Home / Journals / CMC / Vol.1, No.1, 2004
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  • Open Access

    REVIEW

    Trefftz Methods for Time Dependent Partial Differential Equations

    Hokwon A. Cho1, M. A. Golberg2, A. S. Muleshkov1, Xin Li1
    CMC-Computers, Materials & Continua, Vol.1, No.1, pp. 1-38, 2004, DOI:10.3970/cmc.2004.001.001
    Abstract In this paper we present a mesh-free approach to numerically solving a class of second order time dependent partial differential equations which include equations of parabolic, hyperbolic and parabolic-hyperbolic types. For numerical purposes, a variety of transformations is used to convert these equations to standard reaction-diffusion and wave equation forms. To solve initial boundary value problems for these equations, the time dependence is removed by either the Laplace or the Laguerre transform or time differencing, which converts the problem into one of solving a sequence of boundary value problems for inhomogeneous modified Helmholtz equations. These boundary value problems are then… More >

  • Open Access

    ARTICLE

    Transient Response in Cross-Ply Laminated Cylinders and Its Application to Reconstruction of Elastic Constants

    X. Han1,2,3, G. R. Liu1,2, G. Y. Li 1
    CMC-Computers, Materials & Continua, Vol.1, No.1, pp. 39-50, 2004, DOI:10.3970/cmc.2004.001.039
    Abstract An efficient hybrid numerical method is presented for investigating transient response of cross-ply laminated axisymmetric cylinders subjected to an impact load. In this hybrid numerical method, the laminated cylinder is divided into layered cylindrical elements in the thickness direction. The Hamilton principle is used to develop governing equations of the structure. The displacement response is determined by employing the Fourier transformations and the modal analysis. Numerical examples for analyzing transient waves have been provided in axisymmetric laminated cylindrical structures, both for thin cylindrical shells and thick cylinders.
    A computational inverse technique is also presented for reconstructing elastic constants of… More >

  • Open Access

    ARTICLE

    The Effect of the Reynolds Number on Lateral Migration of Nonneutrally-Buoyant Spherical Particles in Poiseuille Flow

    S.-C. Hsiao1, M.S. Ingber2
    CMC-Computers, Materials & Continua, Vol.1, No.1, pp. 51-58, 2004, DOI:10.3970/cmc.2004.001.051
    Abstract The lateral migration of nonneutrally-buoyant spherical particles in Poiseuille flow is investigated numerically using the boundary element method. In particular, the steady, Navier-Stokes equations are solved using a classical domain integration method treating the nonlinear terms as pseudo-body forces. The numerical results for the lateral migration velocity are compared with experimental data. The numerical results indicate that the lateral migration velocity does not scale linearly with the Reynolds number. The methodology is extended to include non-Newtonian power-law fluids. The migration velocity is significantly affected for particles suspended in this class of fluids and can actually change direction for large values… More >

  • Open Access

    REVIEW

    Computational Nano-mechanics and Multi-scale Simulation

    gping Shen1, S. N. Atluri1
    CMC-Computers, Materials & Continua, Vol.1, No.1, pp. 59-90, 2004, DOI:10.3970/cmc.2004.001.059
    Abstract This article provides a review of the computational nanomechanics, from the ab initio methods to classical molecular dynamics simulations, and multi- temporal and spatial scale simulations. The recent improvements and developments are briefly discussed. Their applications in nanomechanics and nanotubes are also summarized. More >

  • Open Access

    ARTICLE

    Elasto-plastic Analysis of Two-dimensional Orthotropic Bodies with the Boundary Element Method

    X.S. Sun1, L.X. Huang1, Y.H. Liu1, Z.Z. Cen1,2
    CMC-Computers, Materials & Continua, Vol.1, No.1, pp. 91-106, 2004, DOI:10.3970/cmc.2004.001.091
    Abstract The Boundary Element Method (BEM) is introduced to analyze the elasto-plastic problems of 2-D orthotropic bodies. With the help of known boundary integral equations and fundamental solutions, a numerical scheme for elasto-plastic analysis of 2-D orthotropic problems with the BEM is developed. The Hill orthotropic yield criterion is adopted in the plastic analysis. The initial stress method and tangent predictor-radial return algorithm are used to determine the stress state in solving the nonlinear equation with the incremental iteration method. Finally, numerical examples show that the BEM is effective and reliable in analyzing elasto-plastic problems of orthotropic bodies. More >

  • Open Access

    ARTICLE

    Dielectric Breakdown Model For An Electrically Impermeable Crack In A Piezoelectric Material

    Tong-Yi Zhang1
    CMC-Computers, Materials & Continua, Vol.1, No.1, pp. 107-116, 2004, DOI:10.3970/cmc.2004.001.107
    Abstract The present work presents a strip Dielectric Breakdown (DB) model for an electrically impermeable crack in a piezoelectric material. In the DB model, the dielectric breakdown region is assumed to be a strip along the crack's front line. Along the DB strip, the electric field strength is equal to the dielectric breakdown strength. The DB model is exactly in analogy with the mechanical Dugdale model. Two energy release rates emerge from the analysis. An applied energy release rate appears when evaluating J-integral along a contour surrounding both the dielectric breakdown strip and the crack tip, whereas a local energy release… More >

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