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  • Open Access


    A New Approach to a Fuzzy Time-Optimal Control Problem

    Ş. Emrah Amrahov1, N. A. Gasilov2, A. G. Fatullayev2

    CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.5, pp. 351-369, 2014, DOI:10.3970/cmes.2014.099.351

    Abstract In this paper, we present a new approach to a time-optimal control problem with uncertainties. The dynamics of the controlled object, expressed by a linear system of differential equations, is assumed to be crisp, while the initial and final phase states are fuzzy sets. We interpret the problem as a set of crisp problems. We introduce a new notion of fuzzy optimal time and transform its calculation to two classical time-optimal control problems with initial and final sets. We examine the proposed approach on an example which is a problem of fuzzy control of mathematical pendulum. More >

  • Open Access


    A Novel Semi-Analytic Meshless Method for Solving Two- and Three-Dimensional Elliptic Equations of General Form with Variable Coefficients in Irregular Domains

    S.Yu. Reutskiy1

    CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.4, pp. 327-349, 2014, DOI:10.3970/cmes.2014.099.327

    Abstract The paper presents a new meshless numerical method for solving 2D and 3D boundary value problems (BVPs) with elliptic PDEs of general form. The coefficients of the PDEs including the main operator part are spatially dependent functions. The key idea of the method is the use of the basis functions which satisfy the homogeneous boundary conditions of the problem. This allows us to seek an approximate solution in the form which satisfies the boundary conditions of the initial problem with any choice of the free parameters. As a result we separate approximation of the boundary conditions and approximation of the… More >

  • Open Access


    Comparison of Four Multiscale Methods for Elliptic Problems

    Y. T. Wu1, Y. F. Nie2, Z. H. Yang1

    CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.4, pp. 297-325, 2014, DOI:10.3970/cmes.2014.099.297

    Abstract Four representative multiscale methods, namely asymptotic homogenization method (AHM), heterogeneous multiscale method (HMM), variational multiscale (VMS) method and multiscale finite element method (MsFEM), for elliptic problems with multiscale coefficients are surveyed. According to the features they possess, these methods are divided into two categories. AHM and HMM belong to the up–down framework. The feature of the framework is that the macroscopic solution is solved first with the help of effective information computed in local domains, and then the multiscale solution is resolved in local domains using the macroscopic solution when necessary. VMS method andMsFEM fall in the uncoupling framework. The… More >

  • Open Access


    Dynamic Anti-plane Crack Analysis in Functional Graded Piezoelectric Semiconductor Crystals

    J. Sladek1,2, V. Sladek1, E. Pan3, D.L. Young4

    CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.4, pp. 273-296, 2014, DOI:10.3970/cmes.2014.099.273

    Abstract This paper presents a dynamic analysis of an anti-plane crack in functionally graded piezoelectric semiconductors. General boundary conditions and sample geometry are allowed in the proposed formulation. The coupled governing partial differential equations (PDEs) for shear stresses, electric displacement field and current are satisfied in a local weak-form on small fictitious subdomains. The derived local integral equations involve one order lower derivatives than the original PDEs. All field quantities are approximated by the moving least-squares (MLS) scheme. After performing spatial integrations, we obtain a system of ordinary differential equations for the involved nodal unknowns. It is noted that the stresses… More >

  • Open Access


    Simulation of Stress Concentration Problems by Hexahedral Hybrid-Trefftz Finite Element Models

    F.L.S. Bussamra1, E.Lucena Neto1, W.M. Ponciano1

    CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.3, pp. 255-272, 2014, DOI:10.3970/cmes.2014.099.255

    Abstract Hybrid-Trefftz stress finite elements have been applied with success to the analysis of linear and non-linear problems in structural mechanics. Two independent fields are approximated: stresses within the elements and displacements on their boundary. The stress field satisfies the Trefftz constraint a priori, i.e., it is extracted from the Navier equation solution. This type of element has provided remarkable improvement in stress predictions compared to the standard displacement-based finite elements. In this work, solution of stress concentration problems is carried out by hexahedral hybrid-Trefftz stress element models. Stress concentration factors and stress intensity factors are then identified and compared with… More >

  • Open Access


    Long-term Analyses of Concrete-Filled Steel Tubular Arches Accounting for Interval Uncertainty

    Yong-Lin Pi1, Mark Andrew Bradford1

    CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.3, pp. 233-253, 2014, DOI:10.3970/cmes.2014.099.233

    Abstract Creep and shrinkage of the concrete core of a concrete-filled steel tubular (CFST) arch under sustained loading are inevitable, and cause a long-term change of the equilibrium configuration of the CFST arch. As the equilibrium configuration changes continuously, the long-term radial and axial displacements of the CFST arch, stress distributions as well as the internal forces in the steel tube and the concrete core change substantially with time. Creep and shrinkage of the concrete core are related to a number of its material parameters such as its creep coefficient, aging coefficient, and shrinkage strain. The values of these parameters differ… More >

  • Open Access


    Stochastic Finite Element Method Reliability Analysis of the Corrugated I-beam Girder

    Damian Sokolowski1, Marcin Kamiński2, Michal Strakowski1

    CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.3, pp. 209-231, 2014, DOI:10.3970/cmes.2014.099.209

    Abstract The main issue in this paper is to present stochastic analysis of the steel plate girder with the corrugated web subjected to Gaussian random fluctuations in its web thickness. Such an analysis is carried out using the Stochastic Finite Element Method based on the generalized stochastic perturbation technique and discretization of structure with the quadrilateral 4-noded shell finite elements. It is numerically implemented using the FEM system ABAQUS and the symbolic algebra system MAPLE, where all the probabilistic procedures are programmed. We compare the perturbation-based results with these obtained from traditional Monte-Carlo simulation and, separately, analytical solution calculated by a… More >

  • Open Access


    Large Eddy Simulation of Three Dimensional Impinging Jets

    Nadjib Ghiti1

    CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.3, pp. 195-208, 2014, DOI:10.3970/cmes.2014.099.195

    Abstract This paper presents a large eddy simulation of three dimensional vertically impinging jet on a horizontal plate. The air impinging jet was simulated using the perturbed method based on a high vortex number in the jet inlet for different ranges of Reynolds number Re= 6000, 8000, 10000, 12000, 14000 and for the same distance between the jet and the impinging plate. The effect of the Reynolds number of the air jet impinging on a horizontal plate was studied; the study showed that the vorticity magnitude is increased with the increasing of the Reynolds number. The turbulent flow jet was decomposed… More >

  • Open Access


    Solving the Cauchy Problem of the Nonlinear Steady-state Heat Equation Using Double Iteration Process

    Weichung Yeih1,2, I-Yao Chan1, Chia-Ming Fan1, Jiang-Jhy Chang1, Chein-Shan Liu3

    CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.2, pp. 169-194, 2014, DOI:10.3970/cmes.2014.099.169

    Abstract In this paper, the Cauchy inverse problem of the nonlinear steady-state heat equation is studied. The double iteration process is used to tackle this problem in which the outer loop is developed based on the residual norm based algorithm (RNBA) while the inner loop determines the evolution direction and the modified Tikhonov's regularization method (MTRM) developed by Liu (Liu, 2012) is adopted. For the conventional iteration processes, a fixed evolution direction such as F, B−1F, BTF or αF+(1-α)BTF is used where F is the residual vector, B is the Jacobian matrix, the superscript '-1' denotes the inverse, the superscript 'T'… More >

  • Open Access


    Pore-Scale Modeling of Navier-Stokes Flow in Distensible Networks and Porous Media

    Taha Sochi1

    CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.2, pp. 151-168, 2014, DOI:10.3970/cmes.2014.099.151

    Abstract In this paper, a pore-scale network modeling method, based on the flow continuity residual in conjunction with a Newton-Raphson non-linear iterative solving technique, is proposed and used to obtain the pressure and flow fields in a network of interconnected distensible ducts representing, for instance, blood vasculature or deformable porous media. A previously derived analytical expression correlating boundary pressures to volumetric flow rate in compliant tubes for a pressure-area constitutive elastic relation has been used to represent the underlying flow model. Comparison to a preceding equivalent method, the one-dimensional Navier-Stokes finite element, was made and the results were analyzed. The advantages… More >

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