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  • Open Access


    On the (Meshless Local Petrov-Galerkin) MLPG-Eshelby Method in Computational Finite Deformation Solid Mechanics - Part II

    Z. D. Han1, S. N. Atluri2,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.3, pp. 199-237, 2014, DOI:10.3970/cmes.2014.097.199

    Abstract This paper presents a new method for the computational mechanics of large strain deformations of solids, as a fundamental departure from the currently popular finite element methods (FEM). The currently widely popular primal FEM: (1) uses element-based interpolations for displacements as the trial functions, and element-based interpolations of displacement-like quantities as the test functions; (2) uses the same type and class of trial & test functions, leading to a Galerkin approach; (3) uses the trial and test functions which are most often continuous at the inter-element boundaries; (4) leads to sparsely populated symmetric tangent stiffness matrices; (5) computes piecewise-linear predictor… More >

  • Open Access


    Enrichment Procedures for Soft Clusters: A Statistical Test and its Applications

    R.D. Phillips1, M.S. Hossain1, L.T. Watson1,2, R.H. Wynne3, Naren Ramakrishnan1

    CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.2, pp. 175-197, 2014, DOI:10.3970/cmes.2014.097.175

    Abstract Clusters, typically mined by modeling locality of attribute spaces, are often evaluated for their ability to demonstrate ‘enrichment’ of categorical features. A cluster enrichment procedure evaluates the membership of a cluster for significant representation in predefined categories of interest. While classical enrichment procedures assume a hard clustering definition, this paper introduces a new statistical test that computes enrichments for soft clusters. Application of the new test to several scientific datasets is given. More >

  • Open Access


    Frequency Domain Based Solution for Certain Class of Wave Equations: An exhaustive study of Numerical Solutions

    Vinita Chellappan1, S. Gopalakrishnan1 and V. Mani1

    CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.2, pp. 131-174, 2014, DOI:10.3970/cmes.2014.097.131

    Abstract The paper discusses the frequency domain based solution for a certain class of wave equations such as: a second order partial differential equation in one variable with constant and varying coefficients (Cantilever beam) and a coupled second order partial differential equation in two variables with constant and varying coefficients (Timoshenko beam). The exact solution of the Cantilever beam with uniform and varying cross-section and the Timoshenko beam with uniform cross-section is available. However, the exact solution for Timoshenko beam with varying cross-section is not available. Laplace spectral methods are used to solve these problems exactly in frequency domain. The numerical… More >

  • Open Access


    Novel Iterative Algorithms Based on Regularization Total Least Squares for Solving the Numerical Solution of Discrete Fredholm Integral Equation

    Zichun Yang1,2,3, Lei Zhang1,4, Yueyun Cao1

    CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.2, pp. 101-130, 2014, DOI:10.3970/cmes.2014.097.101

    Abstract Discretization of inverse problems often leads to systems of linear equations with a highly ill-conditioned coefficient matrix. To find meaningful solutions of such systems, one kind of prevailing and representative approaches is the so-called regularized total least squares (TLS) method when both the system matrix and the observation term are contaminated by some noises. We will survey two such regularization methods in the TLS setting. One is the iterative truncated TLS (TTLS) method which can solve a convergent sequence of projected linear systems generated by Lanczos bidiagonalization. The other one is to convert the Tikhonov regularization TLS problem to an… More >

  • Open Access


    Numerical Solution for the Variable Order Time Fractional Diffusion Equation with Bernstein Polynomials

    Yiming Chen1, Liqing Liu1, Xuan Li1 and Yannan Sun1

    CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.1, pp. 81-100, 2014, DOI:10.3970/cmes.2014.097.081

    Abstract In this paper, Bernstein polynomials method is proposed for the numerical solution of a class of variable order time fractional diffusion equation. Coimbra variable order fractional operator is adopted, as it is the most appropriate and desirable definition for physical modeling. The Coimbra variable order fractional operator can also be regarded as a Caputo-type definition. The main characteristic behind this approach in this paper is that we derive two kinds of operational matrixes of Bernstein polynomials. With the operational matrixes, the equation is transformed into the products of several dependent matrixes which can also be viewed as the system of… More >

  • Open Access


    Axisymmetric and 3-D Numerical Simulations of the Effects of a Static Magnetic Field on Dissolution of Silicon into Germanium

    F. Mechighel1,2,3, N. Armour4, S. Dost4, M. Kadja3

    CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.1, pp. 53-80, 2014, DOI:10.3970/cmes.2014.097.053

    Abstract Numerical simulations were carried out to explain the behavior exhibited in experimental work on the dissolution process of silicon into a germanium melt. The experimental work utilized a material configuration similar to that used in the Liquid Phase Diffusion (LPD) and Melt-Replenishment Czochralski (Cz) growth systems. The experimental dissolution system was modeled by considering axisymmetric and three-dimensional (3-D) domains. In both cases, the governing equations, namely conservation of mass, momentum balance, energy balance, and solute transport balance, were solved using the Finite Element Method.
    Measured concentration profiles and dissolution heights from the experiment samples showed that the application of a… More >

  • Open Access


    How to Select the Value of the Convergence Parameter in the Adomian Decomposition Method

    Lei Lu1,2, Jun-Sheng Duan2,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.1, pp. 35-52, 2014, DOI:10.3970/cmes.2014.097.035

    Abstract In this paper, we investigate the problem of selecting of the convergence parameter c in the Adomian decomposition method. Through the curves of the n-term approximations Φn(t;c) versus c for different specified values of n and t, we demonstrate how to determine the value of c such that the decomposition series has a larger effective region of convergence. More >

  • Open Access


    Eshelby Stress Tensor T: a Variety of Conservation Laws for T in Finite Deformation Anisotropic Hyperelastic Solid & Defect Mechanics, and the MLPG-Eshelby Method in Computational Finite Deformation Solid Mechanics-Part I

    Z. D. Han1, S. N. Atluri2,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.1, pp. 1-34, 2014, DOI:10.3970/cmes.2014.097.001

    Abstract The concept of a stress tensor [for instance, the Cauchy stress σ, Cauchy (1789-1857); the first Piola-Kirchhoff stress P, Piola (1794-1850), and Kirchhoff (1824-1889); and the second Piola-Kirchhoff stress, S] plays a central role in Newtonian continuum mechanics, through a physical approach based on the conservation laws for linear and angular momenta. The pioneering work of Noether (1882-1935), and the extraordinarily seminal work of Eshelby (1916- 1981), lead to the concept of an “energy-momentum tensor” [Eshelby (1951)]. An alternate form of the “energy-momentum tensor” was also given by Eshelby (1975) by taking the two-point deformation gradient tensor as an independent… More >

  • Open Access


    Global Approximation for a Simulation Model Based on the RBF Response Surface Set

    Yin Xiao-Liang1, Wu Yi-Zhong1,2, Wan Li1, Xiong Hui-Yuan3

    CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.6, pp. 429-462, 2014, DOI:10.3970/cmes.2014.103.429

    Abstract The use of multi-dimensional global approximation for a complex black-box function (such as a simulation or an analysis model) is steadily growing in the past decade. It can be applied in many fields such as parameter experiment, sensibility analyses real-time simulation, and design/control optimization. However, the widespread use of approximation methods is hampered by the lack of the ability to approximate a complex simulation model which characterizes the dynamic feature with multiple inputs and multiple outputs (MIMO) in a large domain. In this paper, a novel global approximation method for simulation models based on the RBF response surface set is… More >

  • Open Access


    Image Segmentation Method for Complex Vehicle Lights Based on Adaptive Significance Level Set

    Jia Dongyao1,2, Zhu Huaihua1, Ai Yanke1, Zou Shengxiong1

    CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.6, pp. 411-427, 2014, DOI:10.3970/cmes.2014.103.411

    Abstract The existing study on the image segmentation methods based on the image of vehicle lights is insufficient both at home and abroad, and its segmentation efficiency and accuracy is low as well. On the basis of the analysis of the regional characteristics of vehicle lights and a level set model, an image segmentation method for complex vehicle lights based on adaptive significance level set contour model is proposed in this paper. Adaptive positioning algorithm of the significant initial contour curve based on two-dimensional convex hull is designed to obtain the initial position of evolution curve, thus the adaptive ability of… More >

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