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  • Open Access


    Quasi-Conforming Triangular Reissner-Mindlin Shell Elements by Using Timoshenko's Beam Function

    Changsheng Wang1, Ping Hu1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.5, pp. 325-350, 2012, DOI:10.3970/cmes.2012.088.325

    Abstract Based on the Reissner-Mindlin plate theory, two 3-node triangular flat shell elements QCS31 and QCS32 are proposed by using Timoshenko's beam function within the framework of quasi-conforming technique. The exact displacement function of the Timoshenko's beam is used as the displacement on the element boundary in the bending part and the interpolated inner field function is also derived by the function. In the shear part the re-constitution technique is adopted. The drilling degrees of freedom are added in the membrane part to improve membrane behavior. The proposed elements can be used for the analysis of both moderately thick and thin… More >

  • Open Access


    A Multi-Scale Computational Method Integrating Finite Element Method with Atomic Interactions of Materials

    Bin Gu1,2,3, L. C. Zhang2, Weifeng Yuan1, Youjun Ning1

    CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.4, pp. 309-324, 2012, DOI:10.3970/cmes.2012.088.309

    Abstract Bridging the atomic and continuous analyses is an important aspect in multi-scale mechanics. This paper develops a computational method to integrate the atomic potential of a material with the finite element method. The novelty of this method is that strain energy is calculated from the atomic potential without the assumption in the Cauchy-Born rule that deformation in a virtual atomic cell is homogeneous. In this new method, the virtual atomic cell deformation is interpolated according to the continuum displacements associated with the shape functions. The applications of the method to single crystal Si and Ge bars under uniaxial tension and… More >

  • Open Access


    Prandtl Number Signature on Flow Patterns of Electrically Conducting Fluid in Square Enclosure

    Ridha Djebali1,2, Bernard Pateyron2, Mohamed El Ganaoui3

    CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.4, pp. 293-308, 2012, DOI:10.3970/cmes.2012.088.293

    Abstract We present in this study a numerical investigation of unsteady two-dimensional natural convection of an electrically conducting fluid in a square cavity under an externally imposed magnetic field. A temperature gradient is applied between the two opposing side walls parallel to y-direction, while the floor and ceiling parallel to x-direction are adiabatic. The flow is characterized by the Rayleigh number Ra raged in 103-106, the Prandtl number Pr ranged in 0.01-10, the Hartman number Ha determined by the strength of the imposed magnetic field ranged in 0-100 and its tilting angle from x-axis ranging from 0 to 90 . The… More >

  • Open Access


    A New Optimal Scheme for Solving Nonlinear Heat Conduction Problems

    Chih-Wen Chang1,2, Chein-Shan Liu3

    CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.4, pp. 269-292, 2012, DOI:10.3970/cmes.2012.088.269

    Abstract In this article, we utilize an optimal vector driven algorithm (OVDA) to cope with the nonlinear heat conduction problems (HCPs). From this set of nonlinear ordinary differential equations, we propose a purely iterative scheme and the spatial-discretization of finite difference method for revealing the solution vector x, without having to invert the Jacobian matrix D. Furthermore, we introduce three new ideas of bifurcation, attracting set and optimal combination, which are restrained by two parameters g and a. Several numerical instances of nonlinear systems under noise are examined, finding that the OVDA has a fast convergence rate, great computation accuracy and… More >

  • Open Access


    Robust Numerical Scheme for Singularly Perturbed Parabolic Initial-Boundary-Value Problems on Equidistributed Mesh

    Srinivasan Natesan1, S. Gowrisankar2

    CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.4, pp. 245-268, 2012, DOI:10.3970/cmes.2012.088.245

    Abstract In this article, we propose a parameter-uniform computational technique to solve singularly perturbed parabolic initial-boundary-value problems exhibiting parabolic layers. The domain is discretized with a uniform mesh on the time direction and a nonuniform mesh obtained via equidistribution of a monitor function for the spatial variable. The numerical scheme consists of the implicit-Euler scheme for the time derivative and the classical central difference scheme for the spatial derivative. Truncation error, and stability analysis are carried out. Error estimates are derived, and numerical examples are presented. More >

  • Open Access


    Haar Wavelet Operational Matrix Method for Solving Fractional Partial Differential Equations

    Mingxu Yi1, Yiming Chen1

    CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.3, pp. 229-244, 2012, DOI:10.3970/cmes.2012.088.229

    Abstract In this paper, Haar wavelet operational matrix method is proposed to solve a class of fractional partial differential equations. We derive the Haar wavelet operational matrix of fractional order integration. Meanwhile, the Haar wavelet operational matrix of fractional order differentiation is obtained. The operational matrix of fractional order differentiation is utilized to reduce the initial equation to a Sylvester equation. Some numerical examples are included to demonstrate the validity and applicability of the approach. More >

  • Open Access


    Natural Convection Flow and Heat Transfer in Square Enclosure Asymetrically Heated from Below: A Lattice Boltzmann Comprehensive Study

    Taoufik Naffouti1,2 and Ridha Djebali1,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.3, pp. 211-228, 2012, DOI:10.3970/cmes.2012.088.211

    Abstract This paper reports numerical results of natural convection flow evolving inside confined medium defined by two-dimensional square enclosure containing isothermal hot source placed asymmetrically at bottom wall. The sides-walls are isothermally cooled at a constant temperature; however the ceiling and the rest of bottom wall are insulated. The lattice Boltzmann method is used to solve the dimensionless governing equations with the associated boundary conditions. The flow is monitored by the Grashof number and the Prandtl number taken here 0.71. Numerical simulations are performed to study the effects of Grashof number ranging from 104 to 106, hot source length from 0.1… More >

  • Open Access


    Numerical Investigation on Direct MLPG for2D and 3D Potential Problems

    Annamaria Mazzia1, Giorgio Pini1, Flavio Sartoretto2

    CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.3, pp. 183-210, 2012, DOI:10.3970/cmes.2012.088.183

    Abstract Pure meshless techniques are promising methods for solving Partial Differential Equations (PDE). They alleviate difficulties both in designing discretization meshes, and in refining/coarsening, a task which is demanded e.g. in adaptive strategies. Meshless Local Petrov Galerkin (MLPG) methods are pure meshless techniques that receive increasing attention. Very recently, new methods, called Direct MLPG (DMLPG), have been proposed. They rely upon approximating PDE via the Generalized Moving Least Square method. DMLPG methods alleviate some difficulties of MLPG, e.g. numerical integration of tricky, non-polynomial factors, in weak forms. DMLPG techniques require lower computational costs respect to their MLPG counterparts. In this paper… More >

  • Open Access


    Use of Flow Simulation to Develop Robust Injection and Vent Schemes that Account for Process and Material Variability in Liquid Composite Molding Process

    J. Wang1, E. Andres, P. Simacek, S.G.Advani

    CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.3, pp. 155-182, 2012, DOI:10.3970/cmes.2012.088.155

    Abstract In Liquid Composite Molding (LCM) processes, the process design requires an infusion and venting scheme which will saturate all the empty spaces between the fibers during mold filling resulting in a composite part without voids. However, the inherent material and process variability can change the filling patterns significantly which complicate this task. The objective of this work is to develop methodologies and tools to automate infusion process design and integrate it within the CAD design environment. The methodologies and algorithms developed examine the designed part geometry and material layups for ease of manufacturing with feasible infusion schemes by accounting for… More >

  • Open Access


    Boundary Knot Method: An Overview and Some Novel Approaches

    J.Y. Zhang1, F.Z. Wang2,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.2, pp. 141-154, 2012, DOI:10.3970/cmes.2012.088.141

    Abstract The boundary knot method (BKM) is a kind of boundary-type meshless method, only boundary points are needed in the solution process. Since the BKM is mathematically simple and easy to implement, it is superior in dealing with Helmholtz problems with high wavenumbers and high dimensional problems. In this paper, we give an overview of the traditional BKM with collocation approach and provide three novel approaches for the BKM, as far as they are relevant for the other boundary-type techniques. The promising research directions are expected from an improved BKM aspect. More >

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