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  • Open Access

    ARTICLE

    Numerical Solution for a Class of Linear System of Fractional Differential Equations by the Haar Wavelet Method and the Convergence Analysis

    Yiming Chen1, Xiaoning Han1, Lechun Liu 1

    CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.5, pp. 391-405, 2014, DOI:10.3970/cmes.2014.097.391

    Abstract In this paper, a class of linear system of fractional differential equations is considered. It has been solved by operational matrix of Haar wavelet method which converts the problem into algebraic equations. Moreover the convergence of the method is studied, and three numerical examples are provided to demonstrate the accuracy and efficiency. More >

  • Open Access

    ARTICLE

    Forced Vibrations of a System Consisting of a Pre-strained Highly Elastic Plate under Compressible Viscous Fluid Loading

    S. D. Akbarov1,2, M. I. Ismailov3

    CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.4, pp. 359-390, 2014, DOI:10.3970/cmes.2014.097.359

    Abstract The forced vibration of the system consisting of the pre-stretched plate made of highly-elastic material and half-plane filled by barotropic compressible Newtonian viscous fluid is considered. It is assumed that this forced vibration is caused by the lineal located time-harmonic force acting on the free face plane of the plate. The motion of the pre-stretched plate is written by utilizing of the linearized exact equations of the theory of elastic waves in the initially stressed bodies, but the motion of the compressible viscous fluid is described by the linearized Navier-Stokes equations. The elastic relations of the plate material are described… More >

  • Open Access

    ARTICLE

    An Incremental Kriging Method for Sequential Optimal Experimental Design

    Yaohui Li1,2, Yizhong Wu1,3, Zhengdong Huang1

    CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.4, pp. 323-357, 2014, DOI:10.3970/cmes.2014.097.323

    Abstract Kriging model, which provides an exact interpolation and minimizes the error estimates, is a highly-precise global approximation model in contrast with other traditional response surfaces. Therefore, sequential exploratory experimental design (SEED) with Kriging model is crucial for globally approximating a complex black-box function. However, the more sampling points are, the longer time it would take to update the Kriging model during sequential exploratory design. This paper, therefore, proposes a new construction method called incremental Kriging method (IKM) to improve the constructing efficiency with just a little and controllable loss of accuracy for Kriging model. The IKM, based on the matrix… More >

  • Open Access

    ARTICLE

    Differential Quadrature and Cubature Methods for Steady-State Space-Fractional Advection-Diffusion Equations

    Guofei Pang1, Wen Chen1,2, K.Y. Sze3

    CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.4, pp. 299-322, 2014, DOI:10.3970/cmes.2014.097.299

    Abstract Space-fractional advection-diffusion equation is a promising tool to describe the solute anomalous transport in underground water, and it has been extended to multi-dimensions with the help of weighted, fractional directional diffusion operator [Benson, Wheatcraft and Meerschaert (2000)]. Due to the nonlocal property of the space-fractional derivative, it is always a challenge to develop an efficient numerical solution method. The present paper extends the polynomialbased differential quadrature and cubature methods to the solution of steady-state spatial fractional advection-diffusion equations on a rectangular domain. An improved differential cubature method is proposed which accelerates the solution process considerably. Owing to the global interpolation… More >

  • Open Access

    ARTICLE

    A Solution Procedure for a Vibro-Impact Problem under Fully Correlated Gaussian White Noises

    H.T. Zhu 1

    CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.3, pp. 281-298, 2014, DOI:10.3970/cmes.2014.097.281

    Abstract This study is concerned with a solution procedure to obtain the probability density function (PDF) of a vibro-impact Duffing oscillator under fully correlated external and parametric Gaussian white noises. The proposed solution procedure consists of three steps. In the first step, the Zhuravlev non-smooth coordinate transformation is adopted to introduce an additional impulsive damping term, in which the original vibro-impact oscillator is converted into a new oscillator without any barrier. After that, the PDF of the new oscillator is obtained by solving the Fokker-Planck equation with the exponential-polynomial closure method. Last, the PDF of the original oscillator is formulated in… More >

  • Open Access

    ARTICLE

    A State Space Differential Reproducing Kernel Method for the Buckling Analysis of Carbon Nanotube-Reinforced Composite Circular Hollow Cylinders

    Chih-Ping Wu1,2, Ruei-Yong Jiang1

    CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.3, pp. 239-279, 2014, DOI:10.3970/cmes.2014.097.239

    Abstract A state space differential reproducing kernel (DRK) method is developed for the three-dimensional (3D) buckling analysis of simply-supported, carbon nanotube-reinforced composite (CNTRC) circular hollow cylinders and laminated composite ones under axial compression. The single-walled carbon nanotubes (CNTs) and polymer are used as the reinforcements and matrix, respectively, to constitute the CNTRC cylinder. Three different distributions of CNTs varying in the thickness direction are considered (i.e., the uniform distribution and functionally graded rhombus-, and X-type ones), and the through-thickness distributions of effective material properties of the cylinder are determined using the rule of mixtures. The 3D linear buckling theory is used,… More >

  • Open Access

    ARTICLE

    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

    ARTICLE

    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

    ARTICLE

    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

    ARTICLE

    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 >

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