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  • Open Access

    ARTICLE

    A 2-D Time-Domain BIEM for Dynamic Analysis of Cracked Orthotropic Solids1

    Ch. Zhang2

    CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.3, pp. 381-398, 2002, DOI:10.3970/cmes.2002.003.381

    Abstract A 2-D time-domain boundary integral equation method (BIEM) for transient dynamic analysis of cracked orthotropic solids is presented in this paper. A finite crack in an unbounded orthotropic solid subjected to an impact loading is considered. Hypersingular time-domain traction boundary integral equations (BIEs) are applied in the analysis. A time-stepping scheme is developed for solving the hypersingular time-domain traction BIEs. The scheme uses a convolution quadrature formula for temporal and a Galerkin method for spatial discretizations. Numerical examples are given to show that the presented time-domain BIEM is highly efficient and accurate. More >

  • Open Access

    ARTICLE

    Magnetorheological fluids particles simulation through integration of Monte Carlo method and GPU accelerated technology

    Xinhua Liu1,2, Yongzhi Liu1, Hao Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.91, No.1, pp. 65-80, 2013, DOI:10.3970/cmes.2013.091.065

    Abstract In order to study the rheological characteristics of magnetorheological fluids, a simulation approach through integration of Monte Carlo method and GPU accelerated technology was proposed and the three-dimensional micro-structure of magnetic particles in different strength magnetic fields were simulated. The Monte Carlo method to magnetic particles of magnetorheological fluids and its key steps such as particle modeling, magnetic energy equations calculating and system state updating were elaborated. Moreover, GPU accelerated technology was applied to the simulation of magnetorheological fluids to reduce computational time and a flowchart for the proposed approach was designed. Finally, a physics experiment was carried out and… More >

  • Open Access

    ARTICLE

    Static and Dynamic BEM Analysis of Strain Gradient Elastic Solids and Structures

    S.V. Tsinopoulos1, D. Polyzos2, D.E. Beskos3,4

    CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.2, pp. 113-144, 2012, DOI:10.3970/cmes.2012.086.113

    Abstract This paper reviews the theory and the numerical implementation of the direct boundary element method (BEM) as applied to static and dynamic problems of strain gradient elastic solids and structures under two- and three- dimensional conditions. A brief review of the linear strain gradient elastic theory of Mindlin and its simplifications, especially the theory with just one constant (internal length) in addition to the two classical elastic moduli, is provided. The importance of this theory in successfully modeling microstructural effects on the structural response under both static and dynamic conditions is clearly described. The boundary element formulation of static and… More >

  • Open Access

    ARTICLE

    High-Performance 3D Hybrid/Mixed, and Simple 3D Voronoi Cell Finite Elements, for Macro- & Micro-mechanical Modeling of Solids, Without Using Multi-field Variational Principles

    P. L. Bishay1, S.N. Atluri1

    CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.1, pp. 41-98, 2012, DOI:10.3970/cmes.2012.084.041

    Abstract Higher-order two-dimensional as well as low and higher-order three-dimensional new Hybrid/Mixed (H/M) finite elements based on independently assumed displacement, and judiciously chosen strain fields, denoted by HMFEM-2, are developed here for applications in macro-mechanics. The idea of these new H/M finite elements is based on collocating the components of the independent strain field, with those derived from the independently assumed displacement fields at judiciously and cleverly chosen collocation points inside the element. This is unlike the other techniques used in older H/M finite elements where a two-field variational principle was used in order to enforce both equilibrium and compatibility conditions… More >

  • Open Access

    ARTICLE

    Local Moving Least Square - One-Dimensional IRBFN Technique: Part I - Natural Convection Flows in Concentric and Eccentric Annuli

    D. Ngo-Cong1,2, N. Mai-Duy1, W. Karunasena2, T. Tran-Cong1,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.3, pp. 275-310, 2012, DOI:10.3970/cmes.2012.083.275

    Abstract In this paper, natural convection flows in concentric and eccentric annuli are studied using a new numerical method, namely local moving least square - one dimensional integrated radial basis function networks (LMLS-1D-IRBFN). The partition of unity method is used to incorporate the moving least square (MLS) and one dimensional-integrated radial basis function (1D-IRBFN) techniques in an approach that leads to sparse system matrices and offers a high level of accuracy as in the case of 1D-IRBFN method. The present method possesses a Kronecker-Delta function property which helps impose the essential boundary condition in an exact manner. The method is first… More >

  • Open Access

    ARTICLE

    T-Trefftz Voronoi Cell Finite Elements with Elastic/Rigid Inclusions or Voids for Micromechanical Analysis of Composite and Porous Materials

    L. Dong1, S. N. Atluri2

    CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.2, pp. 183-220, 2012, DOI:10.32604/cmes.2012.083.183

    Abstract In this paper, we develop T-Trefftz Voronoi Cell Finite Elements (VCF -EM-TTs) for micromechanical modeling of composite and porous materials. In addition to a homogenous matrix in each polygon-shaped element, three types of arbitrarily-shaped heterogeneities are considered in each element: an elastic inclusion, a rigid inclusion, or a void. In all of these three cases, an inter-element compatible displacement field is assumed along the element outer-boundary, and interior displacement fields in the matrix as well as in the inclusion are independently assumed as T-Trefftz trial functions. Characteristic lengths are used for each element to scale the T-Trefftz trial functions, in… More >

  • Open Access

    ARTICLE

    Development of T-Trefftz Four-Node Quadrilateral and Voronoi Cell Finite Elements for Macro- & Micromechanical Modeling of Solids

    L. Dong1, S. N. Atluri2

    CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.1, pp. 69-118, 2011, DOI:10.3970/cmes.2011.081.069

    Abstract In this paper, we explore three different ways of developing T-Trefftz finite elements of quadrilateral as well as polygonal shapes. In all of these three approaches, in addition to assuming an inter-element compatible displacement field along the element boundary, an interior displacement field for each element is independently assumed as a linear combination of T-Trefftz trial functions. In addition, a characteristic length is defined for each element to scale the T-Trefftz modes, in order to avoid solving systems of ill-conditioned equations. The differences between these three approaches are that, the compatibility between the independently assumed fields at the boundary and… More >

  • Open Access

    ARTICLE

    Slow Rotation of an Axially Symmetric Particle about Its Axis of Revolution Normal to One or Two Plane Walls

    Yi W. Wan1, Huan J. Keh2

    CMES-Computer Modeling in Engineering & Sciences, Vol.74, No.2, pp. 109-138, 2011, DOI:10.3970/cmes.2011.074.109

    Abstract The steady rotation of an axially symmetric particle about its axis of revolution normal to two plane walls at an arbitrary position between them in a viscous fluid is studied theoretically in the limit of small Reynolds number. The fluid is allowed to slip at the surface of the particle. A method of distribution of a set of spherical singularities along the axis of revolution inside a prolate particle or on the fundamental disk within an oblate particle is used to find the general solution for the fluid velocity distribution that satisfies the boundary conditions at the confining walls and… More >

  • Open Access

    ARTICLE

    The Coupling FEM and Natural BEM for a Certain Nonlinear Interface Problem with Non-Matching Grids

    Ju’e Yang1, Dehao Yu2

    CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.3, pp. 311-330, 2011, DOI:10.3970/cmes.2011.073.311

    Abstract In this paper, we introduce a domain decomposition method with non-matching grids for a certain nonlinear interface problem in unbounded domains. To solve this problem, we discuss a new coupling of finite element method(FE) and natural boundary element(NBE). We first derive the optimal energy error estimate of finite element approximation to the coupled FEM-NBEM problem. Then we use a dual basis multipier on the interface to provide the numerical analysis with non-matching grids.Finally, we give some numerical examples further to confirm our theoretical results. More >

  • Open Access

    ARTICLE

    A C2-Continuous Control-Volume Technique Based on Cartesian Grids and Two-Node Integrated-RBF Elements for Second-Order Elliptic Problems

    D.-A. An-Vo1, N. Mai-Duy1, T. Tran-Cong1

    CMES-Computer Modeling in Engineering & Sciences, Vol.72, No.4, pp. 299-336, 2011, DOI:10.3970/cmes.2011.072.299

    Abstract This paper presents a new control-volume discretisation method, based on Cartesian grids and integrated-radial-basis-function elements (IRBFEs), for the solution of second-order elliptic problems in one and two dimensions. The governing equation is discretised by means of the control-volume formulation and the division of the problem domain into non-overlapping control volumes is based on a Cartesian grid. Salient features of the present method include (i) an element is defined by two adjacent nodes on a grid line, (ii) the IRBF approximations on each element are constructed using only two RBF centres (a smallest RBF set) associated with the two nodes of… More >

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