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  • Open Access

    ARTICLE

    The Finite Point Method for Reaction-Diffusion Systems in Developmental Biology

    Mehdi Tatari1, Maryam Kamranian2, Mehdi Dehghan2

    CMES-Computer Modeling in Engineering & Sciences, Vol.82, No.1, pp. 1-28, 2011, DOI:10.32604/cmes.2011.082.001

    Abstract In this paper, the finite point method (FPM) is presented for solving nonlinear reaction-diffusion systems which are often employed in mathematical modeling in developmental biology. In order to avoid directly solving a coupled nonlinear system, a predicator-corrector scheme is applied. The finite point method is a truly meshfree technique based on the combination of the moving least squares approximation on a cloud of points with the point collocation method to discretize the governing equations. The lack of dependence on a mesh or integration procedure is an important feature, which makes the FPM simple, efficient and applicable to solve nonlinear problems… More >

  • Open Access

    ARTICLE

    Iterative Solution of a System of Nonlinear Algebraic Equations F(x) = 0, Using x· = λ[αR + βP] or x· = λ[αF + βP] R is a Normal to a Hyper-Surface Function of F, P Normal to R, and P* Normal to F

    Chein-Shan Liu1,2, Hong-Hua Dai1, Satya N. Atluri1

    CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.3&4, pp. 335-363, 2011, DOI:10.3970/cmes.2011.081.335

    Abstract To solve an ill- (or well-) conditioned system of Nonlinear Algebraic Equations (NAEs): F(x) = 0, we define a scalar hyper-surface h(x,t) = 0 in terms of x, and a monotonically increasing scalar function Q(t) where t is a time-like variable. We define a vector R which is related to ∂h / ∂x, and a vector P which is normal to R. We define an Optimal Descent Vector (ODV): u = αR + βP where α and β are optimized for fastest convergence. Using this ODV [x· = λu], we derive an Optimal Iterative Algorithm (OIA) to solve F(x)More >

  • Open Access

    ARTICLE

    On application of the Stochastic Finite Volume Method in Navier-Stokes problems

    Marcin Kamiński1, Rafał Leszek Ossowski1

    CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.3&4, pp. 311-334, 2011, DOI:10.3970/cmes.2011.081.311

    Abstract The main aim of this article is numerical solution of the fully coupled Navier-Stokes equations with Gaussian random parameters. It is provided thanks to the specially adopted Finite Volume Method, modified using the generalized stochastic perturbation technique. This Stochastic Finite Volume Method is applied to model 3D problem with uncertainty in liquid viscosity and a coefficient of the heat conduction, separately. Probabilistic moments and characteristics of up to the fourth order are determined with the use of the Response Function Method realized numerically via the polynomial inpterpolation. Although mathematical formulation of the SFVM has been proposed in addition to the… More >

  • Open Access

    ARTICLE

    Computation of the time-dependent Green's function of three dimensional elastodynamics in 3D quasicrystals

    V.G. Yakhno1, H.Çerdik Yaslan2

    CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.3&4, pp. 295-310, 2011, DOI:10.3970/cmes.2011.081.295

    Abstract The time-dependent differential equations of elasticity for 3D quasicrystals are considered in the paper. These equations are written in the form of a vector partial differential equation of the second order with symmetric matrix coefficients. The Green's function is defined for this vector partial differential equation. A new method of the numerical computation of values of the Green's function is proposed. This method is based on the Fourier transformation and some matrix computations. Computational experiments confirm the robustness of our method for the computation of the time-dependent Green's function in icosahedral quasicrystals. More >

  • Open Access

    ARTICLE

    A Hybrid of Interval Wavelets and Wavelet Finite Element Model for Damage Detection in Structures

    Jiawei Xiang1, Toshiro Matsumoto2, Yanxue Wang3, Zhansi Jiang4

    CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.3&4, pp. 269-294, 2011, DOI:10.3970/cmes.2011.081.269

    Abstract Damages occurred in a structure will lead to changes in modal parameters (natural frequencies and modal shapes). The relationship between modal parameters and damage parameters (locations and depths) is very complicated. Single detection method using natural frequencies or modal shapes can not obtain robust damage detection results from the inevitably noise-contaminated modal parameters. To eliminate the complexity, a hybrid approach using both of wavelets on the interval (interval wavelets) method and wavelet finite element model-based method is proposed to detect damage locations and depths. To avoid the boundary distortion phenomenon, Interval wavelets are employed to analyze the finite-length modal shape… More >

  • Open Access

    ARTICLE

    Unified Dispersion Characteristics of Structural Acoustic Waveguides

    Abhijit Sarkar1, M. V. Kunte2, Venkata R. Sonti2

    CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.3&4, pp. 249-268, 2011, DOI:10.3970/cmes.2011.081.249

    Abstract In this article, we show with some formalism that infinite flexible structural acoustic waveguides have a general form for the dispersion equation. The dispersion equation of all such waveguides should conform to a generic form. This allows us to bring out the common features of structural acoustic waveguides. We take three examples to demonstrate this fact, namely, the rectangular, the circular cylindrical and the elliptical geometries. Where necessary, the equations are simplified for applicability to a particular frequency-regime before demonstrating the conformance to the generic form of the dispersion relation. It is then shown that the coupled wavenumber solutions of… More >

  • Open Access

    ARTICLE

    Numerical Analysis of Concrete Composites at the Mesoscale Based on 3D Reconstruction Technology of X-ray CT Images

    C.B. Du1,2, S.Y Jiang2, W. Qin3, Y.M. Zhang2

    CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.3&4, pp. 229-248, 2011, DOI:10.3970/cmes.2011.081.229

    Abstract A numerical analysis of concrete composites at the mesoscale based on three-dimensional (3D) reconstruction technology of X-ray computed tomography (CT) images is presented in this paper. For X-ray CT images of concrete, morphology processing was used to recover complete image information, including borders, and the median filtering method was applied to eliminate potential impurities in the images. The final X-ray CT images obtained after processing for a concrete section were composed of three-value pixels that indicated aggregate particles, mortar matrix and air voids, and the 3D structure of the concrete specimen was reconstructed using the volume data method. The mapping… More >

  • Open Access

    ARTICLE

    A Further Study on Using x· = λ[αR + βP] (P = F − R(F·R) / ||R||2) and x· = λ[αF + βP] (P = R − F(F·R) / ||F||2) in Iteratively Solving the Nonlinear System of Algebraic Equations F(x) = 0

    Chein-Shan Liu1,2, Hong-Hua Dai1, Satya N. Atluri1

    CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.2, pp. 195-228, 2011, DOI:10.3970/cmes.2011.081.195

    Abstract In this continuation of a series of our earlier papers, we define a hyper-surface h(x,t) = 0 in terms of the unknown vector x, and a monotonically increasing function Q(t) of a time-like variable t, to solve a system of nonlinear algebraic equations F(x) = 0. If R is a vector related to ∂h / ∂x, , we consider the evolution equation x· = λ[αR + βP], where P = F − R(F·R) / ||R||2 such that P·R = 0; or x· = λ[αF + βP], where P = R − F(F·R) / ||F||2 such that P*·F =… More >

  • Open Access

    ARTICLE

    On Shear Locking in MLPG Solid-Shell Approach

    T. Jarak1, J. Sorić1

    CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.2, pp. 157-194, 2011, DOI:10.3970/cmes.2011.081.157

    Abstract A solid-shell MLPG approach for the numerical analysis of plates and shells is presented. A special attention is devoted to the transversal shear locking effect that appears in the structure thin limit. The theoretical origins of shear locking in the purely displacement-based approach are analyzed by means of the consistency paradigm. It is shown that the spurious constraints appear in the constrained strain field, which lead to the appearance of shear locking and sub-optimal convergence rates. The behaviour of the mixed MLPG approach in the thin limit is also considered. It is determined that in the mixed paradigm the Kirchhoff-Love… More >

  • Open Access

    ARTICLE

    Coupled Wavenumbers in an Infinite Flexible Fluid-Filled Circular Cylindrical Shell : Comparison between Different Shell Theories

    M. V. Kunte1, Venkata R. Sonti1

    CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.2, pp. 119-156, 2011, DOI:10.3970/cmes.2011.081.119

    Abstract Analytical expressions are found for the wavenumbers in an infinite flexible in vacuo / fluid-filled circular cylindrical shell based on different shell-theories using asymptotic methods. Donnell-Mushtari theory (the simplest shell theory) and four higher order theories, namely Love-Timoshenko, Goldenveizer-Novozhilov, Flügge and Kennard-simplified are considered. Initially, in vacuo and fluid-coupled wavenumber expressions are presented using the Donnell-Mushtari theory. Subsequently, the wavenumbers using the higher order theories are presented as perturbations on the Donnell-Mushtari wavenumbers. Similarly, expressions for the resonance frequencies in a finite shell are also presented, using each shell theory. The basic differences between the theories being what they are,… More >

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