM) in 2D while discussing some special simulation examples.  Here, 2D dynamical wave equations for lossy media, even with a constant source, are discussed for establishing symbolic manipulation of wave propagation problems. The main objective of this contribution is to introduce a comparative study of two suitable numerical methods and to show that both methods can be applied effectively and efficiently to all types of wave propagation problems, both linear and nonlinear cases, by using symbolic computation. However, the results show that the FDM is more appropriate for solving the nonlinear cases in the symbolic solution. Furthermore, some specific complex domain examples of the comparison of electromagnetic waves equations are considered. Calculations are performed through Mathematica software by making some useful contribution to the programme and leveraging symbolic evaluations of FEM and FDM.

Keywords: finite difference method, finite element method, linear-nonlinear PDEs, symbolic computation, wave propagation equations

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Authors: Ayan Chakraborty, BV. Rathish Kumar

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Off-late many models in viscoelasticity, signal processing or anomalous diffusion equations are formulated in fractional calculus. Tempered fractional calculus is the generalization of fractional calculus and in the last few years several important partial differential equations occurring in the different field of science have been reconsidered in this term like diffusion wave equations, Schr$\ddot{o}$dinger equation and so on. In the present paper, a time-dependent tempered fractional diffusion equation of order $\gamma \in (0,1)$ with forcing function is considered. Existence, uniqueness, stability, and regularity of the solution has been proved. Crank-Nicolson discretization is used in the time direction. B spline finite element approximation is implemented. Generally, B-splines basis are useful for representing the geometry of a finite element model, interfacing a finite element analysis program. By utilizing this technique a priori space-time estimate in finite element analysis has been derived and we proved that the convergent order is $\mathcal{O}(h²+T²)$ where $h$ is the space step size and $T$ is the time. A couple of numerical examples have been presented to confirm the accuracy of theoretical results. Finally, we conclude that the studied method is useful for solving tempered fractional diffusion equations.

Keywords: B-spline finite element, error estimates, Gronwall's lemma, stability, tempered fractional

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Authors: Amira M. Othman

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Despite the massive array of literature that engages with the Egyptian legislative system on a theoretical level, very little attention has been dedicated to the comparison between the legislative clauses on the one hand, and the (absence of their) real-world implementation on the other. This paper starts with this discrepancy, focusing on the legal proceedings in some recent cases dubbed ‘political,’ in which defendants received death sentences. Then, it sheds light on the trend of practical disregard of the law on behalf of the criminal justice apparatuses (whether security forces, public prosecution offices, lawyers, judges, prison wardens, and executioners) through the examination of case files and the conduction of interviews with some defense lawyers in the cases in question. It also identifies the resultant state of confusion among prison staff, as manifest in their treatment of defendants even before the death sentences against them is pronounced; in other words, the application of some aspects of the law in certain cases, and their simultaneous disregard of others. Then, the paper explores the effects of such execution of the law on the death row inmates, as it identifies the different strategies through which defendants who are sentenced to death appropriate a number of legal clauses to their benefit, thereby embarrassing - or highly irritating - the judges that pronounce their death sentences. In addition to appropriation, other strategies include the contestation of the law and their presence before the courts in general, as well as the complete disregard and dismissal of the legal system altogether. Finally, the paper investigates the consequent conceptual effect on the first degree families of death row inmates, namely how their daily encounters with the Egyptian legislative system - particularly its emphasis on the absence of the otherwise binding local legislation - continue to shape their conceptions of the ‘law,’ of ‘justice,’ and their trust in the ‘state.’

Keywords: death penalty, Egyptian law absence, justice, political cases

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Authors: Emmanuel Chinagorom Nwadike, Joseph Tagbo Nwabanne, Matthew Ndubuisi Abonyi, Onyemazu Andrew Azaka

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This research focused on the modeling of the convective drying of aerial yam using finite element methods. The thermo-gravimetric analyzer was used to determine the thermal stability of the sample. An aerial yam sample of size 30 x 20 x 4 mm was cut with a mold designed for the purpose and dried in a convective dryer set at 4m/s fan speed and temperatures of 68.58 and 60.56°C. The volume shrinkage of the resultant dried sample was determined by immersing the sample in a toluene solution. The finite element analysis was done with PDE tools in Matlab 2015. Seven kinetic models were employed to model the drying process. The result obtained revealed three regions in the thermogravimetric analysis (TGA) profile of aerial yam. The maximum thermal degradation rates of the sample occurred at 432.7°C. The effective thermal diffusivity of the sample increased as the temperature increased from 60.56°C to 68.58°C. The finite element prediction of moisture content of aerial yam at an air temperature of 68.58°C and 60.56°C shows R² of 0.9663 and 0.9155, respectively. There was a good agreement between the finite element predicted moisture content and the measured moisture content, which is indicative of a highly reliable finite element model developed. The result also shows that the best kinetic model for the aerial yam under the given drying conditions was the Logarithmic model with a correlation coefficient of 0.9991.

Keywords: aerial yam, finite element, convective, effective, diffusivity

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Authors: Rilwan Kayode Apalowo, Dimitrios Chronopoulos

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An approach for identifying the geometric and material characteristics of layered composite structures through an inverse wave and finite element methodology is proposed. These characteristics are obtained through multi-frequency single shot measurements. However, it is established that the frequency regime of the measurements does not matter, meaning that both ultrasonic and structural dynamics frequency spectra can be employed. Taking advantage of a full FE (finite elements) description of the periodic composite, the scheme is able to account for arbitrarily complex structures. In order to demonstrate the robustness of the presented scheme, it is applied to a sandwich composite panel and results are compared with that of experimental characterization techniques. Excellent agreement is obtained with the experimental measurements.

Keywords: structural identification, non-destructive evaluation, finite elements, wave propagation, layered structures, ultrasound

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Authors: João Paulo Pascon

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A constitutive model accounting for large strains, thermoviscoplasticity, and ductile damage evolution is proposed in the present work. To this end, a fully Lagrangian framework is employed, considering plane stress conditions and multiplicative split of the deformation gradient. The full model includes Gurson’s void growth, nucleation and coalescence, plastic work heating, strain and strain-rate hardening, thermal softening, and heat conductivity. The contribution of the work is the combination of all the above-mentioned features within the finite-strain setting. The model is implemented in a computer code using triangular finite elements and nonlinear analysis. Two mechanical examples involving ductile damage and finite strain levels are analyzed: an inhomogeneous tension specimen and the necking problem. Results demonstrate the capabilities of the developed formulation regarding ductile fracture and large deformations.

Keywords: ductile damage model, finite element method, large strains, thermoviscoplasticity

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Authors: Ashkan Golgoon, Souhayl Sadik, Arash Yavari

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Eigenstrains in nonlinear solids are created due to anelastic effects such as non-uniform temperature distributions, growth, remodeling, and defects. Eigenstrains understanding is indispensable, as they can generate residual stresses and strongly affect the overall response of solids. Here, we study the residual stress and deformation fields of an incompressible isotropic infinite wedge with a circumferentially-symmetric distribution of finite eigenstrains. We construct a material manifold, whose Riemannian metric explicitly depends on the eigenstrain distribution, thereby we turn the problem into a classical nonlinear elasticity problem, where we find an embedding of the Riemannian material manifold into the ambient Euclidean space. In particular, we find exact solutions for the residual stress and deformation fields of a neo-Hookean wedge having a symmetric inclusion with finite radial and circumferential eigenstrains. Moreover, we numerically solve a similar problem when a symmetric Mooney-Rivlin inhomogeneity with finite eigenstrains is placed in a neo-Hookean wedge. Generalization of the eigenstrain problem to other geometries are also discussed.

Keywords: finite eigenstrains, geometric mechanics, inclusion, inhomogeneity, nonlinear elasticity

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Authors: A. Bhandari, S. Mukherjee

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Two frames in a Hilbert space are called woven or weaving if all possible merge combinations between them generate frames of the Hilbert space with uniform frame bounds. Weaving frames are powerful tools in wireless sensor networks which require distributed data processing. Considering the practical applications, this article deals with finite woven frames. We provide methods of constructing finite woven frames, in particular, bounded linear operators are used to construct woven frames from a given frame. Several examples are discussed. We also introduce the notion of woven frame sequences and characterize them through the concepts of gaps and angles between spaces.

Keywords: frames, woven frames, gap, angle

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Authors: Carlos Caro, Ernest Bladé, Pedro Acosta, Camilo Lesmes

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The drying-wet process is one of the topics to be more careful in distributed hydrological modeling using finite volume schemes as a means of solving the equations of Saint Venant. In a hydrologic and hydraulic computer model, surface flow phenomena depend mainly on the different flow accumulation and subsequent runoff generation. These accumulations are generated by routing, cell by cell, from the heights of water, which begin to appear due to the rain at each instant of time. Determine when it is considered a dry cell and when considered wet to include in the full calculation is an issue that directly affects the quantification of direct runoff or generation of flow at the end of a zone of contribution by accumulations flow generated from cells or finite volume.

Keywords: hydrology, transport processes, hydrological modelling, finite volume schemes

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Authors: Xi Yang, Bulent Chavdar, Alan Vonseggern, Taylan Altan

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Fracture in hot precision forging of engine valves was investigated in this paper. The entire valve forging procedure was described and the possible cause of the fracture was proposed. Finite Element simulation was conducted for the forging process, with commercial Finite Element code DEFORMTM. The effects of material properties, the effect of strain rate and temperature were considered in the FE simulation. Two fracture criteria were discussed and compared, based on the accuracy and reliability of the FE simulation results. The selected criterion predicted the fracture location and shows the trend of damage increasing with good accuracy, which matches the experimental observation. Additional modification of the punch shapes was proposed to further reduce the tendency of fracture in forging. Finite Element comparison shows a great potential of such application in the mass production.

Keywords: hotforging, engine valve, fracture, tooling

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Authors: Ionel D. Craiu, Mihai Nedelcu

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Thin-walled cylinders are often used by the offshore industry as columns of floating installations. Based on observed strains, the inverse Finite Element Method (iFEM) may rebuild the deformation of structures. Structural Health Monitoring uses this approach extensively. However, the number of in-situ strain gauges is what determines how accurate it is, and for shell structures with complicated deformation, this number can easily become too high for practical use. Any thin-walled beam member's complicated deformation can be modeled by the Generalized Beam Theory (GBT) as a linear combination of pre-specified cross-section deformation modes. GBT uses bar finite elements as opposed to shell finite elements. This paper proposes an iFEM/GBT formulation for the shape sensing of thin-walled cylinders based on these benefits. This method significantly reduces the number of strain gauges compared to using the traditional inverse-shell finite elements. Using numerical simulations, dent damage detection is achieved by comparing the strain distributions of the undamaged and damaged members. The effect of noise on strain measurements is also investigated.

Keywords: damage detection, generalized beam theory, inverse finite element method, shape sensing

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Authors: Sara Zadunaisky Ehrlich, Batia Seroussi, Anat Stavans

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Text structure is a parameter of text quality. This study investigated the structure of written argumentative texts produced by elementary school age children. We set two objectives: to identify and trace the structural components of the argumentative texts and to investigate whether reading comprehension skills were correlated with text structure. 293 school children from 2nd to 5th grades were asked to write two argumentative texts about informal or everyday life controversial topics and completed two reading tasks that targeted different levels of text comprehension. The findings indicated, on the one hand, significant developmental differences between mature and more novice writers in terms of text length and mean proportion of clauses produced for a better elaboration of the different text components. On the other hand, with certain fluctuations, no meaningful differences were found in terms of presence of text structure: at all grade levels, elementary school children produced the basic and minimal structure that included the writer's argument and reasons or arguments' supports. Counter-arguments were scarce even in the upper grades. While the children captured that essentially an argument must be justified, the more the number of supports produced, the fewer the clauses the children produced. Last, weak to mild relations were found between reading comprehension and argumentative text structure. Nevertheless, children who scored higher on sophisticated questions that require inferential or world knowledge displayed more elaborated structures in terms of text length and size of supports to the writer's argument. These findings indicate how school-age children perceive the basic template of an argument with future implications regarding how to elaborate written arguments.

Keywords: argumentative text, text structure, elementary school children, written argumentations

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Authors: Ivan Baravy

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Interpolation problem, as it was initially posed in terms of polynomials, is well researched. However, further mathematical developments extended it significantly. Trigonometric interpolation is widely used in Fourier analysis, while its generalized representation as exponential interpolation is applicable to such problem of mathematical physics as modelling of Ziegler-Biersack-Littmark repulsive interatomic potentials. Formulated for finite fields, this problem arises in decoding Reed--Solomon codes. This paper shows the relation between different interpretations of the problem through the class of matrices of special structure - Hankel matrices.

Keywords: Berlekamp-Massey algorithm, exponential interpolation, finite fields, Hankel matrices, Hankel polynomials

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Authors: Khaled Moaddy

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In this paper, we present a fast and accurate numerical scheme for the solution of a Laplace equation with Dirichlet boundary conditions. The non-standard finite difference scheme (NSFD) is applied to construct the numerical solutions of a Laplace equation with two different Dirichlet boundary conditions. The solutions obtained using NSFD are compared with the solutions obtained using the standard finite difference scheme (SFD). The NSFD scheme is demonstrated to be reliable and efficient.

Keywords: standard finite difference schemes, non-standard schemes, Laplace equation, Dirichlet boundary conditions

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Authors: R. K. Apalowo, D. Chronopoulos

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A Finite Element (FE) based scheme is presented for quantifying guided wave interaction with Localised Nonlinear Structural Damage (LNSD) within structures of arbitrary layering and geometric complexity. The through-thickness mode-shape of the structure is obtained through a wave and finite element method. This is applied in a time domain FE simulation in order to generate time harmonic excitation for a specific wave mode. Interaction of the wave with LNSD within the system is computed through an element activation and deactivation iteration. The scheme is validated against experimental measurements and a WFE-FE methodology for calculating wave interaction with damage. Case studies for guided wave interaction with crack and delamination are presented to verify the robustness of the proposed method in classifying and identifying damage.

Keywords: layered structures, nonlinear ultrasound, wave interaction with nonlinear damage, wave finite element, finite element

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Authors: Jamal Laaouine, Mohammed Elhassani Charkani

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Let p be a prime and let b be an integer. MDS b-symbol codes are a direct generalization of MDS codes. The γ-constacyclic codes of length pˢ over the finite commutative chain ring Fₚm [u]/ < u² > had been classified into four distinct types, where is a nonzero element of the field Fₚm. Let C₃ be a code of Type 3. In this paper, we obtain the b-symbol distance db(C₃) of the code C₃. Using this result, necessary and sufficient conditions under which C₃ is an MDS b-symbol code are given.

Keywords: constacyclic code, repeated-root code, maximum distance separable, MDS codes, b-symbol distance, finite chain rings

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Authors: Mojtaba Aghamiri Esfahani, Mohammad Karkon, Seyed Majid Hosseini Nezhad, Reza Hosseini-Ara

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In this study, the effect of uncertainty in elastic modulus of a plate on free vibration response is investigated. For this purpose, the elastic modulus of the plate is modeled as stochastic variable with normal distribution. Moreover, the distance autocorrelation function is used for stochastic field. Then, by applying the finite element method and Monte Carlo simulation, stochastic finite element relations are extracted. Finally, with a numerical test, the effect of uncertainty in the elastic modulus on free vibration response of a plate is studied. The results show that the effect of uncertainty in elastic modulus of the plate cannot play an important role on the free vibration response.

Keywords: stochastic finite elements, plate bending, free vibration, Monte Carlo, Neumann expansion method.

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Authors: K. P. Mredula, D. C. Vakaskar

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The article traces developments and evolution of various algorithms developed for solving partial differential equations using the significant combination of wavelet with few already explored solution procedures. The approach depicts a study over a decade of traces and remarks on the modifications in implementing multi-resolution of wavelet, finite difference approach, finite element method and finite volume in dealing with a variety of partial differential equations in the areas like plasma physics, astrophysics, shallow water models, modified Burger equations used in optical fibers, biology, fluid dynamics, chemical kinetics etc.

Keywords: multi-resolution, Haar Wavelet, partial differential equation, numerical methods

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Authors: Amin H. Almasria, Rajai Z. Alrousanb, Al-Harith Manasrah

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The collapse of a light weight pedestrian bridges due to vehicle collision is investigated and studied in detail using a dynamic nonlinear finite element analysis. Typical bridge widely used in Jordan is studied and modeled under truck collision using one dimensional beam finite element in order to minimize analysis time due to the dynamic nature of the problem. Truck collision with the bridge is simulated at different speeds and locations of collisions using dynamic explicit finite element scheme with material nonlinearity taken into account. Energy absorption of bridge is investigated through principle of energy conservation, where truck kinetic energy is assumed to be stored in the bridge as strain energy. Weak failure points in the bridges were identified, and modifications are proposed in order to strengthen the bridge structure and prevent total collapse. The proposed design modifications on bridge structure were successful in allowing the bridge to fail locally rather than globally and expected to help in saving lives.

Keywords: finite element method, dynamic impact, pedestrian bridges, strain energy, collapse failure

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Authors: Lee Feng Koo, Tze Jin Wong, Pang Hung Yiu, Nik Mohd Asri Nik Long

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Greater common divisor (GCD) attack is an attack that relies on the polynomial structure of the cryptosystem. This attack required two plaintexts differ from a fixed number and encrypted under same modulus. This paper reports a security reaction of Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field under GCD attack. Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field was exposed mathematically to the GCD attack using GCD and Dickson polynomial. The result shows that the cryptanalyst is able to get the plaintext without decryption by using GCD attack. Thus, the study concluded that it is highly perilous when two plaintexts have a slight difference from a fixed number in the same Elliptic curve group over finite field.

Keywords: decryption, encryption, elliptic curve, greater common divisor

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Authors: C. Juntarasaid, T. Pulngern, S. Chucheepsakul

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A formulation of postbuckling analysis of end supported rods under self-weight has been presented by the variational method. The variational formulation involving the strain energy due to bending and the potential energy of the self-weight, are expressed in terms of the intrinsic coordinates. The variational formulation is accomplished by introducing the Lagrange multiplier technique to impose the boundary conditions. The finite element method is used to derive a system of nonlinear equations resulting from the stationary of the total potential energy and then Newton-Raphson iterative procedure is applied to solve this system of equations. The numerical results demonstrate the postbluckled configurations of end supported rods under self-weight. This finite element method based on variational formulation expressed in term of intrinsic coordinate is highly recommended for postbuckling analysis of end-supported rods under self-weight.

Keywords: postbuckling, finite element method, variational method, intrinsic coordinate

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Authors: Pyung Soo Kim, Eung Hyuk Lee, Mun Suck Jang

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A packet loss probability (PLP) estimation filter with finite memory structure is proposed to estimate the packet rate mean and variance of the input traffic process in real-time while removing undesired system and measurement noises. The proposed PLP estimation filter is developed under a weighted least square criterion using only the finite traffic measurements on the most recent window. The proposed PLP estimation filter is shown to have several inherent properties such as unbiasedness, deadbeat, robustness. A guideline for choosing appropriate window length is described since it can affect significantly the estimation performance. Using computer simulations, the proposed PLP estimation filter is shown to be superior to the Kalman filter for the temporarily uncertain system. One possible explanation for this is that the proposed PLP estimation filter can have greater convergence time of a filtered estimate as the window length M decreases.

Keywords: packet loss probability estimation, finite memory filter, infinite memory filter, Kalman filter

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Authors: P. M. Keshtiban, M. Zdshakoyan, G. Faragi

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Different severe plastic deformation (SPD) methods are the most successful ways to build nano-structural materials from coarse grain samples without changing the cross-sectional area. One of the most widely used methods in the SPD process is equal channel angler pressing (ECAP). In this paper, ECAP process on Al1050 sheets was evaluated at room temperature by both experiments and finite element method. Since, one of the main objectives of SPD processes is to achieve high equivalent plastic strain (PEEQ) in one cycle, the values of PEEQ obtained by finite element simulation. Also, force-displacement curve achieved by FEM. To study the changes of mechanical properties, micro-hardness tests were conducted on samples and improvement in the mechanical properties were investigated. Results show that there is the good proportion between FEM, theory and experimental results.

Keywords: AL1050, experiments, finite element method, severe plastic deformation

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Authors: Mohammed A. Sakr, Tarek M. Khalifa, Walid N. Mansour

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Fiber reinforced polymer (FRP) installation is a very effective way to repair and strengthen structures that have become structurally weak over their life span. This technique attracted the concerning of researchers during the last two decades. This paper presents a simple uniaxial nonlinear finite element model (UNFEM) able to accurately estimate the load-carrying capacity, different failure modes and the interfacial stresses of reinforced concrete (RC) continuous beams flexurally strengthened with externally bonded FRP plates on the upper and lower fibers. Results of the proposed finite element (FE) model are verified by comparing them with experimental measurements available in the literature. The agreement between numerical and experimental results is very good. Considering fracture energy of adhesive is necessary to get a realistic load carrying capacity of continuous RC beams strengthened with FRP. This simple UNFEM is able to help design engineers to model their strengthened structures and solve their problems.

Keywords: continuous beams, debonding, finite element, fibre reinforced polymer

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Authors: Camille A. Issa, Omar Masri

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In the study, the commercial finite element software Abaqus was used to develop a three-dimensional nonlinear finite element model capable of simulating the pull-out test of reinforcing bars from underwater concrete. The results of thirty-two pull-out tests that have different parameters were implemented in the software to study the effect of the concrete cover, the bar size, the use of stirrups, and the compressive strength of concrete. The interaction properties used in the model provided accurate results in comparison with the experimental bond-slip results, thus the model has successfully simulated the pull-out test. The results of the finite element model are used to better understand and visualize the distribution of stresses in each component of the model, and to study the effect of the various parameters used in this study including the role of the stirrups in preventing the stress from reaching to the sides of the specimens.

Keywords: pull-out test, bond strength, underwater concrete, nonlinear finite element analysis, abaqus

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Authors: Changsoo Chon, Sangkuy Han, Donghyun Seo, Jihyung Park, Bokku Kang, Hansung Kim, Keyoungjin Chun, Cheolwoong Ko

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The purpose of the study is to develop a finite element model based on 3D bone structural images of Micro-CT and to analyze the stress distribution for the osteoporosis mouse femora. In this study, results of finite element analysis show that the early osteoporosis of mouse model decreased a bone density in trabecular region; however, the bone density in cortical region increased.

Keywords: micro-CT, finite element analysis, osteoporosis, bone strength

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Authors: Abdur Rosyid, Mohamed El-Madany, Mohanad Alata

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Due to simplicity and low cost, rotordynamic system is often modeled by using lumped parameters. Recently, finite elements have been used to model rotordynamic system as it offers higher accuracy. However, it involves high degrees of freedom. In some applications such as control design, this requires higher cost. For this reason, various model reduction methods have been proposed. This work demonstrates the quality of model reduction of rotor-bearing-support system through substructuring. The quality of the model reduction is evaluated by comparing some first natural frequencies, modal damping ratio, critical speeds and response of both the full system and the reduced system. The simulation shows that the substructuring is proven adequate to reduce finite element rotor model in the frequency range of interest as long as the numbers and the locations of master nodes are determined appropriately. However, the reduction is less accurate in an unstable or nearly-unstable system.

Keywords: rotordynamic, finite element model, timoshenko beam, 3D solid elements, Guyan reduction method

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Authors: Foo Kok, Varun Thangamani

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Rectangular cavities with a full-span or finite-width configuration have been the basis of much previous research on cavity flows. However, much less attention has been given to the influence of sidewalls, in particular, on low-speed cavity flows. In this study, the flow characteristics of two separate low-speed finite-width cavities with a Reynolds number of 𝑅𝑒𝐷 = 10⁴ are examined using large eddy simulations. Two different lateral boundary conditions are used to investigate the influence of sidewalls on the self-sustaining oscillations and the three-dimensional flow fields inside the cavities. The results show that the full-span finite width cavities are less sensitive to the sidewall effect at a low length-to-width ratio 𝐿/𝐷. The increase in 𝐿/𝐷 leads to a departure from two-dimensional instability and results in the loss of spanwise homogeneity. The analysis of the spanwise flow structures shows that these effects correspond closely to the declination of the centrifugal force from the primary recirculation zone. Such effects are also reflected in the distinct modulation of the secondary vortices in the primary recirculation zone, which suggests that the instabilities observed in the full-span finite-width cavity flows are predominantly dependent on the secondary motion from the primary recirculation zone.

Keywords: LES, cavity flows, unsteady shear layer, instability modes, secondary flow

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Authors: Alexander P. Smirnov, Sergey A. Matveev, Dmitry A. Zheltkov, Eugene E. Tyrtyshnikov

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We propose a new computational technique for multidimensional (multicomponent) Smoluchowski coagulation equation. Using low-rank approximations in Tensor Train format of both the solution and the coagulation kernel, we accelerate the classical finite-difference Runge-Kutta scheme keeping its level of accuracy. The complexity of the taken finite-difference scheme is reduced from O(N^2d) to O(d^2 N log N ), where N is the number of grid nodes and d is a dimensionality of the problem. The efficiency and the accuracy of the new method are demonstrated on concrete problem with known analytical solution.

Keywords: tensor train decomposition, multicomponent Smoluchowski equation, runge-kutta scheme, convolution

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