Search results for: Galerkin finite element method

Authors: Snezhana G. Gocheva-Ilieva, Ivan H. Feschiev

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In this study integral form and new recursive formulas for Favard constants and some connected with them numeric and Fourier series are obtained. The method is based on preliminary integration of Fourier series which allows for establishing finite recursive representations for the summation. It is shown that the derived recursive representations are numerically more effective than known representations of the considered objects.

Keywords: Effective summation of series, Favard constants, finite recursive representations, Fourier series

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Authors: Nadine Ali Hassan, Ngoc Son Nguyen, Didier Marot, Fateh Bendahmane

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This paper aims at presenting a study of the effect of scalping methods on the mechanical properties of coarse soils by resorting to numerical simulations based on the discrete element method (DEM) and experimental triaxial tests. Two reconstitution methods are used, designated as scalping method and substitution method. Triaxial compression tests are first simulated on a granular materials with a grap graded particle size distribution by using the DEM. We study the effect of these reconstitution methods on the stress-strain behavior of coarse soils with different fine contents and with different ways to control the densities of the scalped and substituted materials. Experimental triaxial tests are performed on original mixtures of sands and gravels with different fine contents and on their corresponding scalped and substituted samples. Numerical results are qualitatively compared to experimental ones. Agreements and discrepancies between these results are also discussed.

Keywords: Coarse soils, scalping, substitution, discrete element method, triaxial test.

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Authors: K. Machida, H. Yamada

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Displacement measurement was conducted on compact normal and shear specimens made of acrylic homogeneous material subjected to mixed-mode loading by digital image correlation. The intelligent hybrid method proposed by Nishioka et al. was applied to the stress-strain analysis near the crack tip. The accuracy of stress-intensity factor at the free surface was discussed from the viewpoint of both the experiment and 3-D finite element analysis. The surface images before and after deformation were taken by a CMOS camera, and we developed the system which enabled the real time stress analysis based on digital image correlation and inverse problem analysis. The great portion of processing time of this system was spent on displacement analysis. Then, we tried improvement in speed of this portion. In the case of cracked body, it is also possible to evaluate fracture mechanics parameters such as the J integral, the strain energy release rate, and the stress-intensity factor of mixed-mode. The 9-points elliptic paraboloid approximation could not analyze the displacement of submicron order with high accuracy. The analysis accuracy of displacement was improved considerably by introducing the Newton-Raphson method in consideration of deformation of a subset. The stress-intensity factor was evaluated with high accuracy of less than 1% of the error.

Keywords: Digital image correlation, mixed mode, Newton-Raphson method, stress intensity factor.

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Authors: M. Zarebnia, R. Parvaz

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In this paper, numerical solutions of the nonlinear Benjamin-Bona-Mahony-Burgers (BBMB) equation are obtained by a method based on collocation of cubic B-splines. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The L∞ and L2 in the solutions show the efficiency of the method computationally.

Keywords: Benjamin-Bona-Mahony-Burgers equation, Cubic Bspline, Collocation method, Finite difference.

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Authors: Adrian T. Plesca

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This paper describes a three-dimensional thermal model of the current path included in the low voltage power circuit breakers. The model can be used to analyse the thermal behaviour of the current path during both steady-state and transient conditions. The current path lengthwise temperature distribution and timecurrent characteristic of the terminal connections of the power circuit breaker have been obtained. The influence of the electric current and voltage drop on main electric contact of the circuit breaker has been investigated. To validate the three-dimensional thermal model, some experimental tests have been done. There is a good correlation between experimental and simulation results.

Keywords: Current path, power circuit breakers, temperature distribution, thermal analysis.

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Authors: Boukelkoul Lahcen

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The cumulative costs for O&M may represent as much as 65%-90% of the turbine's investment cost. Nowadays the cost effectiveness concept becomes a decision-making and technology evaluation metric. The cost of energy metric accounts for the effect replacement cost and unscheduled maintenance cost parameters. One key of the proposed approach is the idea of maintaining the WTs which can be captured via use of a finite state Markov chain. Such a model can be embedded within a probabilistic operation and maintenance simulation reflecting the action to be done. In this paper, an approach of estimating the cost of O&M is presented. The finite state Markov model is used for decision problems with number of determined periods (life cycle) to predict the cost according to various options of maintenance.

Keywords: Cost, finite state, Markov model, operation, maintenance.

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Authors: B. Engel, Sara Salman Hassan Al-Maeeni

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Human consumption of the Earth's resources increases the need for a sustainable development as an important ecological, social, and economic theme. Re-engineering of machine tools, in terms of design and failure analysis, is defined as steps performed on an obsolete machine to return it to a new machine with the warranty that matches the customer requirement. To understand the future fatigue behavior of the used machine components, it is important to investigate the possible causes of machine parts failure through design, surface, and material inspections. In this study, the failure modes of the shaft of the rotary draw bending machine are inspected. Furthermore, stress and deflection analysis of the shaft subjected to combined torsion and bending loads are carried out by an analytical method and compared with a finite element analysis method. The theoretical fatigue strength, correction factors, and fatigue life sustained by the shaft before damaged are estimated by creating a stress-cycle (S-N) diagram. In conclusion, it is seen that the shaft can work in the second life, but it needs some surface treatments to increase the reliability and fatigue life.

Keywords: Failure analysis, fatigue life, FEM analysis, shaft, stress analysis.

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Authors: Carlos H. Cuadra

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Seismic isolation can be used as a retrofit method for historical buildings with the advantage that minimum intervention on super-structure is required. However, selection of isolation devices depends on weight and stiffness of upper structure. In this study, two buildings are considered for analyses to evaluate the applicability of this retrofitting methodology. Both buildings are located at Akita prefecture in the north part of Japan. One building is a wooden structure that corresponds to the old council meeting hall of Noshiro city. The second building is a brick masonry structure that was used as house of a foreign mining engineer and it is located at Ani town. Ambient vibration measurements were performed on both buildings to estimate their dynamic characteristics. Then, target period of vibration of isolated systems is selected as 3 seconds is selected to estimate required stiffness of isolation devices. For wooden structure, which is a light construction, it was found that natural rubber isolators in combination with friction bearings are suitable for seismic isolation. In case of masonry building elastomeric isolator can be used for its seismic isolation. Lumped mass systems are used for seismic response analysis and it is verified in both cases that seismic isolation can be used as retrofitting method of historical construction. However, in the case of the light building, most of the weight corresponds to the reinforced concrete slab that is required to install isolation devices.

Keywords: Historical building, finite element method, masonry structure, seismic isolation, wooden structure.

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Authors: Ngoc Trung Ngo, Buddhima Indraratna, Cholachat Rujikiathmakjornr

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For several hundred years, the design of railway tracks has practically remained unchanged. Traditionally, rail tracks are placed on a ballast layer due to several reasons, including economy, rapid drainage, and high load bearing capacity. The primary function of ballast is to distributing dynamic track loads to sub-ballast and subgrade layers, while also providing lateral resistance and allowing for rapid drainage. Upon repeated trainloads, the ballast becomes fouled due to ballast degradation and the intrusion of fines which adversely affects the strength and deformation behaviour of ballast. This paper presents the use of three-dimensional discrete element method (DEM) in studying the shear behaviour of the fouled ballast subjected to direct shear loading. Irregularly shaped particles of ballast were modelled by grouping many spherical balls together in appropriate sizes to simulate representative ballast aggregates. Fouled ballast was modelled by injecting a specified number of miniature spherical particles into the void spaces. The DEM simulation highlights that the peak shear stress of the ballast assembly decreases and the dilation of fouled ballast increases with an increase level of fouling. Additionally, the distributions of contact force chain and particle displacement vectors were captured during shearing progress, explaining the formation of shear band and the evolutions of volumetric change of fouled ballast.

Keywords: Railway ballast, coal fouling, discrete element modelling, discrete element method.

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Authors: Esmaeil Poursaeidi, Mostafa Kamalzadeh Yazdi

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Different problems may causes distortion of the rotor, and hence vibration, which is the most severe damage of the turbine rotors. In many years different techniques have been developed for the straightening of bent rotors. The method for straightening can be selected according to initial information from preliminary inspections and tests such as nondestructive tests, chemical analysis, run out tests and also a knowledge of the shaft material. This article covers the various causes of excessive bends and then some applicable common straightening methods are reviewed. Finally, hot spotting is opted for a particular bent rotor. A 325 MW steam turbine rotor is modeled and finite element analyses are arranged to investigate this straightening process. Results of experimental data show that performing the exact hot spot straightening process reduced the bending of the rotor significantly.

Keywords: Distortion, FEM, Hot Spot Area, Rotor Straightening

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Authors: Ke Wang, Zhi-Qiang Zhang, Z. Chen

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A submerged horizontal plate type breakwater is pointed out as an efficient wave protection device for cage culture in marine fishery. In order to reveal the wave elimination principle of this type breakwater, boundary element method is utilized to investigate this problem. The flow field and the trajectory of water particles are studied carefully. The flow field analysis shows that: the interaction of incident wave and adverse current above the plate disturbs the water domain drastically. This can slow down the horizontal velocity and vertical velocity of the water particles.

Keywords: boundary element method, plate type breakwater, flow field analysis

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Authors: Luciano Garelli, Marco Schauer, Jorge D’Elia, Mario A. Storti, Sabine C. Langer

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This paper discuss a coupling strategy of two different software packages to provide fluid structure interaction (FSI) analysis. The basic idea is to combine the advantages of the two codes to create a powerful FSI solver for two and three dimensional analysis. The fluid part is computed by a program called PETSc-FEM a software developed at Centro de Investigaci´on de M´etodos Computacionales –CIMEC. The structural part of the coupled process is computed by the research code elementary Parallel Solver – (ELPASO) of the Technische Universit¨at Braunschweig, Institut f¨ur Konstruktionstechnik (IK).

Keywords: Computational Fluid Dynamics (CFD), Fluid Structure Interaction (FSI), Finite Element Method (FEM).

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Authors: Bashar Albaalbaki, Roger E. Khayat

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This work is a comparative study on the effect of Delaunay triangulation algorithms on discretization error for conduction-convection conservation problems. A structured triangulation and many unstructured Delaunay triangulations using three popular algorithms for node placement strategies are used. The numerical method employed is the vertex-centered finite volume method. It is found that when the computational domain can be meshed using a structured triangulation, the discretization error is lower for structured triangulations compared to unstructured ones for only low Peclet number values, i.e. when conduction is dominant. However, as the Peclet number is increased and convection becomes more significant, the unstructured triangulations reduce the discretization error. Also, no statistical correlation between triangulation angle extremums and the discretization error is found using 200 samples of randomly generated Delaunay and non-Delaunay triangulations. Thus, the angle extremums cannot be an indicator of the discretization error on their own and need to be combined with other triangulation quality measures, which is the subject of further studies.

Keywords: Conduction-convection problems, Delaunay triangulation, discretization error, finite volume method.

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Authors: Ren Jian, Yang Shulin

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In this paper, the difference between the Alternating Direction Method (ADM) and the Non-Splitting Method (NSM) is investigated, while both methods applied to the simulations for 2-D multimaterial radiation diffusion issues. Although the ADM have the same accuracy orders with the NSM on the uniform meshes, the accuracy of ADM will decrease on the distorted meshes or the boundary of domain. Numerical experiments are carried out to confirm the theoretical predication.

Keywords: Alternating Direction Method, Non-SplittingMethod, Radiation Diffusion.

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Authors: Nhat Linh Ho, Thanh-Phong Dao, Shyh-Chour Huang, Hieu Giang Le

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This paper presents a design and optimization for a compliant gripper. The gripper is constructed based on the concept of compliant mechanism with flexure hinge. A passive force regulation mechanism is presented to control the grasping force a micro-sized object instead of using a sensor force. The force regulation mechanism is designed using the planar springs. The gripper is expected to obtain a large range of displacement to handle various sized objects. First of all, the statics and dynamics of the gripper are investigated by using the finite element analysis in ANSYS software. And then, the design parameters of the gripper are optimized via Taguchi method. An orthogonal array L₉ is used to establish an experimental matrix. Subsequently, the signal to noise ratio is analyzed to find the optimal solution. Finally, the response surface methodology is employed to model the relationship between the design parameters and the output displacement of the gripper. The design of experiment method is then used to analyze the sensitivity so as to determine the effect of each parameter on the displacement. The results showed that the compliant gripper can move with a large displacement of 213.51 mm and the force regulation mechanism is expected to be used for high precision positioning systems.

Keywords: Flexure hinge, compliant mechanism, compliant gripper, force regulation mechanism, Taguchi method, response surface methodology, design of experiment.

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Authors: Thana Ananacha

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This paper reports the numerical and experimental performances of Double Glass Wall are investigated. Two configurations were considered namely, the Double Clear Glass Wall (DCGW) and the Double Translucent Glass Wall (DTGW). The coupled governing equations as well as boundary conditions are solved using the finite element method (FEM) via COMSOLTM Multiphysics. Temperature profiles and flow field of the DCGW and DTGW are reported and discussed. Different constant heat fluxes were considered as 400 and 800 W.m-2 the corresponding initial condition temperatures were 30.5 and 38.5ºC respectively. The results show that the simulation results are in agreement with the experimental data. Conclusively, the model considered in this study could reasonable be used simulate the thermal and ventilation performance of the DCGW and DTGW configurations.

Keywords: Thermal simulation, Double Glass Wall, Velocity field.

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Authors: Changwen Li

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In this paper, we investigate the influence of Ssemipermutable and weakly S-supplemented subgroups on the pnilpotency of finite groups. Some recent results are generalized.

Keywords: S-semipermutable, weakly S-supplemented, pnilpotent.

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Authors: Jaipong Kasemsuwan

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A numerical solution of the initial boundary value problem of the suspended string vibrating equation with the particular nonlinear damping term based on the finite difference scheme is presented in this paper. The investigation of how the second and third power terms of the nonlinear term affect the vibration characteristic. We compare the vibration amplitude as a result of the third power nonlinear damping with the second power obtained from previous report provided that the same initial shape and initial velocities are assumed. The comparison results show that the vibration amplitude is inversely proportional to the coefficient of the damping term for the third power nonlinear damping case, while the vibration amplitude is proportional to the coefficient of the damping term in the second power nonlinear damping case.

Keywords: Finite-difference method, the nonlinear damped equation, the numerical simulation, the suspended string equation

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Authors: Tao Qu, Chandra Prakash, Vikas Tomar

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The interfaces between organic and inorganic phases in natural materials have been shown to be a key factor contributing to their high performance. This work analyzes crack propagation in a 2-ply laminate subjected to uniaxial tensile mode-I crack propagation loading that has laminate properties derived based on biological material constituents (marine exoskeleton- chitin and calcite). Interfaces in such laminates are explicitly modeled based on earlier molecular simulations performed by authors. Extended finite element method and cohesive zone modeling based simulations coupled with theoretical analysis are used to analyze crack propagation. Analyses explicitly quantify the effect that interface mechanical property variation has on the delamination as well as the transverse crack propagation in examined 2-ply laminates.

Keywords: Chitin, composites, interfaces, fracture.

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Authors: Farhad Asgari Mehrabadi, Mohammad Reza Khoshravan

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In the present study, fracture behavior of woven fabric-reinforced glass/epoxy composite laminates under mode III crack growth was experimentally investigated and numerically modeled. Two methods were used for the calculation of the strain energy release rate: the experimental compliance calibration (CC) method and the Virtual Crack Closure Technique (VCCT). To achieve this aim ECT (Edge Crack Torsion) was used to evaluate fracture toughness in mode III loading (out of plane-shear) at different crack lengths. Load–displacement and associated energy release rates were obtained for various case of interest. To calculate fracture toughness JIII, two criteria were considered including non-linearity and maximum points in load-displacement curve and it is observed that JIII increases with the crack length increase. Both the experimental compliance method and the virtual crack closure technique proved applicable for the interpretation of the fracture mechanics data of woven glass/epoxy laminates in mode III.

Keywords: Mode III, Fracture, Composite, Crack growth Finite Element.

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Authors: M. Abdulkawi, Z. K. Eshkuvatov, N. M. A. Nik Long

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This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels.

Keywords: Singular integral equations, Cauchy kernel, Chebyshev polynomials, interpolation.

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Authors: Foad Nazari, Seyed Mahmood Hosseini, Mohammad Hossein Abolbashari, Mohammad Hassan Abolbashari

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The present study is concerned with the optimal design of functionally graded plates using particle swarm optimization (PSO) algorithm. In this study, meshless local Petrov-Galerkin (MLPG) method is employed to obtain the functionally graded (FG) plate’s natural frequencies. Effects of two parameters including thickness to height ratio and volume fraction index on the natural frequencies and total mass of plate are studied by using the MLPG results. Then the first natural frequency of the plate, for different conditions where MLPG data are not available, is predicted by an artificial neural network (ANN) approach which is trained by back-error propagation (BEP) technique. The ANN results show that the predicted data are in good agreement with the actual one. To maximize the first natural frequency and minimize the mass of FG plate simultaneously, the weighted sum optimization approach and PSO algorithm are used. However, the proposed optimization process of this study can provide the designers of FG plates with useful data.

Keywords: Optimal design, natural frequency, FG plate, hybrid meshless method, MLPG method, ANN approach, particle swarm optimization.

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Authors: Shreya Thusoo, Karan Modi, Rajesh Kumar, Hitesh Madahar

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Over the years, it has been extensively established that the practice of assuming a structure being fixed at base, leads to gross errors in evaluation of its overall response due to dynamic loadings and overestimations in design. The extent of these errors depends on a number of variables; soil type being one of the major factor. This paper studies the effect of Soil Structure Interaction (SSI) on multistorey buildings with varying under-laying soil types after proper validation of the effect of SSI. Analysis for soft, stiff and very stiff base soils has been carried out, using a powerful Finite Element Method (FEM) software package ANSYS v14.5. Results lead to some very important conclusions regarding time period, deflection and acceleration responses.

Keywords: Dynamic response, multi-storey building, Soil-Structure Interaction.

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Authors: Vijay Kumar Kukreja, Ravneet Kaur

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In this paper, one dimensional advection diffusion model is analyzed using finite difference method based on Crank-Nicolson scheme. A practical problem of filter cake washing of chemical engineering is analyzed. The model is converted into dimensionless form. For the grid Ω × ω = [0, 1] × [0, T], the Crank-Nicolson spatial derivative scheme is used in space domain and forward difference scheme is used in time domain. The scheme is found to be unconditionally convergent, stable, first order accurate in time and second order accurate in space domain. For a test problem, numerical results are compared with the analytical ones for different values of parameter.

Keywords: Consistency, Crank-Nicolson scheme, Gerschgorin circle, Lax-Richtmyer theorem, Peclet number, stability.

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Authors: Hyun-Ho Lee, Kee-Won Kim

Abstract:

The arithmetic operations over GF(2m) have been extensively used in error correcting codes and public-key cryptography schemes. Finite field arithmetic includes addition, multiplication, division and inversion operations. Addition is very simple and can be implemented with an extremely simple circuit. The other operations are much more complex. The multiplication is the most important for cryptosystems, such as the elliptic curve cryptosystem, since computing exponentiation, division, and computing multiplicative inverse can be performed by computing multiplication iteratively. In this paper, we present a parallel computation algorithm that operates Montgomery multiplication over finite field using redundant basis. Also, based on the multiplication algorithm, we present an efficient semi-systolic multiplier over finite field. The multiplier has less space and time complexities compared to related multipliers. As compared to the corresponding existing structures, the multiplier saves at least 5% area, 50% time, and 53% area-time (AT) complexity. Accordingly, it is well suited for VLSI implementation and can be easily applied as a basic component for computing complex operations over finite field, such as inversion and division operation.

Keywords: Finite field, Montgomery multiplication, systolic array, cryptography.

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Authors: Zhang Lei, Liu Min, Liu Botao

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In order to improve the simulation effects of space cold black environment, this paper described a rectangular channel plate heat sink. By using fluid mechanics theory and finite element method, the internal fluid flow and heat transfer in heat sink was numerically simulated to analyze the impact of channel structural on fluid flow and heat transfer. The result showed that heat sink temperature uniformity is well, and the impact of channel structural on the heat sink temperature uniformity is not significant. The channel depth and spacing are important factors which affect the fluid flow and heat transfer in the heat sink. The two factors of heat transfer and resistance need to be considered comprehensively to determine the optimal flow structure parameters.

Keywords: heat transfer, heat sink, numerical simulation

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Authors: N. M. Nusi, M. Othman, M. Suleiman, F. Ismail, N. Alias

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In this paper, an alternating implicit block method for solving two dimensional scalar wave equation is presented. The new method consist of two stages for each time step implemented in alternating directions which are very simple in computation. To increase the speed of computation, a group of adjacent points is computed simultaneously. It is shown that the presented method increase the maximum time step size and more accurate than the conventional finite difference time domain (FDTD) method and other existing method of natural ordering.

Keywords: FDTD, Scalar wave equation, alternating direction implicit (ADI), alternating group explicit (AGE), asymmetric approximation.

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Authors: M. Benachour, N. Benachour, M. Benguediab

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In this paper fatigue crack initiation and propagation in notched plate under constant amplitude loading through tensile residual stress field of 2024 T351 Al-alloy plate were investigated. Residual stress field was generated by plastic deformation using finite element method (FEM) where isotropic hardening in Von Mises model was applied. Simulation of fatigue behavior was made on AFGROW code. It was shown that the fatigue crack initiation and propagation were affected by level of residual stress filed. In this investigation, the presence of tensile residual stresses at notch (hole) reduces considerably the total fatigue life. It was shown that the decreasing in stress reduces the fatigue crack growth rates.

Keywords: Residual stress, fatigue crack initiation, fatigue crack growth, Al-alloy.

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Authors: Bahi-Eddine Lahouel, Mohamed Guenfoud

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In this study, a vibration analysis was carried out of symmetric angle-ply laminated composite plates with and without square hole when subjected to compressive loads, numerically. A buckling analysis is also performed to determine the buckling load of laminated plates. For each fibre orientation, the compression load is taken equal to 50% of the corresponding buckling load. In the analysis, finite element method (FEM) was applied to perform parametric studies, the effects of degree of orthotropy and stacking sequence upon the fundamental frequencies and buckling loads are discussed. The results show that the presence of a constant compressive load tends to reduce uniformly the natural frequencies for materials which have a low degree of orthotropy. However, this reduction becomes non-uniform for materials with a higher degree of orthotropy.

Keywords: Vibration, Buckling, Cutout, Laminated composite, FEM

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Authors: H. S. Haroyan, V. R. Tadevosyan

Abstract:

High gain broadband plasmonic slot nano-antenna has been considered. The theory of plasmonic slot nano-antenna (PSNA) has been developed. The analytical model takes into account also the electrical field inside the metal due to imperfectness of metal in optical range, as well as numerical investigation based on finite element method (FEM) has been realized. It should be mentioned that Yagi-Uda configuration improves directivity in the plane of structure. In contrast, in this paper the possibility of directivity improvement of proposed PSNA in perpendicular plane of structure by using reflection metallic surface placed under the slot in fixed distance has been demonstrated. It is well known that a directivity improvement brings to the antenna gain increasing. This method of diagram improving is also well known from RF antenna design theory. Moreover the improvement of directivity in the perpendicular plane gives more flexibility in such application as improving the light and atom, ion, molecule interactions by using such type of plasmonic slot antenna. By the analogy of dipole type optical antennas the widening of working wavelengths has been realized by using bowtie geometry of slots, which made the antenna broadband.

Keywords: Broadband antenna, high gain, slot nano-antenna, plasmonics.

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