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    EDITORIAL

    Editorial

    S. N. Atluri1
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 1-4, 2003, DOI:10.3970/cmes.2003.004.001
    Abstract This article has no abstract. More >

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    939

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    ARTICLE

    On Simple Formulations of Weakly-Singular Traction & Displacement BIE, and Their Solutions through Petrov-Galerkin Approaches

    Z. D. Han1, S. N. Atluri1
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 5-20, 2003, DOI:10.3970/cmes.2003.004.005
    Abstract Using the directly derived non-hyper singular integral equations for displacement gradients [as in Okada, Rajiyah, and Atluri (1989a)], simple and straight-forward derivations of weakly singular traction BIE's for solids undergoing small deformations are presented. A large number of ``intrinsic properties'' of the fundamental solutions in elasticity are developed, and are used in rendering the tBIE and dBIE to be only weakly-singular, in a very simple manner. The solutions of the weakly singular tBIE and dBIE through either global Petrov-Galerkin type ``boundary element methods'', or, alternatively, through the meshless local Petrov-Galerkin (MLPG) methods, are discussed. As special cases, the Galerkin type… More >

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    1010

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    ARTICLE

    A Level Set Approach to Optimal Homogenized Coefficients

    Dongwoo Sheen1, Sangwon Seo2, Jinwoo Cho3
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 21-30, 2003, DOI:10.3970/cmes.2003.004.021
    Abstract The reconstructing optimal microstructures of given homogenized coefficients of steady diffusion equation is studied. In the reconstruction, the governing equation of level set function is approximated by adding viscosity term and the numerical procedure for the evolution of the level set function for the solution is examined. The numerical experiments of reconstruction are obtained by applying a finite element method with locally fitted mesh. More >

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    893

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    ARTICLE

    A New Application of the Panel Clustering Method for 3D SGBEM

    A. Aimi1, M. Diligenti1, F. Lunardini1, A. Salvadori2
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 31-50, 2003, DOI:10.3970/cmes.2003.004.031
    Abstract This paper is devoted to the study of a new application of the Panel Clustering Method [Hackbusch and Sauter (1993); Hackbusch and Nowak (1989)]. By considering a classical 3D Neumann screen problem in its boundary integral formulation discretized with the Galerkin BEM, which requires the evaluation of double integrals with hypersingular kernel, we recall and use some recent results of analytical evaluation of the inner hypersingular integrals. Then we apply the Panel Clustering Method (PCM) for the evaluation of the outer integral. For this approach error estimate is shown. Numerical examples and comparisons with classical PCM technique are presented. More >

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    929

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    ARTICLE

    Crack Propagation Modeling by Remeshing Using the Cell Method (CM)

    E. Ferretti1
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 51-72, 2003, DOI:10.3970/cmes.2003.004.051
    Abstract A numerical code for modeling crack propagation using the cell method is proposed. The Mohr-Coulomb criterion is used to compute the direction of crack propagation, and the new crack geometry is realized by an intra-element propagation technique. Automatic remeshing is then activated. Applications in Mode I and Mixed Mode are presented to illustrate the robustness of the implementation. More >

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    919

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    ARTICLE

    Performance Computations and Design Criterion of Airfoils in Unsteady Viscous Flows

    Rosario M. A. Marretta1, Giovanni Lombardi2, Roberto Antinoro1
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 73-84, 2003, DOI:10.3970/cmes.2003.004.073
    Abstract An approach based on Lighthill's transpiration velocity is explored and proposed for a new design criterion for airfoils in unsteady and viscous flows. This criterion confines its methodologies to the close proximity of the laminar and turbulent boundary layer and it shows good efficiency in predicting and calculating the wake evolution regions in a wide range of operating unsteady parameters. Also, the criterion is capable of predicting low Mach number, attached flow-fields as accurately as the full Navier-Stokes solutions when the massive flow separation is avoided. The agreement of the present results with those empirically and theoretically determined is very… More >

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    1013

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    ARTICLE

    Indirect RBFN Method with Thin Plate Splines for Numerical Solution of Differential Equations

    N. Mai-Duy, T. Tran-Cong1
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 85-102, 2003, DOI:10.3970/cmes.2003.004.085
    Abstract This paper reports a mesh-free Indirect Radial Basis Function Network method (IRBFN) using Thin Plate Splines (TPSs) for numerical solution of Differential Equations (DEs) in rectangular and curvilinear coordinates. The adjustable parameters required by the method are the number of centres, their positions and possibly the order of the TPS. The first and second order TPSs which are widely applied in numerical schemes for numerical solution of DEs are employed in this study. The advantage of the TPS over the multiquadric basis function is that the former, with a given order, does not contain the adjustable shape parameter (i.e. the… More >

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    972

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    ARTICLE

    A Mathematical Framework Towards a Unified Set of Discontinuous State-Phase Hierarchical Time Operators for Computational Dynamics

    R.Kanapady1, K.K.Tamma2
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 103-118, 2003, DOI:10.3970/cmes.2003.004.103
    Abstract Of general interest here is the time dimension aspect wherein discretized operators in time may be continuous or discontinuous; and of particular interest and focus here is the design of time discretized operators in the context of discontinuous state-phase for computational dynamics applications. Based on a generalized bi-discontinuous time weighted residual formulation, the design leading to a new unified set of hierarchical energy conserving and energy dissipating time discretized operators are developed for the first time that are fundamentally useful for time adaptive computations for dynamic problems. Unlike time discontinuous Galerkin approaches, the design is based upon a time discontinuous… More >

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    939

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    ARTICLE

    A Hybrid Experimental-Numerical Study on the Mechanism of Three-Dimensional Dynamic Fracture

    T. Nishioka1, F. Stan1
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 119-140, 2003, DOI:10.3970/cmes.2003.004.119
    Abstract In this paper we investigate the essentially unexplored area of three-dimensional dynamic fracture mechanics. The general objective sought by this investigation is the understanding of three-dimensional dynamic crack propagation and arrest, and, specifically, the effect that the specimen thickness has on the dynamic fracture mechanism. In particular, in the context of the present paper, it is intended to provide a summary of the achievements on the issue of three-dimensional dynamic fracture parameters. Furthermore, the behavior of the three-dimensional field near the crack front is investigated. The issue that will be addressed is the extent of regions over which plane stress… More >

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    962

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    ARTICLE

    Further Developments in the MLPG Method for Beam Problems

    I. S. Raju1, D. R. Phillips2
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 141-160, 2003, DOI:10.3970/cmes.2003.004.141
    Abstract An accurate and yet simple Meshless Local Petrov-Galerkin (MLPG) formulation for analyzing beam problems is presented. In the formulation, simple weight functions are chosen as test functions as in the conventional MLPG method. Linear test functions are also chosen, leading to a variation of the MLPG method that is computationally efficient compared to the conventional implementation. The MLPG method is evaluated by applying the formulation to a variety of patch tests, thin beam problems, and problems with load discontinuities. The formulation successfully reproduces exact solutions to machine accuracy when higher order power and spline functions are chosen as test functions… More >

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    953

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    ARTICLE

    Elastostatic Deformations of a Thick Plate by using a Higher-Order Shear and Normal Deformable Plate Theory and two Meshless Local Petrov-Galerkin (MLPG) Methods

    L. F. Qian1,3, R. C. Batra2, L. M. Chen3
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 161-176, 2003, DOI:10.3970/cmes.2003.004.161
    Abstract We use two meshless local Petrov-Galerkin formulations, namely, the MLPG1 and the MLPG5, to analyze infinitesimal deformations of a homogeneous and isotropic thick elastic plate with a higher-order shear and normal deformable plate theory. It is found that the two MLPG formulations give results very close to those obtained by other researchers and also by the three-dimensional analysis of the problem by the finite element method. More >

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    1291

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    912

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    ARTICLE

    Analysis of Materials with Strain-Gradient Effects: A Meshless Local Petrov-Galerkin(MLPG) Approach, with Nodal Displacements only

    Z.Tang, S. Shen, S.N. Atluri1
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 177-196, 2003, DOI:10.3970/cmes.2003.004.177
    Abstract A meshless numerical implementation is reported of the 2-D Fleck-Hutchinson phenomenological strain-gradient theory, which fits within the framework of the Toupin-Mindlin theories and deals with first-order strain gradients and the associated work-conjugate higher-order stresses. From a mathematical point of view, the two-dimensional Toupin-Mindlin strain gradient theory is a generalization of the Poisson-Kirchhoff plate theories, involving, in addition to the fourth-order derivatives of the displacements, also a second-order derivative. In the conventional displacement-based approaches in FEM, the interpolation of displacement requires C$^{1}$ --continuity (in order to ensure convergence of the finite element procedure for 4$^{th}$ order theories), which inevitably involves very… More >

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    1032

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    ARTICLE

    A Boundary Element Method for Acoustic Scattering from Non-axisymmetric and Axisymmetric Elastic Shells

    J. P. Agnantiaris1, D. Polyzos1,2
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 197-212, 2003, DOI:10.3970/cmes.2003.004.197
    Abstract A Boundary Element Method (BEM), for the three-dimensional solution of both non-axisymmetric and axisymmetric coupled acoustic-elastic problems in the frequency domain, is presented. The present BEM makes use of the Burton and Miller integral equation for infinite acoustic spaces, while elastic structures are dealt with the standard boundary integral equation of elastodynamics. The axisymmetric formulation involves the use of the fast Fourier transform algorithm. Highly accurate numerical algorithms are used for the evaluation of singular integrals, while nearly singular integrals are treated, also with high accuracy, through the use of practical numerical techniques, for both the axisymmetric and non-axisymmetric cases.… More >

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