Search results for: Numerical Modelling of Dry Stone Masonry Structures Based on Finite-Discrete Element Method

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

Abstract:

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: Lina Yan, Shiheng Wang, Ke Wang

Abstract:

A preconditioned Jacobi (PJ) method is provided for solving fuzzy linear systems whose coefficient matrices are crisp Mmatrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the preconditioned Jacobi method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.

Keywords: preconditioning, M-matrix, Jacobi method, fuzzy linear system (FLS).

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Authors: H. M. Mobarak, Helen Wu, Keqin Xiao

Abstract:

In this work, a three-dimensional finite element model was developed to investigate the crack breathing behavior at different crack locations considering the effect of unbalance force. A two-disk rotor with a crack is simulated using ABAQUS. The duration of each crack status (open, closed and partially open/closed) during a full shaft rotation was examined to analyse the crack breathing behavior. Unbalanced shaft crack breathing behavior was found to be different at different crack locations. The breathing behavior of crack along the shaft length is divided into different regions depending on the unbalance force and crack location. The simulated results in this work can be further utilised to obtain the time-varying stiffness matrix of the cracked shaft element under the influence of unbalance force.

Keywords: Crack breathing, crack location, slant crack, unbalance force, rotating shaft.

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Authors: N. A. Ibrahim, A. Kudus, I. Daud, M. R. Abu Bakar

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Competing risks survival data that comprises of more than one type of event has been used in many applications, and one of these is in clinical study (e.g. in breast cancer study). The decision tree method can be extended to competing risks survival data by modifying the split function so as to accommodate two or more risks which might be dependent on each other. Recently, researchers have constructed some decision trees for recurrent survival time data using frailty and marginal modelling. We further extended the method for the case of competing risks. In this paper, we developed the decision tree method for competing risks survival time data based on proportional hazards for subdistribution of competing risks. In particular, we grow a tree by using deviance statistic. The application of breast cancer data is presented. Finally, to investigate the performance of the proposed method, simulation studies on identification of true group of observations were executed.

Keywords: Competing risks, Decision tree, Simulation, Subdistribution Proportional Hazard.

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Authors: A. Suñol, D. Vucinic, S.Vanlanduit, T. Markova, A. Aksenov, I. Moskalyov

Abstract:

Feeder is one of the airships of the Multibody Advanced Airship for Transport (MAAT) system, under development within the EU FP7 project. MAAT is based on a modular concept composed of two different parts that have the possibility to join; respectively they are the so-called Cruiser and Feeder, designed on the lighter than air principle. Feeder, also named ATEN (Airship Transport Elevator Network), is the smaller one which joins the bigger one, Cruiser, also named PTAH (Photovoltaic modular Transport Airship for High altitude),envisaged to happen at 15km altitude. During the MAAT design phase, the aerodynamic studies of the both airships and their interactions are analyzed. The objective of these studies is to understand the aerodynamic behavior of all the preselected configurations, as an important element in the overall MAAT system design. The most of these configurations are only simulated by CFD, while the most feasible one is experimentally analyzed in order to validate and thrust the CFD predictions. This paper presents the numerical and experimental investigation of the Feeder “conical like" shape configuration. The experiments are focused on the aerodynamic force coefficients and the pressure distribution over the Feeder outer surface, while the numerical simulation cover also the analysis of the velocity and pressure distribution. Finally, the wind tunnel experiment is compared with its CFD model in order to validate such specific simulations with respective experiments and to better understand the difference between the wind tunnel and in-flight circumstances.

Keywords: MAAT project Feeder, CFD simulations, wind tunnel experiments, lateral wind influence.

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Authors: Susmita Sahoo, Madhumanti Datta, Rajib Kar

Abstract:

Fast delay estimation methods, as opposed to simulation techniques, are needed for incremental performance driven layout synthesis. On-chip inductive effects are becoming predominant in deep submicron interconnects due to increasing clock speed and circuit complexity. Inductance causes noise in signal waveforms, which can adversely affect the performance of the circuit and signal integrity. Several approaches have been put forward which consider the inductance for on-chip interconnect modelling. But for even much higher frequency, of the order of few GHz, the shunt dielectric lossy component has become comparable to that of other electrical parameters for high speed VLSI design. In order to cope up with this effect, on-chip interconnect has to be modelled as distributed RLCG line. Elmore delay based methods, although efficient, cannot accurately estimate the delay for RLCG interconnect line. In this paper, an accurate analytical delay model has been derived, based on first and second moments of RLCG interconnection lines. The proposed model considers both the effect of inductance and conductance matrices. We have performed the simulation in 0.18μm technology node and an error of as low as less as 5% has been achieved with the proposed model when compared to SPICE. The importance of the conductance matrices in interconnect modelling has also been discussed and it is shown that if G is neglected for interconnect line modelling, then it will result an delay error of as high as 6% when compared to SPICE.

Keywords: Delay Modelling; On-Chip Interconnect; RLCGInterconnect; Ramp Input; Damping; VLSI

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Authors: Min Wang , Shuyuan Yang

Abstract:

The paper presents a method of designing ultrawide band (UWB) pulse array beamformer in the case of nearfield. Firstly the principle of space-time processing of UWB pulse array is discussed. The radical beampattern transform based on spherical coordinates is employed to solve the nearfield beamforming of UWB pulse array. The frequency invariant technology is considered for the frequency dependent beampattern of UWB pulse array. We use a multirate bank scheme of to implement the FI beamformer of UWB pulse array. By using multirate filters in each element channel, it can make the response of the UWB array to avoid distortion in the whole band. The simulation resultes are given to prove the efficiency and feasibility of this method.

Keywords: UWB pulse array, frequency invariant, multiratebank, nearfield beamformer, radical transform

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Authors: Jafar Biazar, Behzad Ghanbari

Abstract:

In this paper, we are concerned with the further study for system of nonlinear equations. Since systems with inaccurate function values or problems with high computational cost arise frequently in science and engineering, recently such systems have attracted researcher-s interest. In this work we present a new method which is independent of function evolutions and has a quadratic convergence. This method can be viewed as a extension of some recent methods for solving mentioned systems of nonlinear equations. Numerical results of applying this method to some test problems show the efficiently and reliability of method.

Keywords: System of nonlinear equations.

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Authors: Prasun Hajra, Ranjan Dasgupta

Abstract:

Petri Net being one of the most useful graphical tools for modelling complex asynchronous systems, we have used Petri Net to model multi-track railway level crossing system. The roadway has been augmented with four half-size barriers. For better control, a three stage control mechanism has been introduced to ensure that no road-vehicle is trapped on the level crossing. Timed Petri Net is used to include the temporal nature of the signalling system. Safeness analysis has also been included in the discussion section.

Keywords: Modelling, Timed Petri Net, Railway Level Crossing, Safeness Condition.

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Authors: Henri Champliaud, Zhengkun Feng, Ngan Van Lê, Javad Gholipour

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In this article, a method is presented to effectively estimate the deformed shape of a thick plate due to line heating. The method uses a fifth order spline interpolation, with up to C3 continuity at specific points to compute the shape of the deformed geometry. First and second order derivatives over a surface are the resulting parameters of a given heating line on a plate. These parameters are determined through experiments and/or finite element simulations. Very accurate kriging models are fitted to real or virtual surfaces to build-up a database of maps. Maps of first and second order derivatives are then applied on numerical plate models to evaluate their evolving shapes through a sequence of heating lines. Adding an optimization process to this approach would allow determining the trajectories of heating lines needed to shape complex geometries, such as Francis turbine blades.

Keywords: Deformation, kriging, fifth order spline interpolation, first, second and third order derivatives, C3 continuity, line heating, plate forming, thermal forming.

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Authors: Mahmoud Roushdy, Mohamed El Naggar, Ahmed Yehia Abdelaziz

Abstract:

Anchored sheet pile has been used worldwide as front quay walls for decades. With the increase in vessel drafts and weights, those sheet pile walls need to be upgraded by increasing the depth of the dredging line in front of the wall. One of the upgrades for the sheet pile wall is to add a separated platform to the system, where the platform is structurally separated from the front wall. The platform is structurally separated from the front wall. This paper presents a numerical investigation utilizing finite element analysis on the behavior of separated relieve platforms installed within existing anchored sheet pile quay walls. The investigation was done in two steps: a verification step followed by a parametric study. In the verification step, the numerical model was verified based on field measurements performed by others. The validated model was extended within the parametric study to a series of models with different backfill soils, separation gap width, and number of pile rows supporting the platform. The results of the numerical investigation show that using stiff clay as backfill soil (neglecting consolidation) gives better performance for the front wall and the first pile row adjacent to sandy backfills. The degree of compaction of the sandy backfill slightly increases lateral deformations but reduces bending moment acting on pile rows, while the effect is minor on the front wall. In addition, the increase in the separation gap width gradually increases bending moments on the front wall regardless of the backfill soil type, while this effect is reversed on pile rows (gradually decrease). Finally, the paper studies the possibility of deepening the basin along with the separation to take advantage of the positive separation effect on piles, and front wall.

Keywords: Anchored sheet pile, relieving platform, separation gap, upgrade quay wall.

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Authors: Ali Raad Hassan, G. Thanigaiyarasu, V. Ramamurti

Abstract:

Natural frequencies and dynamic response of a spur gear sector are investigated using a two dimensional finite element model that offers significant advantages for dynamic gear analyses. The gear teeth are analyzed for different operating speeds. A primary feature of this modeling is determination of mesh forces using a detailed contact analysis for each time step as the gears roll through the mesh. Transient mode super position method has been used to find horizontal and vertical components of displacement and dynamic stress. The finite element analysis software ANSYS has been used on the proposed model to find the natural frequencies by Block Lanczos technique and displacements and dynamic stresses by transient mode super position method. A comparison of theoretical (natural frequency and static stress) results with the finite element analysis results has also been done. The effect of rotational speed of the gears on the dynamic response of gear tooth has been studied and design limits have been discussed.

Keywords: Natural frequency, Modal and transientanalysis, Spur gear, Dynamic stress.

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Authors: A. M. Tahsini

Abstract:

Computational study of two dimensional supersonic reacting hydrogen-air flows is performed to investigate the nitrogen effects on ignition delay time for premixed and diffusion flames. Chemical reaction is treated using detail kinetics and the advection upstream splitting method is used to calculate the numerical inviscid fluxes. The results show that just in stoichiometric condition for both premixed and diffusion flames, there is monotone dependency of the ignition delay time to the nitrogen addition. In other situations, the optimal condition from ignition viewpoint should be found using numerical investigations.

Keywords: Diffusion flame, Ignition delay time, Mixing layer, Numerical simulation, Premixed flame, Supersonic flow.

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Authors: Smarajit Ghosh , Karma Sonam Sherpa

Abstract:

This paper reports a new and accurate method for load-flow solution of radial distribution networks with minimum data preparation. The node and branch numbering need not to be sequential like other available methods. The proposed method does not need sending-node, receiving-node and branch numbers if these are sequential. The proposed method uses the simple equation to compute the voltage magnitude and has the capability to handle composite load modelling. The proposed method uses the set of nodes of feeder, lateral(s) and sub lateral(s). The effectiveness of the proposed method is compared with other methods using two examples. The detailed load-flow results for different kind of load-modellings are also presented.

Keywords: Load−flow, Feeder, Lateral, Power, Voltage, Composite, Exponential

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Authors: M. Chaichanyut, S. Tungjitkusolmun

Abstract:

This paper is concerned with microwave (MW) ablation for a liver cancer tissue by using helix antenna. The antenna structure supports the propagation of microwave energy at 2.45 GHz. A 1½ turn spiral catheter-based microwave antenna applicator has been developed. We utilize the three-dimensional finite element method (3D FEM) simulation to analyze where the tissue heat flux, lesion pattern and volume destruction during MW ablation. The configurations of helix antenna where Helix air-core antenna and Helix Dielectric-core antenna. The 3D FEMs solutions were based on Maxwell and bio-heat equations. The simulation protocol was power control (10 W, 300s). Our simulation result, both helix antennas have heat flux occurred around the helix antenna and that can be induced the temperature distribution similar (teardrop). The region where the temperature exceeds 50°C the microwave ablation was successful (i.e. complete destruction). The Helix air-core antenna and Helix Dielectric-core antenna, ablation zone or axial ratios (Widest/length) were respectively 0.82 and 0.85; the complete destructions were respectively 4.18 cm³ and 5.64 cm³

Keywords: Liver cancer, Helix antenna, Finite element, Microwave ablation.

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Authors: Zarina Bibi Ibrahim, Mohamed Suleiman, Khairil Iskandar Othman

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In this paper, a direct method based on variable step size Block Backward Differentiation Formula which is referred as BBDF2 for solving second order Ordinary Differential Equations (ODEs) is developed. The advantages of the BBDF2 method over the corresponding sequential variable step variable order Backward Differentiation Formula (BDFVS) when used to solve the same problem as a first order system are pointed out. Numerical results are given to validate the method.

Keywords: Backward Differentiation Formula, block, secondorder.

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Authors: M. M. Toufigh, A. R. Ahangarasr, A. Ouria

Abstract:

Among many different methods that are used for optimizing different engineering problems mathematical (numerical) optimization techniques are very important because they can easily be used and are consistent with most of engineering problems. Many studies and researches are done on stability analysis of three dimensional (3D) slopes and the relating probable slip surfaces and determination of factors of safety, but in most of them force equilibrium equations, as in simplified 2D methods, are considered only in two directions. In other words for decreasing mathematical calculations and also for simplifying purposes the force equilibrium equation in 3rd direction is omitted. This point is considered in just a few numbers of previous studies and most of them have only given a factor of safety and they haven-t made enough effort to find the most probable slip surface. In this study shapes of the slip surfaces are modeled, and safety factors are calculated considering the force equilibrium equations in all three directions, and also the moment equilibrium equation is satisfied in the slip direction, and using nonlinear programming techniques the shape of the most probable slip surface is determined. The model which is used in this study is a 3D model that is composed of three upper surfaces which can cover all defined and probable slip surfaces. In this research the meshing process is done in a way that all elements are prismatic with quadrilateral cross sections, and the safety factor is defined on this quadrilateral surface in the base of the element which is a part of the whole slip surface. The method that is used in this study to find the most probable slip surface is the non-linear programming method in which the objective function that must get optimized is the factor of safety that is a function of the soil properties and the coordinates of the nodes on the probable slip surface. The main reason for using non-linear programming method in this research is its quick convergence to the desired responses. The final results show a good compatibility with the previously used classical and 2D methods and also show a reasonable convergence speed.

Keywords: Non-linear programming, numerical optimization, slope stability, 3D analysis.

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Authors: S. N. Deepa, G. Sugumaran

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This paper proposes a new algebraic scheme to design a PID controller for higher order linear time invariant continuous systems. Modified PSO (MPSO) based model order formulation techniques have applied to obtain the effective formulated second order system. A controller is tuned to meet the desired performance specification by using pole-zero cancellation method. Proposed PID controller is attached with both higher order system and formulated second order system. The closed loop response is observed for stabilization process and compared with general PSO based formulated second order system. The proposed method is illustrated through numerical example from literature.

Keywords: Higher order systems, model order formulation, modified particle swarm optimization, PID controller, pole-zero cancellation.

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Authors: Thanh-Phong Dao, Shyh-Chour Huang

Abstract:

This study presents a quasi-zero stiffness (QZS) vibration isolator using flexure-based spring mechanisms which afford both negative and positive stiffness elements, which enable self-adjustment. The QZS property of the isolator is achieved at the equilibrium position. A nonlinear mathematical model is then developed, based on the pre-compression of the flexure-based spring mechanisms. The dynamics are further analyzed using the Harmonic Balance method. The vibration attention efficiency is illustrated using displacement transmissibility, which is then compared with the corresponding linear isolator. The effects of parameters on performance are also investigated by numerical solutions. The flexure-based spring mechanisms are subsequently designed using the concept of compliant mechanisms, with evaluation by ANSYS software, and simulations of the QZS isolator.

Keywords: Vibration isolator, quasi-zero stiffness, flexure-based spring mechanisms, compliant mechanism.

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Authors: Zuodong Liang, Dong-Sheng Jeng

Abstract:

Seabed instability around an offshore pipeline is one of key factors that need to be considered in the design of offshore infrastructures. Unlike previous investigations, a three-dimensional numerical model for the wave-induced soil response around an offshore pipeline is proposed in this paper. The numerical model was first validated with 2-D experimental data available in the literature. Then, a parametric study will be carried out to examine the effects of wave, seabed characteristics and confirmation of pipeline. Numerical examples demonstrate significant influence of wave obliquity on the wave-induced pore pressures and the resultant seabed liquefaction around the pipeline, which cannot be observed in 2-D numerical simulation.

Keywords: Pore pressure, 3D wave model, seabed liquefaction, pipeline.

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Authors: Seong Do Kim, Woo Young Jung

Abstract:

Recently, damages due to typhoons and strong wind are on the rise. Considering this issue, we evaluated the performance of soundproofing walls based on the strong wind fragility by means of numerical analysis. Among the components of the soundproof wall, aluminum frame was the most vulnerable member, thus we have considered different section of aluminum frame in the determination of wind fragility. Wind load was randomly generated using Monte Carlo Simulation method. Moreover, limit state was based on the test standard of road construction soundproofing wall. In this study, the strong wind fragility was determined by considering the influence factors of wind exposure category, soundproof wall’s installation position, and shape of aluminum frame section. Results of this study could be used to determine the section shape of the frame that has high resistance to the wind during construction of the soundproofing wall.

Keywords: Aluminum frame soundproofing wall, Monte Carlo Simulation, numerical simulation, wind fragility.

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Authors: Djamal Hamadi, Sifeddine Abderrahmani, Toufik Maalem, Oussama Temami

Abstract:

In recent years many finite elements have been developed for plate bending analysis. The formulated elements are based on the strain based approach. This approach leads to the representation of the displacements by higher order polynomial terms without the need for the introduction of additional internal and unnecessary degrees of freedom. Good convergence can also be obtained when the results are compared with those obtained from the corresponding displacement based elements, having the same total number of degrees of freedom. Furthermore, the plate bending elements are free from any shear locking since they converge to the Kirchhoff solution for thin plates contrarily for the corresponding displacement based elements. In this paper the efficiency of the strain based approach compared to well known displacement formulation is presented. The results obtained by a new formulated plate bending element based on the strain approach and Kirchhoff theory are compared with some others elements. The good convergence of the new formulated element is confirmed.

Keywords: Displacement fields, finite elements, plate bending, Kirchhoff theory, strain based approach.

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Authors: A. Ja, J. Belabid, A. Cheddadi

Abstract:

This paper reports the numerical simulation of doublediffusive natural convection flows within a horizontal annular filled with a saturated porous medium. The analysis concerns the influence of the different parameters governing the problem, namely, the Rayleigh number Ra, the Lewis number Le and the buoyancy ratio N, on the heat and mass transfer and on the flow structure, in the case of a fixed radius ratio R = 2. The numerical model used for the discretization of the dimensionless equations governing the problem is based on the finite difference method, using the ADI scheme. The study is focused on steady-state solutions in the cooperation situation.

Keywords: Natural convection, double-diffusion, porous medium, annular geometry, finite differences.

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Authors: Omid Sharifi, Member, ACM, Zeki Bayram, Member, ACM

Abstract:

We demonstrate through a sample application, Ebanking, that the Web Service Modelling Language Ontology component can be used as a very powerful object-oriented database design language with logic capabilities. Its conceptual syntax allows the definition of class hierarchies, and logic syntax allows the definition of constraints in the database. Relations, which are available for modelling relations of three or more concepts, can be connected to logical expressions, allowing the implicit specification of database content. Using a reasoning tool, logic queries can also be made against the database in simulation mode.

Keywords: Semantic web, ontology, E-banking, database, WSML, WSMO, E-R diagram.

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Authors: S. D. Nedelcut, V. Proca, D. M. Purcaru

Abstract:

At present, the tendency to implement the conditionbased maintenance (CBM), which allows the optimization of the expenses for equipment monitoring, is more and more evident; also, the transformer substations with remote monitoring are increasingly used. This paper reviews all the advantages of the on-line monitoring and presents an equipment for on-line monitoring of bushings, which is the own contribution of specialists who are the authors of this paper. The paper presents a study of the temperature field, using the finite element method. For carrying out this study, the 3D modelling of the above mentioned bushing was performed. The analysis study is done taking into account the extreme thermal stresses, focusing at the level of the first cooling wing section of the ceramic insulator. This fact enables to justify the tanδ variation in time, depending on the transformer loading and the environmental conditions. With a view to reducing the variation of dielectric losses in bushing insulation, the use of ferrofuids instead of mineral oils is proposed.

Keywords: Monitoring, dielectric losses, ferrofluids, bushing.

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Authors: Mohamed Omar

Abstract:

Superelastic Shape Memory Alloy (SMA) is accepted when it used as connection in steel structures. The seismic behaviour of steel frames with SMA is being assessed in this study. Three eightstorey steel frames with different SMA systems are suggested, the first one of which is braced with diagonal bracing system, the second one is braced with nee bracing system while the last one is which the SMA is used as connection at the plastic hinge regions of beams. Nonlinear time history analyses of steel frames with SMA subjected to two different ground motion records have been performed using Seismostruct software. To evaluate the efficiency of suggested systems, the dynamic responses of the frames were compared. From the comparison results, it can be concluded that using SMA element is an effective way to improve the dynamic response of structures subjected to earthquake excitations. Implementing the SMA braces can lead to a reduction in residual roof displacement. The shape memory alloy is effective in reducing the maximum displacement at the frame top and it provides a large elastic deformation range. SMA connections are very effective in dissipating energy and reducing the total input energy of the whole frame under severe seismic ground motion. Using of the SMA connection system is more effective in controlling the reaction forces at the base frame than other bracing systems. Using SMA as bracing is more effective in reducing the displacements. The efficiency of SMA is dependant on the input wave motions and the construction system as well.

Keywords: Finite element analysis, seismic response, shapesmemory alloy, steel frame, superelasticity

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Authors: Yasser R. Tawfic, Mohamed A. Eid

Abstract:

Foundation differential settlement and supported structure tilting are an occasionally occurred engineering problem. This may be caused by overloading, changes in ground soil properties or unsupported nearby excavations. Engineering thinking points directly toward the logic solution for such problem by uplifting the settled side. This can be achieved with deep foundation elements such as micro-piles and macro-piles™, jacked piers, and helical piers, jet grouted mortar columns, compaction grout columns, cement grouting or with chemical grouting, or traditional pit underpinning with concrete and mortar. Although, some of these techniques offer economic, fast and low noise solutions, many of them are quite the contrary. For tilted structures, with the limited inclination, it may be much easier to cause a balancing settlement on the less-settlement side which shall be done carefully in a proper rate. This principal has been applied in Leaning Tower of Pisa stabilization with soil extraction from the ground surface. In this research, the authors attempt to introduce a new solution with a different point of view. So, the micro-tunneling technique is presented in here as an intended ground deformation cause. In general, micro-tunneling is expected to induce limited ground deformations. Thus, the researchers propose to apply the technique to form small size ground unsupported holes to produce the target deformations. This shall be done in four phases: 1. Application of one or more micro-tunnels, regarding the existing differential settlement value, under the raised side of the tilted structure. 2. For each individual tunnel, the lining shall be pulled out from both sides (from jacking and receiving shafts) in the slow rate. 3. If required, according to calculations and site records, an additional surface load can be applied on the raised foundation side. 4. Finally, a strengthening soil grouting shall be applied for stabilization after adjustment. A finite element based numerical model is presented to simulate the proposed construction phases for different tunneling positions and tunnels group. For each case, the surface settlements are calculated and induced plasticity points are checked. These results show the impact of the suggested procedure on the tilted structure and its feasibility. Comparing results also show the importance of the position selection and tunnels group gradual effect. Thus, a new engineering solution is presented to one of the structural and geotechnical engineering challenges.

Keywords: Differential settlement, micro-tunnel, soil-structure interaction, tilted structures.

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Authors: Farnaz G. Nezami, Mir B. Aryanezhad, Seyed J. Sadjadi

Abstract:

In this paper a nonlinear model is presented to demonstrate the relation between production and marketing departments. By introducing some functions such as pricing cost and market share loss functions it will be tried to show some aspects of market modelling which has not been regarded before. The proposed model will be a constrained signomial geometric programming model. For model solving, after variables- modifications an iterative technique based on the concept of geometric mean will be introduced to solve the resulting non-standard posynomial model which can be applied to a wide variety of models in non-standard posynomial geometric programming form. At the end a numerical analysis will be presented to accredit the validity of the mentioned model.

Keywords: Geometric programming, marketing, nonlinear optimization, production.

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

Abstract:

In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: Dissipation, Oscillatory solutions, Phase-lag, Runge- Kutta methods.

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Authors: Shengfeng Li, Rujing Wang

Abstract:

In this paper, we present two new one-step iterative methods based on Thiele-s continued fraction for solving nonlinear equations. By applying the truncated Thiele-s continued fraction twice, the iterative methods are obtained respectively. Analysis of convergence shows that the new methods are fourth-order convergent. Numerical tests verifying the theory are given and based on the methods, two new one-step iterations are developed.

Keywords: Iterative method, Fixed-point iteration, Thiele's continued fraction, Order of convergence.

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