Search results for: finite volume schemes

Authors: Asabe Ahmad Tijani, Y. A. Yahaya

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The paper considers the derivation of implicit Adams-Moulton type method, with k=4 and 5. We adopted the method of interpolation and collocation of power series approximation to generate the continuous formula which was evaluated at off-grid and some grid points within the step length to generate the proposed block schemes, the schemes were investigated and found to be consistent and zero stable. Finally, the methods were tested with numerical experiments to ascertain their level of accuracy.

Keywords: Adam-Moulton Type (AMT), off-grid, block method, consistent and zero stable

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Authors: Yang Cao

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Analyzing the oral production of Chinese-speaking learners of English as a second language (L2), we can find a large variety of verb inflections – Why does it seem so hard for them to use consistent correct past morphologies in obligatory past contexts? Failed Functional Features Hypothesis (FFFH) attributes the rather non-target-like performance to the absence of [±past] feature in their L1 Chinese, arguing that for post puberty learners, new features in L2 are no more accessible. By contrast, Missing Surface Inflection Hypothesis (MSIH) tends to believe that all features are actually acquirable for late L2 learners, while due to the mapping difficulties from features to forms, it is hard for them to realize the consistent past morphologies on the surface. However, most of the studies are limited to the verb morphologies in finite clauses and few studies have ever attempted to figure out these learners’ performance in non-finite clauses. Additionally, it has been discussed that Chinese learners may be able to tell the finite/infinite distinction (i.e. the [±finite] feature might be selected in Chinese, even though the existence of [±past] is denied). Therefore, adopting a self-paced reading task (SPR), the current study aims to analyze the processing patterns of Chinese-speaking learners of L2 Russian, in order to find out if they are sensitive to misuse of tense morphologies in both finite and non-finite clauses and whether they are sensitive to the finite/infinite distinction presented in Russian. The study targets L2 Russian due to its systematic morphologies in both present and past tenses. A native Russian group, as well as a group of English-speaking learners of Russian, whose L1 has definitely selected both [±finite] and [±past] features, will also be involved. By comparing and contrasting performance of the three language groups, the study is going to further examine and discuss the two theories, FFFH and MSIH. Preliminary hypotheses are: a) Russian native speakers are expected to spend longer time reading the verb forms which violate the grammar; b) it is expected that Chinese participants are, at least, sensitive to the misuse of inflected verbs in non-finite clauses, although no sensitivity to the misuse of infinitives in finite clauses might be found. Therefore, an interaction of finite and grammaticality is expected to be found, which indicate that these learners are able to tell the finite/infinite distinction; and c) having selected [±finite] and [±past], English-speaking learners of Russian are expected to behave target-likely, supporting L1 transfer.

Keywords: features, finite clauses, morphosyntax, non-finite clauses, past morphologies, present morphologies, Second Language Acquisition, self-paced reading task, verb inflections

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Authors: T. Mushiri, K. Tengende, C. Mbohwa, T. Garikayi

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This paper introduces finite element analysis of Run off Mine (ROM) silo subjected to dynamic loading. The proposed procedure is based on the use of theoretical equations to come up with pressure and forces exerted by Platinum Group Metals (PGMs) ore to the silo wall. Finite Element Analysis of the silo involves the use of CAD software (AutoCAD) for3D creation and CAE software (T-FLEX) for the simulation work with an optimization routine to minimize the mass and also ensure structural stiffness and stability. In this research an efficient way to design and analysis of a silo in 3D T-FLEX (CAD) program was created the silo to stay within the constrains and so as to know the points of failure due dynamic loading.

Keywords: reinforced concrete silo, finite element analysis, T-FLEX software, AutoCAD

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Authors: Nikhil Padhye, Ellen Kintz, Dan Dorci

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Recent years have seen a rising interest in study and applications of materially uniform thin-structures (plates/shells) subject to finite-bending and stretching deformations. We introduce a well-posed 2D-model involving finite-bending and stretching of thin-structures to approximate the three-dimensional equilibria. Key features of this approach include: Non-Uniform Rational B-Spline (NURBS)-based spatial discretization for finite elements, method of dynamic relaxation to predict stable equilibria, and no a priori kinematic assumption on the deformation fields. The approach is validated against the benchmark problems,and the use of NURBS for spatial discretization facilitates exact spatial representation and computation of curvatures (due to C1-continuity of interpolated displacements) for this higher-order accuracy 2D-model.

Keywords: Isogeometric Analysis, Plates/Shells , Finite Element Methods, Dynamic Relaxation

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Authors: Temami Oussama, Bessais Lakhdar, Hamadi Djamal, Abderrahmani Sifeddine

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The analysis of complex structures encourages the engineer to make simplifying assumptions, sometimes attempting the analysis of the whole structure as complex as it is, and it can be done using the finite element method (FEM). In the modeling of complex structures by finite elements, various elements can be used: beam element, membrane element, solid element, plates and shells elements. These elements formulated according to the classical formulation and do not generally share the same nodal degrees of freedom, which complicates the development of a compatible model. The compatibility of the elements with each other is often a difficult problem for modeling complicated structure. This compatibility is necessary to ensure the convergence. To overcome this problem, we have proposed finite elements with a rotational degree of freedom. The study used is based on the strain approach formulation with 2D and 3D formulation with different degrees of freedom at each node. For the comparison and confrontation of results; the finite elements available in ABAQUS/Standard are used.

Keywords: compatibility requirement, complex structures, finite elements, modeling, strain approach

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Authors: Ahmad R. Zamani, Luigi Sanguigno, Angelo R. Maligno

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A 3D woven composite, designed for automotive applications, is studied using Abaqus Finite Element (FE) software suite. Python scripts were developed to build FE models of the woven composite in Complete Abaqus Environment (CAE). They can read TexGen or WiseTex files and automatically generate consistent meshes of the fabric and the matrix. A user menu is provided to help define parameters for the FE models, such as type and size of the elements in fabric and matrix as well as the type of matrix-fabric interaction. Node-to-node constraints were imposed to guarantee periodicity of the deformed shapes at the boundaries of the representative volume element of the composite. Tensile loads in three axes and biaxial loads in x-y directions have been applied at different Fibre Volume Fractions (FVFs). A simple damage model was implemented via an Abaqus user material (UMAT) subroutine. Existing tools for homogenization were also used, including voxel mesh generation from TexGen as well as Abaqus Micromechanics plugin. Linear relations between homogenised elastic properties and the FVFs are given. The FE models of composite exhibited balanced behaviour with respect to warp and weft directions in terms of both stiffness and strength.

Keywords: 3D woven composite (3DWC), meso-scale finite element model, homogenisation of elastic material properties, Abaqus Python scripting

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Authors: Heng Han, Zhilei Liang, Xiangong Zhou

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In this paper, the finite element method is used to study the temperature field of the main cable of the suspension bridge, and the calculation method of the average temperature of the cross-section of the main cable suitable for the construction control of the cable system is proposed; By comparing and analyzing the temperature field of the main cable with five diameters, a reasonable diameter limit for calculating the average temperature of the cross section of the main cable by finite element method is proposed. The results show that the maximum error of this method is less than 1℃, which meets the requirements of construction control accuracy; For the main cable with a diameter greater than 400mm, the surface temperature measuring points combined with the finite element method shall be used to calculate the average cross-section temperature.

Keywords: suspension bridge, main cable, temperature field, finite element

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Authors: Youb Said, Fourar Ali

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To describe the influence of bottom roughness on the free surface flows by numerical modeling, a two-dimensional model was developed. The equations of continuity and momentum (Naviers Stokes equations) are solved by the finite volume method. We considered a turbulent flow in an open channel with a bottom roughness. For our simulations, the K-ε model was used. After setting the initial and boundary conditions and solve the equations set, we were able to achieve the following results: vortex forming in the hollow causing substantial energy dissipation in the obstacle areas that form the bottom roughness. The comparison of our results with experimental ones shows a good agreement in terms of the results in the rough area. However, in other areas, differences were more or less important. These differences are in areas far from the bottom, especially the free surface area just after the bottom. These disagreements are probably due to experimental constants used by the k-ε model.

Keywords: modeling, free surface flow, turbulence, bottom roughness, finite volume, K-ε model, energy dissipation

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Authors: Karan Modi, Rajesh Kumar, Jyoti Katiyar, Shreya Thusoo

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This paper presents Finite Element Method (FEM) for analyzing the internal responses generated in thin rectangular plates with various edge conditions and rigidity conditions. Comparison has been made between the FEM (ANSYS software) results for displacement, stresses and moments generated with and without the consideration of hole in plate and different aspect ratios. In the end comparison for responses in plain and composite square plates has been studied.

Keywords: ANSYS, finite element method, plates, static analysis

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Authors: Najibullah M, Soumendra Nath Kuiry

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Dams and reservoirs are perceived for their estimable alms to irrigation, water supply, flood control, electricity generation, etc. which civilize the prosperity and wealth of society across the world. Meantime the dam breach could cause devastating flood that can threat to the human lives and properties. Failures of large dams remain fortunately very seldom events. Nevertheless, a number of occurrences have been recorded in the world, corresponding in an average to one to two failures worldwide every year. Some of those accidents have caused catastrophic consequences. So it is decisive to predict the dam break flow for emergency planning and preparedness, as it poses high risk to life and property. To mitigate the adverse impact of dam break, modeling is necessary to gain a good understanding of the temporal and spatial evolution of the dam-break floods. This study will mainly deal with one-dimensional (1D) dam break modeling. Less commonly used in the hydraulic research community, another possible option for modeling the rapidly varied dam-break flows is the extended Boussinesq equations (BEs), which can describe the dynamics of short waves with a reasonable accuracy. Unlike the Shallow Water Equations (SWEs), the BEs taken into account the wave dispersion and non-hydrostatic pressure distribution. To capture the dam-break oscillations accurately it is very much needed of at least fourth-order accurate numerical scheme to discretize the third-order dispersion terms present in the extended BEs. The scope of this work is therefore to develop an 1D fourth-order accurate in both space and time Boussinesq model for dam-break flow analysis by using finite-volume / finite difference scheme. The spatial discretization of the flux and dispersion terms achieved through a combination of finite-volume and finite difference approximations. The flux term, was solved using a finite-volume discretization whereas the bed source and dispersion term, were discretized using centered finite-difference scheme. Time integration achieved in two stages, namely the third-order Adams Basforth predictor stage and the fourth-order Adams Moulton corrector stage. Implementation of the 1D Boussinesq model done using PYTHON 2.7.5. Evaluation of the performance of the developed model predicted as compared with the volume of fluid (VOF) based commercial model ANSYS-CFX. The developed model is used to analyze the risk of cascading dam failures similar to the Panshet dam failure in 1961 that took place in Pune, India. Nevertheless, this model can be used to predict wave overtopping accurately compared to shallow water models for designing coastal protection structures.

Keywords: Boussinesq equation, Coastal protection, Dam-break flow, One-dimensional model

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Authors: Z. Bouchama, N. Essounbouli, A. Hamzaoui, M. N. Harmas

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A new robust finite time synergetic controller is presented based on recently developed synergetic control methodology and a terminal attractor technique. A Fast Terminal Synergetic Control (FTSC) is proposed for controlling DC-DC buck converter. Unlike Synergetic Control (SC) and sliding mode control, the proposed control scheme has the characteristics of finite time convergence and chattering free phenomena. Simulation of stabilization and reference tracking for buck converter systems illustrates the approach effectiveness while stability is assured in the Lyapunov sense and converse Lyapunov results involving scalar differential inequalities are given for finite-time stability.

Keywords: dc-dc buck converter, synergetic control, finite time convergence, terminal synergetic control, fast terminal synergetic control, Lyapunov

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Authors: Zineddine Bouyahiaoui, Rabah Haoui

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The aim of this work is to analyze a flow around the axisymmetric blunt body taken into account the chemical and vibrational nonequilibrium flow. This work concerns the entry of spacecraft in the atmosphere of the planet Mars. Since the equations involved are non-linear partial derivatives, the volume method is the only way to solve this problem. The choice of the mesh and the CFL is a condition for the convergence to have the stationary solution.

Keywords: blunt body, finite volume, hypersonic flow, viscous flow

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Authors: F. J. Ma, A. K. H. Kwan

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Crack caused by shrinkage movement of concrete is a serious problem especially when restraint is provided. It may cause severe serviceability and durability problems. The existing prediction methods for crack width of concrete due to shrinkage movement are mainly numerical methods under simplified circumstances, which do not agree with each other. To get a more unified prediction method applicable to more sophisticated circumstances, finite element crack width analysis for shrinkage effect should be developed. However, no existing finite element analysis can be carried out to predict the crack width of concrete due to shrinkage movement because of unsolved reasons of conventional finite element analysis. In this paper, crack width analysis implemented by finite element analysis is presented with pseudo-discrete crack model, which combines traditional smeared crack model and newly proposed crack queuing algorithm. The proposed pseudo-discrete crack model is capable of simulating separate and single crack without adopting discrete crack element. And the improved finite element analysis can successfully simulate the stress redistribution when concrete is cracked, which is crucial for predicting crack width, crack spacing and crack number.

Keywords: crack queuing algorithm, crack width analysis, finite element analysis, shrinkage effect

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Authors: Sifeddine Abderrahmani, Sonia Bouafia

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The finite element method is the most practical tool for the analysis of structures, whatever the geometrical shape and behavior. It is extensively used in many high-tech industries, such as civil or military engineering, for the modeling of bridges, motor bodies, fuselages, and airplane wings. Additionally, experience demonstrates that engineers like modeling their structures using the most basic finite elements. Numerous models of finite elements may be utilized in the numerical analysis depending on the interpolation field that is selected, and it is generally known that convergence to the proper value will occur considerably more quickly with a good displacement pattern than with a poor pattern, saving computation time. The method for creating finite elements using the strain approach (S.B.A.) is presented in this presentation. When the results are compared with those provided by equivalent displacement-based elements, having the same total number of degrees of freedom, an excellent convergence can be obtained through some application and validation tests using recently developed membrane elements, plate bending elements, and flat shell elements. The effectiveness and performance of the strain-based finite elements in modeling structures are proven by the findings for deflections and stresses.

Keywords: finite elements, plate bending, strain approach, displacement formulation, shell element

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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: Akif Kutlu, Merve Ermis, Nihal Eratlı, Mehmet H. Omurtag

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The objective of this study is to investigate the forced vibration analysis of a planar curved beam lying on elastic foundation by using the mixed finite element method. The finite element formulation is based on the Timoshenko beam theory. In order to solve the problems in frequency domain, the element matrices of two nodded curvilinear elements are transformed into Laplace space. The results are transformed back to the time domain by the well-known numerical Modified Durbin’s transformation algorithm. First, the presented finite element formulation is verified through the forced vibration analysis of a planar curved Timoshenko beam resting on Winkler foundation and the finite element results are compared with the results available in the literature. Then, the forced vibration analysis of a planar curved beam resting on Winkler-Pasternak foundation is conducted.

Keywords: curved beam, dynamic analysis, elastic foundation, finite element method

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Authors: Aamir Mubashar, Ibrahim Fiaz

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This research presents a three-dimensional finite element modelling strategy to simulate damage in a quasi-static three-point bending analysis of woven twill 2/2 type carbon fibre reinforced plastic (CFRP) composite on a micro-meso level using cohesive zone modelling technique. A meso scale finite element model comprised of a number of plies was developed in the commercial finite element code Abaqus/explicit. The interfaces between the plies were explicitly modelled using cohesive zone elements to allow for debonding by crack initiation and propagation. Load-deflection response of the CRFP within the quasi-static range was obtained and compared with the data existing in the literature. This provided validation of the model at the global scale. The outputs resulting from the global model were then used to develop a simulation model capturing the micro-meso scale material features. The sub-model consisted of a refined mesh representative volume element (RVE) modelled in texgen software, which was later embedded with cohesive elements in the finite element software environment. The results obtained from the developed strategy were successful in predicting the overall load-deflection response and the damage in global and sub-model at the flexure limit of the specimen. Detailed analysis of the effects of the micro-scale features was carried out.

Keywords: woven composites, multi-scale modelling, cohesive zone, finite element model

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Authors: Tawanda Mushiri, Charles Mbohwa

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The performance of door assembly is very significant for the vehicle design. In the present paper, the finite element method is used in the development processes of the door assembly. The stiffness, strength, modal characteristic, and anti-extrusion of a newly developed passenger vehicle door assembly are calculated and evaluated by several finite element analysis commercial software. The structural problems discovered by FE analysis have been modified and finally achieved the expected door structure performance target of this new vehicle. The issue in focus is to predict the performance of the door assembly by powerful finite element analysis software, and optimize the structure to meet the design targets. It is observed that this method can be used to forecast the performance of vehicle door efficiently when it’s designed. In order to reduce lead time and cost in the product development of vehicles more development will be made virtually.

Keywords: vehicle door, structure, strength, stiffness, modal characteristic, anti-extrusion, Finite Element Method

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Authors: Utkan Caliskan

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Two types of numerical codes based on finite volume method are developed in order to solve compressible Euler equations to simulate the flow through forward facing step channel. Both algorithms have AUSM+- up (Advection Upstream Splitting Method) scheme for flux splitting and two-stage Runge-Kutta scheme for time stepping. In this study, the flux calculations differentiate between the algorithm based on OpenFOAM mesh format which is called 'face-based' algorithm and the basic algorithm which is called 'element-based' algorithm. The face-based algorithm avoids redundant flux computations and also is more flexible with hybrid grids. Moreover, some of OpenFOAM’s preprocessing utilities can be used on the mesh. Parallelization of the face based algorithm for which atomic operations are needed due to the shared memory model, is also presented. For several mesh sizes, 2.13x speed up is obtained with face-based approach over the element-based approach.

Keywords: cell centered finite volume method, compressible Euler equations, OpenFOAM mesh format, OpenMP

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Authors: Adel. M. Sharaf, Foad H. Gandoman

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Nowadays, Photovoltaic-PV Farms/ Parks and large PV-Smart Grid Interface Schemes are emerging and commonly utilized in Renewable Energy distributed generation. However, PV-hybrid-Dc-Ac Schemes using interface power electronic converters usually has negative impact on power quality and stabilization of modern electrical network under load excursions and network fault conditions in smart grid. Consequently, robust FACTS based interface schemes are required to ensure efficient energy utilization and stabilization of bus voltages as well as limiting switching/fault onrush current condition. FACTS devices are also used in smart grid-Battery Interface and Storage Schemes with PV-Battery Storage hybrid systems as an elegant alternative to renewable energy utilization with backup battery storage for electric utility energy and demand side management to provide needed energy and power capacity under heavy load conditions. The paper presents a robust interface PV-Li-Ion Battery Storage Interface Scheme for Distribution/Utilization Low Voltage Interface using FACTS stabilization enhancement and dynamic maximum PV power tracking controllers. Digital simulation and validation of the proposed scheme is done using MATLAB/Simulink software environment for Low Voltage- Distribution/Utilization system feeding a hybrid Linear-Motorized inrush and nonlinear type loads from a DC-AC Interface VSC-6-pulse Inverter Fed from the PV Park/Farm with a back-up Li-Ion Storage Battery.

Keywords: AC FACTS, smart grid, stabilization, PV-battery storage, Switched Filter-Compensation (SFC)

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Authors: Dhruv Mehta, Alexander van Zuijlen, Hester Bijl

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Large Eddy Simulation (LES) numerically resolves the large energy-containing eddies of a turbulent flow, while modelling the small dissipative eddies. On a wind farm, these large scales carry the energy wind turbines extracts and are also responsible for transporting the turbines’ wakes, which may interact with downstream turbines and certainly with the atmospheric boundary layer (ABL). In this situation, it is important to conserve the energy that these wake’s carry and which could be altered artificially through numerical dissipation brought about by the schemes used for the spatial discretisation and temporal integration. Numerical dissipation has been reported to cause the premature recovery of turbine wakes, leading to an over prediction in the power produced by wind farms.An energy-conserving scheme is free from numerical dissipation and ensures that the energy of the wakes is increased or decreased only by the action of molecular viscosity or the action of wind turbines (body forces). The aim is to create an LES package with energy-conserving schemes to simulate wind turbine wakes correctly to gain insight into power-production, wake meandering etc. Such knowledge will be useful in designing more efficient wind farms with minimal wake interaction, which if unchecked could lead to major losses in energy production per unit area of the wind farm. For their research, the authors intend to use the Energy-Conserving Navier-Stokes code developed by the Energy Research Centre of the Netherlands.

Keywords: energy-conserving schemes, modelling turbulence, Large Eddy Simulation, atmospheric boundary layer

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Authors: K. Noah, F.-S. Lien

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In Computational Fluid Dynamics (CFD), there are a variety of numerical methods, of which some depend on macroscopic model representatives. These models can be solved by finite-volume, finite-element or finite-difference methods on a microscopic description. However, the lattice Boltzmann method (LBM) is considered to be a mesoscopic particle method, with its scale lying between the macroscopic and microscopic scales. The LBM works well for solving incompressible flow problems, but certain limitations arise from solving compressible flows, particularly at high Mach numbers. An improved lattice Boltzmann model for compressible flow problems is presented in this research study. A higher-order Taylor series expansion of the Maxwell equilibrium distribution function is used to overcome limitations in LBM when solving high-Mach-number flows. Large eddy simulation (LES) is implemented in LBM to simulate turbulent jet flows. The results have been validated with available experimental data for turbulent compressible free jet flow at subsonic speeds.

Keywords: compressible lattice Boltzmann method, multiple relaxation times, large eddy simulation, turbulent jet flows

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Authors: A. M. Sagir

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This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y^'''= f(x,y,y^',y^'' ), y(α)=y_0,〖y〗^' (α)=β,y^('' ) (α)=μ with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non-stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: block method, hybrid, linear multistep, self-starting, third order ordinary differential equations

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Authors: Thomas Rowan, Mohammed Seaid

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A fast finite volume solver for multi-layered shallow water flows with mass exchange and an erodible bed is developed. This enables the user to solve a number of complex sediment-based problems including (but not limited to), dam-break over an erodible bed, recirculation currents and bed evolution as well as levy and dyke failure. This research develops methodologies crucial to the under-standing of multi-sediment fluvial mechanics and waterway design. In this model mass exchange between the layers is allowed and, in contrast to previous models, sediment and fluid are able to transfer between layers. In the current study we use a two-step finite volume method to avoid the solution of the Riemann problem. Entrainment and deposition rates are calculated for the first time in a model of this nature. In the first step the governing equations are rewritten in a non-conservative form and the intermediate solutions are calculated using the method of characteristics. In the second stage, the numerical fluxes are reconstructed in conservative form and are used to calculate a solution that satisfies the conservation property. This method is found to be considerably faster than other comparative finite volume methods, it also exhibits good shock capturing. For most entrainment and deposition equations a bed level concentration factor is used. This leads to inaccuracies in both near bed level concentration and total scour. To account for diffusion, as no vertical velocities are calculated, a capacity limited diffusion coefficient is used. The additional advantage of this multilayer approach is that there is a variation (from single layer models) in bottom layer fluid velocity: this dramatically reduces erosion, which is often overestimated in simulations of this nature using single layer flows. The model is used to simulate a standard dam break. In the dam break simulation, as expected, the number of fluid layers utilised creates variation in the resultant bed profile, with more layers offering a higher deviation in fluid velocity . These results showed a marked variation in erosion profiles from standard models. The overall the model provides new insight into the problems presented at minimal computational cost.

Keywords: erosion, finite volume method, sediment transport, shallow water equations

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Authors: Ekin Ozer

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Assessment of structural reliability is essential for efficient use of civil infrastructure which is subjected hazardous events. Dynamic analysis of finite element models is a commonly used tool to simulate structural behavior and estimate its performance accordingly. However, theoretical models purely based on preliminary assumptions and design drawings may deviate from the actual behavior of the structure. This study proposes up-to-date reliability estimation procedures which engages actual bridge vibration data modifying finite element models for finite element model updating and performing reliability estimation, accordingly. The proposed method utilizes vibration response measurements of bridge structures to identify modal parameters, then uses these parameters to calibrate finite element models which are originally based on design drawings. The proposed method does not only show that reliability estimation based on updated models differs from the original models, but also infer that non-updated models may overestimate the structural capacity.

Keywords: earthquake engineering, engineering vibrations, reliability estimation, structural health monitoring

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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: Chung-Nan Lee, Sheng-Wei Chu, You-Chiun Wang

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LTE (Long Term Evolution) employs the eMBMS (evolved Multimedia Broadcast/Multicast Service) protocol to deliver video streams to a multicast group of users. However, it requires all multicast members to receive a video stream in the same transmission rate, which would degrade the overall service quality when some users encounter bad channel conditions. To overcome this problem, this paper provides two efficient resource allocation schemes in such LTE network: The symbol synchronization (S2) scheme assumes that the macro and pico eNodeBs use the same frequency channel to deliver the video stream to all users. It then adopts a multicast transmission index to guarantee the fairness among users. On the other hand, the resource reuse (R2) scheme allows eNodeBs to transmit data on different frequency channels. Then, by introducing the concept of frequency reuse, it can further improve the overall service quality. Extensive simulation results show that the S2 and R2 schemes can respectively improve around 50% of fairness and 14% of video quality as compared with the common maximum throughput method.

Keywords: LTE networks, multicast, resource allocation, layered video

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Authors: Hudson Akewe

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This research presents complementary results with wider applications on convergence and rate of convergence of classical fixed point theory in Banach spaces to the world of the theory of fixed points of mappings defined in classes of spaces of measurable functions, known in the literature as modular function spaces. The study gives a comprehensive survey of various iterative fixed point results for the classes of multivalued ρ-contractive-like, ρ-quasi-contractive-like, ρ-quasi-contractive, ρ-Zamfirescu and ρ-contraction mappings in the framework of modular function spaces. An example is presented to demonstrate the applicability of the implicit-type iterative schemes to the system of ordinary differential equations. Furthermore, numerical examples are given to show the rate of convergence of the various explicit Kirk-type and implicit Kirk-type iterative schemes under consideration. Our results complement the results obtained on normed and metric spaces in the literature. Also, our methods of proof serve as a guide to obtain several similar improved results for nonexpansive, pseudo-contractive, and accretive type mappings.

Keywords: implicit Kirk-type iterative schemes, multivalued mappings, convergence results, fixed point

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Authors: Rilwan Kayode Apalowo, Dimitrios Chronopoulos

Abstract:

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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