Home / Journals / CMES / Vol.99, No.4, 2014
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  • Open Access

    ARTICLE

    Dynamic Anti-plane Crack Analysis in Functional Graded Piezoelectric Semiconductor Crystals

    J. Sladek1,2, V. Sladek1, E. Pan3, D.L. Young4
    CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.4, pp. 273-296, 2014, DOI:10.3970/cmes.2014.099.273
    Abstract This paper presents a dynamic analysis of an anti-plane crack in functionally graded piezoelectric semiconductors. General boundary conditions and sample geometry are allowed in the proposed formulation. The coupled governing partial differential equations (PDEs) for shear stresses, electric displacement field and current are satisfied in a local weak-form on small fictitious subdomains. The derived local integral equations involve one order lower derivatives than the original PDEs. All field quantities are approximated by the moving least-squares (MLS) scheme. After performing spatial integrations, we obtain a system of ordinary differential equations for the involved nodal unknowns. It is noted that the stresses… More >

  • Open Access

    ARTICLE

    Comparison of Four Multiscale Methods for Elliptic Problems

    Y. T. Wu1, Y. F. Nie2, Z. H. Yang1
    CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.4, pp. 297-325, 2014, DOI:10.3970/cmes.2014.099.297
    Abstract Four representative multiscale methods, namely asymptotic homogenization method (AHM), heterogeneous multiscale method (HMM), variational multiscale (VMS) method and multiscale finite element method (MsFEM), for elliptic problems with multiscale coefficients are surveyed. According to the features they possess, these methods are divided into two categories. AHM and HMM belong to the up–down framework. The feature of the framework is that the macroscopic solution is solved first with the help of effective information computed in local domains, and then the multiscale solution is resolved in local domains using the macroscopic solution when necessary. VMS method andMsFEM fall in the uncoupling framework. The… More >

  • Open Access

    ARTICLE

    A Novel Semi-Analytic Meshless Method for Solving Two- and Three-Dimensional Elliptic Equations of General Form with Variable Coefficients in Irregular Domains

    S.Yu. Reutskiy1
    CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.4, pp. 327-349, 2014, DOI:10.3970/cmes.2014.099.327
    Abstract The paper presents a new meshless numerical method for solving 2D and 3D boundary value problems (BVPs) with elliptic PDEs of general form. The coefficients of the PDEs including the main operator part are spatially dependent functions. The key idea of the method is the use of the basis functions which satisfy the homogeneous boundary conditions of the problem. This allows us to seek an approximate solution in the form which satisfies the boundary conditions of the initial problem with any choice of the free parameters. As a result we separate approximation of the boundary conditions and approximation of the… More >

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