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This paper deals with the numerical investigation of ellipticity of the boundary value problem for isothermal finite strain elasto-plasticity. Ellipticity can be lost when softening occurs. A discontinuity surface then appears in the considered material body and this is associated with the ill-posedness of the boundary value problem. In the paper the condition for ellipticity loss is derived using the deformation gradient and the first Piola-Kirchhoff stress tensor. Next, the obtained condition is implemented and numerically tested within symbolic-numerical tools AceGen and AceFEM using the benchmark of an elongated rectangular plate with imperfection in plane stress and plane strain conditions. [ABSTRACT FROM AUTHOR]

The main purpose of the suspension system is to absorb the vibrations from wheels. To compromise between the two conflicting criteria i.e. road holding and ride comfort, passive suspension system is most suitable. The passenger discomfort is caused due to unwanted vibrations which are transmitted through unsprung mass. The numerical analysis using Simulink MATLAB software is used to determine Ride comfort of two suspension systems based on quarter car model. The experimental setup is developed and vibration analysis is performed using multichannel FFT analyser. The mathematical analysis result of the two different models of the suspensions is compared with experimental analysis. The aim of paper is to investigate effect of sprung mass on ride comfort at constant speed with input 0.1m peak stroke which generated a waveform resembling to half sine wave. The mathematical model is developed and analysed in Simulink MATLAB software. [ABSTRACT FROM AUTHOR]

The main aim of this paper is an experimental and numerical analysis of the dynamic behavior of an active rotor with three composite blades. The study focuses on developing an effective FE modeling technique of a macro fiber composite element (denoted as MFC or active element) for the dynamic tests of active structures. The active rotor under consideration consists of a hub with a drive shaft, three grips and three glass-epoxy laminate blades with embedded active elements. A simplified FE model of the macro fiber composite element exhibiting the d33 piezoelectric effect is developed using the Abaqus software package. The discussed transducer is modeled as quasi-homogeneous piezoelectric material, and voltage is applied to the opposite faces of the element. In this case, the effective (equivalent) piezoelectric constant d33 * is specified. Both static and dynamic tests are performed to verify the proposed model. First, static deflections of the active blade caused by the voltage signal are determined by numerical and experimental analyses. Next, a numerical modal analysis of the active rotor is performed. The eigenmodes and corresponding eigenfrequencies are determined by the Lanczos method. The influence of the model parameters (i.e., the effective piezoelectric constant d33 *, voltage signal, angular velocity) on the dynamics of the active rotor is examined. Finally, selected numerical results are validated in experimental tests. The experimental findings demonstrate that the structural stiffening effect caused by the active element strongly depends on the value of the effective piezoelectric constant. [ABSTRACT FROM AUTHOR]

In this paper, we consider some aspects of the numerical analysis of the mathematical model of fractional Duffing with a derivative of variable fractional order of the Riemann-Liouville type. Using numerical methods: an explicit finite-difference scheme based on the Grunwald-Letnikov and Adams-Bashford-Moulton approximations (predictor-corrector), the proposed numerical model is found. These methods have been verified with a test case. It is shown that the predictor-corrector method has a faster convergence than the method according to the explicit finite-difference scheme. For these schemes, using Runge's rule, estimates of the computational accuracy were made, which tended to unity with an increase in the number of calculated grid nodes. [ABSTRACT FROM AUTHOR]

An application of small aerial vehicles is described in this paper which presents an optimization of the camber position ever-changing using models and numerical analysis. During this study, the mechanics performance of a wing must be investigated over a profile of camber of 20 percent length of the chord from edge. The model was initially modelled using a software package and by adjusting the morphing wing system's modularity and reconfigurability. The angle of attack is also explored following a comparative analysis of the mechanics parameters. A considerable effect of morphing flap camber profiles on mechanics performance is observed in the results. As a supplementary validation, we provide an analysis of wind characteristics through ANSYS; we obtain the pressure coefficients, lift (CL), drag (CD), and lift-to-drag ratio (CL/ CD). The correlation between the CL, (CL/CD) and drag cut back simulations for several preferred shapes is analyzed when getting the results. For that reason forward in optimizing the cambered profile when morphing edges because the mathematical analysis associated with it has been shown improvements in CL from 15% to 30% when morphing edges. [ABSTRACT FROM AUTHOR]

Carl David Tolmé Runge was a German mathematician. In 1895 he brought about a revolution in the science of what has become numerical analysis. Numerical approximation to the solution of ordinary differential equations had been based on the method of Euler. but it suffered from a low convergence rate. Runge's discovery in his 1895 paper brought the so-called order from 1 up to 2. This development was followed within a few years by extensions of his techniques which brought the possible order up to 4. The analysis of order conditions for early work on Runge-Kutta methods was based on the use of a scalar test problem y' = f (x, y), but for high order method derivations and other applications, it is appropriate to use instead an autonomous high dimensional test problem y' = f (y). Because of the special requirements of stiff problems, implicit Runge-Kutta methods have an importance of their own and these developments are briefly surveyed. The intricate manipulations required to analyse the order of complicated methods has lead to an algebraic theory and its formulation as B-series. Finally, the special applications to structure-preserving algorithms are introduced. [ABSTRACT FROM AUTHOR]

In this paper, the simple fractional iterative differential equation will be the focus of study Dβv(s) = vn(s); v(s0) = a: where s0; v0 ∈ I = [0, b], and 0 < β < 1. One class of the iterative fractional differential equations is the simple iterative fractional differential equation. In this paper, the local existence and uniqueness results for the fractional order of degree n of simple iterative fractional differential equation are proven and the solutions found by using power series. [ABSTRACT FROM AUTHOR]

The paper proposes an approach to determining the boundary of possible impact loads for a gasturbine locomotive cab involved in the collision with an obstacle, which would allow the cab to retain its necessary durability. This boundary defines the region of safe operation for the locomotive cab considering various parameters of locomotive movement. If the parameters of the movement and the obstacle lie within the region, the safety of personnel and equipment in the cab will be provided. [ABSTRACT FROM AUTHOR]

The adjoint method is usually used to identify uncertain parameters in large-scale shallow water flow models. This requires the implementation of the adjoint model, which is huge programming effort. The work presented in this paper is based on stochastic simultaneous perturbation of all model parameters to generate a search direction and avoids the implementation of the adjoint of the original nonlinear model. The SPSA based calibration approach has been implemented for the estimation of the depth values in a shallow sea model of the entire European continental shelf. The results demonstrate that the SPSA method give comparable results to steepest descent method with little computational cost. [ABSTRACT FROM AUTHOR]

The paper proposes a numerical investigation based on RANS computation for solving the viscous flow around a ship podded propulsion unit. A set of computations has been performed to better understand the influences exerted by different configurations on the wake structure in the propeller disk in the pushing type case. The RANS computation method is employed to evaluate the flow field structure around the podded propulsion units and the forces acting on it. Hydrodynamic design podded system has not, so far, been fully established in the propeller-pod-strut system. It is necessary to use a reliable procedure in the design of such propulsion systems to increase the propulsion efficiency. In an attempt to meet these needs, the present paper introduces a numerical procedure to analyze the hydrodynamic performance of the propeller and steering system using a combined lifting line and RANS methods. [ABSTRACT FROM AUTHOR]

This paper deals with stability in the numerical solution of general one-dimensional partial differential equations with variable coefficients. We will generalize stability results for central finite difference schemes on non-uniform grids that were obtained by In’t Hout & Volders (2009) for the Black-Scholes equation. Subsequently we will apply our stability results to the CEV model. [ABSTRACT FROM AUTHOR]

In this paper, we established some new integral inequalities of Hadamard-type for co-ordinated convex functions by using a new integral identity and fairly elementary analysis. [ABSTRACT FROM AUTHOR]

The paper presents a numerical analysis of the class of mathematical models of linear fractional oscillators, which is the Cauchy problem for a differential equation with derivatives of fractional orders in the sense of Gerasimov-Caputo. A method based on an explicit nonlocal finite-difference scheme (ENFDS) and the Adams-Bashfort-Moulton (ABM) method are considered as tools for numerical analysis. An analysis of the errors of the methods is carried out, it is shown that the ABM method is more accurate and converges faster to an exact solution than the ENFDS method. [ABSTRACT FROM AUTHOR]

The paper presents a practical implementation of hybrid simulation using Real Time Finite Element Method (RTFEM). Hybrid simulation is a technique for investigating dynamic material and structural properties of mechanical systems by performing numerical analysis and experiment at the same time. It applies to mechanical systems with elements too difficult or impossible to model numerically. These elements are tested experimentally, while the rest of the system is simulated numerically. Data between the experiment and numerical simulation are exchanged in real time. Authors use Finite Element Method to perform the numerical simulation. The following paper presents the general algorithm for hybrid simulation using RTFEM and possible improvements of the algorithm for computation time reduction developed by the authors. The paper focuses on practical implementation of presented methods, which involves testing of a mountain bicycle frame, where the shock absorber is tested experimentally while the rest of the frame is simulated numerically. [ABSTRACT FROM AUTHOR]

The paper considers the influence of the assumed error indicator on the final adapted mesh. Provided that threshold values of an error are increased by applying the adaptive procedure, it turns out that final mesh depends on the assumed error indicator. In the paper, there were used the standard error estimates and the error indicator proposed by the author. The proposed error indicator is based on applying hierarchically generalized finite difference method (FDM). In the case of the proposed error indicator, the final adapted mesh is the most optimal for the exact solution. [ABSTRACT FROM AUTHOR]

In this paper, we define bi-periodic Fibonacci and Lucas polynomials and investigate properties of these polynomials which generalized of bi-periodic Fibonacci and Lucas numbers. We also obtain some new algebraic properties on these numbers and polynomials. [ABSTRACT FROM AUTHOR]

In this paper we present a new numerical method for solving fractional differential equations (FDEs) based on Genocchi polynomials operational matrix through collocation method. The operational matrix of fractional integration in Riemann-Liouville sense is derived. The upper bound for the error of the operational matrix of fractional integration is also shown. The properties of Genocchi polynomials are utilized to reduce the given problems to a system of algebraic equations. Illustrative examples are finally given to show the simplicity, accuracy and applicability of the method. [ABSTRACT FROM AUTHOR]

In this paper we present and discuss some new developments of Hardy-type inequalities, namely to derive (a) Hardy-type inequalities via a convexity approach, (b) refined scales of Hardy-type inequalities with other 'breaking points' than p = 1 via superquadratic and superterzatic functions, (c) scales of conditions to characterize modern forms of weighted Hardy-type inequalities. [ABSTRACT FROM AUTHOR]

This paper discusses a discretisation scheme which is based on point collocation and integrated radial basis function networks (IRBFNs) for the solution of elliptic differential equations (DEs). The use of IRBFNs to represent the field variable in a given DE gives several advantages over the case of using conventional RBFNs and polynomials. Some numerical examples are included for demonstration purposes. [ABSTRACT FROM AUTHOR]

Two-dimensional, time-dependent, reactive Navier—Stokes equations involving the effects of viscosity, thermal conduction, molecular diffusion and turbulence etc. were solved to obtain a deep insight into gaseous detonation vortex-like structures and its induced mechanism. Detailed chemical reaction model, together with standard κ-[variant_greek_epsilon] turbulence model, was employed in this paper. Numerical simulation indicates that a large amount of vortex-like structure emerges in detonation flow field due to its intrinsic three-dimensional structure. Vortex-like structure can also be induced by wall geometry with an abrupt cross-section area change. Shock wave interacts with slip line, which in turn causes the formation of vortex-like structure. In nature, all these induce the instability of slip line, so it is the slip line instability that is the essential reason for the emergence of vortex-like structure. Additionally, the difference of vortex-like structure between an ordinary detonation and a marginal detonation was compared. In an ordinary detonation, the vorticity magnitude of vortex-like structure is different, even for two vortex-like structures in the same pair. With increasing the distance away from leading front, the vorticity magnitude gradually decays. Slip line in a marginal detonation is more unstable and produces more vortex-like structures. [ABSTRACT FROM AUTHOR]

In this paper we discuss solutions in Casoratian form for H1, which is the simplest member in ABS list of lattice equations. By investigating the condition satisfied by the Casoratian basic column we propose a generalization, which yields solutions which are different form solitons. These solutions can be considered as limit solutions of solitons. Similar generalizations can apply to other lattice equations in ABS list, such as H2, H3 and Q1. [ABSTRACT FROM AUTHOR]

Generation scheduling is a crucial challenge in power systems especially under new environment of liberalization of electricity industry. A new Lagrangian relaxation method for unit commitment (UC) has been presented for solving generation scheduling problem. This paper focuses on the economical aspect of UC problem, while the previous hour scheduling as a very important issue is studied. In this paper generation scheduling of present hour has been conducted by considering the previous hour scheduling. The impacts of hot/cold start-up cost have been taken in to account in this paper. Case studies and numerical analysis presents significant outcomes while it demonstrates the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We investigated certain kinds of vertex correlation in networks formed by traces of random walkers. In this paper, the sign of correlation between degree and local clustering on adjacent vertices is interpreted based on the capacity for new creation of links for highly connected vertices. These interpretations are consistent with numerical simulation of network evolution. Other types of correlation can be related with each other. It is interesting that the local rules of network evolution determined by the movement of random walkers naturally provide large clustering coefficients and various finite vertex correlations. [ABSTRACT FROM AUTHOR]

Asymmetric Incremental Forming exalts the advantages of Incremental Forming process since no dies are strictly necessary. In this way complex geometries may be manufactured with a very simple clamping equipment. On the other hand, this characteristic determines some intrinsic drawbacks which penalise its industrial suitability; first of all, the dimensional control of the manufactured part is a still open point for researchers all over the world. Several approaches have been already proposed in the last years to solve the problem, resulting only in partial solutions. At the same time, up to now, the numerical simulation did not supply significant aid to the designers, due to the problem complexity and the very long simulation time when an elasto-plastic analysis has to be carried out. For this reason an experimental trial and error approach is often preferred. An innovative approach is represented by the application of numerical analysis based on a coupled explicit-implicit formulation. In this paper, some results of a wide research on the application of explicit-implicit code for the dimensional accuracy analysis are proposed. Both the problems related to the dimensional accuracy and springback phenomenon after the manufacturing step and the trimming operation are analysed from an experimental and a numerical point of view. In this way, some relevant issues, as well as the FEM capability, have been derived by the comparisons with the experiments. All the details are widely discussed in the paper. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

The crucial task in the prevention of ductile fracture is the availability of a tool for the prediction of such defect occurrence. The technical literature presents a wide investigation on this topic and many contributions have been given by many authors following different approaches. The main class of approaches regards the development of fracture criteria: generally, such criteria are expressed by determining a critical value of a damage function which depends on stress and strain paths: ductile fracture is assumed to occur when such critical value is reached during the analysed process. There is a relevant drawback related to the utilization of ductile fracture criteria; in fact each criterion usually has good performances in the prediction of fracture for particular stress - strain paths, i.e. it works very well for certain processes but may provide no good results for other processes. On the other hand, the approaches based on damage mechanics formulation are very effective from a theoretical point of view but they are very complex and their proper calibration is quite difficult. In this paper, two different approaches are investigated to predict fracture occurrence in cold forming operations. The final aim of the proposed method is the achievement of a tool which has a general reliability i.e. it is able to predict fracture for different forming processes. The proposed approach represents a step forward within a research project focused on the utilization of innovative predictive tools for ductile fracture. The paper presents a comparison between an artificial neural network design procedure and an approach based on statistical tools; both the approaches were aimed to predict fracture occurrence/absence basing on a set of stress and strain paths data. The proposed approach is based on the utilization of experimental data available, for a given material, on fracture occurrence in different processes. More in detail, the approach consists in the analysis of experimental tests in which fracture occurs followed by the numerical simulations of such processes in order to track the stress-strain paths in the workpiece region where fracture is expected. Such data are utilized to build up a proper data set which was utilized both to train an artificial neural network and to perform a statistical analysis aimed to predict fracture occurrence. The developed statistical tool is properly designed and optimized and is able to recognize the fracture occurrence. The reliability and predictive capability of the statistical method were compared with the ones obtained from an artificial neural network developed to predict fracture occurrence. Moreover, the approach is validated also in forming processes characterized by a complex fracture mechanics. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

A cellular automation method is one of calculation methods, which allows for modeling of complex joint phenomena that take place in material during and after the deformation in the meso- and micro-scale. The phenomena, which can be taken into consideration with high precision, are processes connected with microstructure evolution. For modeling by cellular automata (CA) are mainly used two-dimensional ones, because of more expensive calculations by three-dimensional CA. But three-dimensional phenomena cannot be generally reduced to two-dimensional solution. In the paper a description of a modified three-dimensional CA is presented. The model of microstructure contains three parts: deformation of grains, recrystallization and grains growth after recrystallization. Recrystallization is considered as a process without division on the different kinds (dynamic, metadynamic or static). It consists of two stages: nucleation and new grains growth. Nucleation rate and grain growth rate are dependent on parameters of deformation. In the model such parameters as temperature, strain, strain rate, dislocation density, crystallographic orientation and some others are taken into account. Along with calculation of microstructure evolution, model allows for prediction of mechanical properties, for example flow stress. A flow stress calculations reckon processes of hardening and softening using model of the dislocation density development in consideration with an effect of the recrystallization. Some results of simulations based on 3D cellular automaton are presented in the paper. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

In forging process, formability is limited by ductile fracture. In many cases forgeability is determined by the occurrence of ductile fracture and therefore limitations are set by the appearance of surface or internal cracks within regions that are highly strained due to extensive material flow. In this paper, the continuum damage mechanics framework for ductile materials developed by Lemaitre has been utilized numerically. A constitutive elastic-plastic-damage model has been implemented inside the finite element code ABAQUS. In forming process, crack closure effects have a strong influence on damage evolution. Therefore, it is necessary to split the tensile and compression stresses in damage evolution and deal with them separately. A modified version of Lemaitre model has been implemented and utilized through the study. The prediction of the surface cracks in forging is analyzed numerically. The results could correctly predict the location of surface cracks in the forging process. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

This paper has tried to apply the response surface approximate method in the structural optimization techniques to develop aluminum beverage can ends. Geometrical parameters of the end shell are selected as design variables. The analysis points in the design space are assigned using an orthogonal array in the design-of-experiment technique. Finite element analysis code is used to simulate the deforming behavior and to calculate buckling strength and central panel displacement of the end shell under internal pressure. On the basis of the numerical analysis results, the response surface of the buckling strength and panel growth are approximated in terms of the design variables. By using a numerical optimization program, the weight of the end shell is minimized subject to constraints of the buckling strength, panel growth suppression and other design requirements. A numerical example on 202 end shell optimization problem has been shown in this paper. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

In this paper, several sufficient conditions were obtained for the normalized Wright functions to be in the new subclasses S*(α,β), K(α, β) and C(α, β), α, ∈ [ 0,1) of analytic functions in the open unit disk. [ABSTRACT FROM AUTHOR]

This paper deals with the implementation of a volume penalization technique in a lattice Boltzmann model, in order to compute flows around obstacles. The penalization term is introduced into the lattice Boltzmann equation via a forcing term. Numerical examples (flows over a square obstacle, and past a circular cylinder) show that a good agreement with results from the literature was obtained. [ABSTRACT FROM AUTHOR]

In this paper, we study the Fibonacci sequence and Pell sequence and developed generating matrices for them. First we proved two results on the even sum of the Fibonacci sequence and the Pell sequence, using the generating matrix approach. We then deduce the odd sums, some identities and recursive formulas for these two sequences. [ABSTRACT FROM AUTHOR]

This paper aims to propose a new method in decomposing ???? into circuits. Our method introduces two new strategies: Wing Strategy (WinS) and Endpoint Strategy (Endp-S). WinS contains first wing and second wing, while Endp-S contains first endpoint and second endpoint. The crucial task for generating circuits in WinS is two vertices of K4 are fixed to be the first wing, meanwhile in Endp-S, the vertices of the first wing are then put into the first endpoint, consecutively. Once the set of circuits are produced from these strategies, the drawing of that circuits can be obtained. [ABSTRACT FROM AUTHOR]

In this paper, a leader-following consensus on discrete time scales is investigated.We propose and prove conditions ensuring a leader-following consensus on an arbitrary time scale. The presented results are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

In this paper we are concerned with the predictor-corrector implementation of a class of numerical integrators which can be considered as energy-conserving variants of the Gauss collocation methods. [ABSTRACT FROM AUTHOR]

In this paper, a new Runge-Kutta-Nystro¨m (RKN) method of fourth algebraic order is constructed. The new method is based on Dormand's Runge-Kutta-Nystro¨m method of algebraic order four, by using the idea of phase-lag of order infinity, a new method for solving second-order ordinary differential equations (ODE) with oscillatory solutions is derived. Numerical tests show that the new method is more accurate than other existing methods that based on the minimal phase-lag theory. [ABSTRACT FROM AUTHOR]

The present paper is a continuation of our paper [4]. The problem to be studied is the non-impact of algebraic property on the convergence properties of the μ-th root base of special monogenic polynomials. These convergence properties are the investigation of the relation between the effectiveness in closed balls of a given base and that of its μ-th root base, and also the relation between their rate of increase. Our result which is concerned with effectiveness in closed balls is quite different from its corresponding one for the square root case in complex settings. [ABSTRACT FROM AUTHOR]

Recently, many documents or messages from an organization need to be signed by more than one person. For that reason, many threshold signatures based on various problems in number theory have been developed. In this paper, a threshold signature scheme based on two most popular number theory problems, namely factoring and discrete logarithms, was proposed. The advantage of this new scheme is based on the fact that it is very hard to solve both factoring and discrete logarithms problems simultaneously. This scheme is also shown secure against several attacks and requires a reasonable time complexity in both signing and verifying phase. [ABSTRACT FROM AUTHOR]

In this paper, we present a numerical scheme based on an adaptation of the standard homotopy-perturbation method (HPM) is applied to the Chaotic Ro¨ssler system. The standard HPM is converted into a hybrid numeric-analytic method called the multistage HPM (MHPM). Comparisons with the fourth-order Runge-Kutta method (RK4) and standard HPM show that the MHPM is a reliable method for nonlinear equations. [ABSTRACT FROM AUTHOR]

This paper presents a derivative-free nonmonotone hybrid tabu search to compute a solution of overdetermined systems of inequalities and equalities through the global optimization of an appropriate merit function. The proposed algorithm combines global and local searches aiming to reduce computational effort. Preliminary numerical results show the effectiveness of the combined heuristic. [ABSTRACT FROM AUTHOR]

In this paper, we investigate backward stochastic differential equations (BSDEs) driven by Brownian motion. We propose a class of Euler type numerical methods with one parameter based on random walk framework for one-dimensional Brownian motion. The convergence of such schemes is proved. [ABSTRACT FROM AUTHOR]